A Notebook on Instrumentation System I

A Notebook on Instrumentation System I Prepared By Er. Shree Krishna Khadka teaching.official @gmail.com

Inside 1. 2. 3. 4. 5. 6.

Instrumentation Basics – Introduction Measurements Variables and Transducers Signal Conditioning and Processing Signal Transmissions Output Devices

Instrumentation-I

HWHIC GSSE BLEX IV

Chapter 1 Introduction 

Instrumentation is that piece of equipments that may be used to supply the information of some physical quantity, which is usually referred as a variable. This variable may be fixed or time varying quantity.



An Instrumentation System is a physical system, which is a collection of physical objects connected in such a way to give the desired output response e.g. an electronic amplifier, communication satellite orbiting the earth etc.



Instrumentation System may be defined as an assembly of various instruments and other components interconnected to measure, analyze and control the physical quantities. A physical system can be modeled in a number of ways depending upon the Specific problem to be dealt with the required accuracy e.g. and electronic amplifier may be modeled as an inter-connection of linear lumped elements.





Instrumentation System can be classified into two main categories. They are:

(i)

Analog Instrumentation System

(ii)

Digital Instrumentation System

Analog Instrumentation System deals with measurement of information in analog form. An analog signal may be defined as a continuous function, such as plot of current/voltage against time or displacement against force.



Digital Instrumentation System handles measurement of information in digital form. A digital quantity consists of a number of discrete and discontinuous pulses whose time relationship contains information regarding magnitude or the nature of quantity.

Prepared By: SriKisna Khadka 2006 Batch

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HWHIC GSSE BLEX IV

General Instrumentation System All Instrumentation System can be generally described by a simple Block-Diagram as shown in figure bellows

SENSOR OR TRANSDUCER

PROCESSOR

DISPLAY OR RECORD

Fig: Block Diagram of General Instrumentation System

Legend: 1. 2. 3. 4.

Physical Variable – I/P to the Sensor/Transducer (Primary Sensing Element). Electronic Signal – O/P from the Sensor/Transducer – I/P to the Processor. Processed Data/Information – O/P from Processor – I/P to the Display/Record (End Devices). Visual or Recorded O/P as a Result – To Observer.

Here the General Instrumentation System consists of three major parts. (i) (ii) (iii)

Sensor/Transducer Processor and Display or Record/Storages

Sensor

Sensor is a very low energy device that performs an energy conversion for the purpose of making a measurement. The Sensor converts energy from one to another. The second being related to the original in some predefined way. It is desirable that an Electromotive Fore obtained from the sensor/transducer is proportional to the quantity being measured and is use as I/P to the Instrumentation System. So, Sensor/Transducer is defined as a device, which when actuated by one form of energy is capable of converting it into another form of energy. In any Instrumentation System the main function of transducer is to convert physical quantity into equivalent electronic signal, which may be acceptable for the whole system. Prepared By: SriKisna Khadka 2006 Batch

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General Requirements of Sensor/Transducer in Instrumentation System 1. Accuracy: It is obvious that an instrumentation transducer must be accurate. It is essential to know how the output signal from transducer is related to the input physical quantities. 2. Stability: A Sensor must be stable to provide reproducible data for time and time again for any changes of its properties like temperature, humidity, gravity, time etc; which means that it cannot be used as primary I/P device for the Instrumentation System. 3. Reliability: The presence of sensor must not disturb the system being measured in any way, if it is to provide accurate data. In any measurement it cannot be achieved, so sensor is made to provide a minimum disturbance to the system being measured.

Processor The electronic signal produced by most of the transducers is generally very small and must be modified to become useful for instrumentation system. This modification of electrical signal is carried out by second block of the Instrumentation System called processor. The processor operates on the output signal of the sensor to modify it to a form that can be used to suitably present or store the data. Different functions that can be performed by the processor are: 1. Amplification: The process of increasing the amplitude or the strength of the sensor output signal without varying it in any other way is known as the amplification function of the processor. 2. Modulation and Demodulation: The process of imposing or removing a signal upon another signal is modulation and is called carrier i.e. it is used to convey the original information. Modulation puts the information/data on these carriers while demodulation recovers the original information/data from the carrier. 3. Frequency Selection (Filtering): The process, where a signal containing a group of different frequencies are filtered allowing only certain desired frequency to pass, while blocking all other frequencies. 4. Transmission: The process of taking a signal from one point in the space and conveying it undistorted to another point. 5. Isolation: It is the process of maintaining a signal such that it cannot be modified by any interference signals or random noises. 6. Logic: The process where the contained signal interacts with another according to present rule that allows elementary decision to be made. 7. Conversion: It is the process of transferring a signal from analog to digital format or vice-versa. Prepared By: SriKisna Khadka 2006 Batch

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General Requirements of Processor in Instrumentation System Similar to the sensor, the processor has several requirements that must be met if it is used to be in the instrumentation system. 1. Accuracy 2. Stability 3. Reliability 4. The processor shouldn’t load the sensor Since the processor is connected to the output of the sensor, this process of connection must not distort the signal produced by the sensor in any way. When distortion occurs from the connection, it is due to the loading and it results in additional inaccuracy being introduced into the measurement. So the processor in an Instrumentation System must provide a minimum loading error to the sensor. 5. The processor should provide sufficient signal to output The processor must be capable of providing the signal required by the next block of the Instrumentation System. If the output signal of the sensor is known and the required signal to drive the storage or display is known, the processor must be design so that it can affect the modification of output signal from the sensor to provide the input signal to display or record device.

Display or Storage The final block of General Instrumentation System is the ‘Display & Storage’. The function of this block is to present and in some case store the data for further use. The display device presents instantaneous data, so that it can be read out from the instrument by human. But it doesn’t remember any part of the data. There are several types of display device, they are: - Analog Scale: e.g. Common Electric Meter - Digital Readout: e.g. Digital Multimeter - Audio Output: e.g. Loud Speaker - Screened Display: e.g. CRT, LCD, Flat Panel Solid State Display System - Indicating Display: e.g. Indicating Lamp Storage device differs from the display device in which a permanent record of the data is kept. This record may appear as a chart, a printed page or invisible electrical/optical/magnetic signal. The examples of such storage device are: - Chart Recorder - Photographic Recording - Printer/Plotter - Electronic Memory e.g. SIM, ATM Card - Magnetic Recording e.g. Tape, Floppy Disk - Optical Recording e.g. CD, DVD Prepared By: SriKisna Khadka 2006 Batch

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General Requirements of Display & Storage in Instrumentation System The display and storage block of Instrumentation System has similar requirements to those of other block. They are as follows: 1. Accuracy 2. Reliability 3. Stability 4. Readability Information/Data which when outputted in recorded form like from printer as hard copy or in visual form like from display monitor as soft copy must be easily readable and can be understood by the observer/human. In order to prove the sufficient accuracy of any Instrumentation System, it is the fact that the output from the system must be equivalent to the primary input as given to the primary sensing element. Example: Microprocessor Controlled Temperature System (MCTS): Based on the concepts we discussed in the general instrumentation system, we can examine a typical microprocessor controlled temperature system. This system is expected to read the temperature in a room, display the temperature ate a liquid crystal display (LCD) panel, turn on fan if the temperature is above a set point, and turn on a heater if the temperature is below a set point. Temperature Sensor

A/D Converter

Fan

Heater

Input Port I

Output Port II

Output Port II

ROM/ EPROM

R/W Memory

Output Port III

Micro Processor

LCD Fig: Microprocessor Controlled Temperature System


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1. Microprocessor:

The above figure shows a processor with a system bus. The processor will read the binary instructions from memory and execute those instructions continuously. It will read the temperature, display it at the LCD display panel, and turn on/off the fan and the heater based on the temperature. 2. Memory:

The system includes two types of memory. ROM will be used to store the program, called the monitor program that is responsible for providing the necessary instructions to the processor to monitor the system. This will be a permanent program stored in ROM and will not be altered. The R/W memory is needed for temporary storage of data. 3. Input:

In this system, we need a device that can translate temperature into an equivalent electrical signal; a device that translates one form of energy into another form is called a transducer. On these days temperature sensors are available as integrated circuits. A temperature sensor is a three-terminal semiconductor electronic device that generates a voltage signal that is proportional to the temperature However, this is an analog signal and since the processor is capable of handling only binary bits. Therefore, this signal must be converted into digital bits. The analog-to-digital converter performs that function. It is an electronic semiconductor chip that converts an input analog signal into the equivalent eight binary output signals. In microprocessor-based systems, devices that provide binary inputs are connected to the processor using devices such as buffers called input ports. In our system A/D converter is an input port, and it will be assigned a binary number called an address. The microprocessor reads this digital signal from the input port. 4. Output:

The above figure shows three output devices: fan, heater and liquid crystal display (LCD). These devices are connected to the processor using latches called output ports. Fan: This is an output device, identified as Port 1 that is turned on by the processor when the temperature reaches a set higher limit. Heater: This is also an output device, identified as Port 2 that is turned on by the processor when the temperature reaches a set lower limit. Liquid Crystal Display(LCD): This display is made of crystal material placed between two plates in the form of a dot matrix or segments. It can display letters, decimal digits, or graphic characters. The LCD in above figure will be used to display temperatures. 5. System Software (Programs):

The program that runs the system is called monitor program or system software. Generally, the entire program is divided into subtasks and written as independent modules, and it is stored in ROM or EPROM. When the system is reset, the microprocessor reads the binary command from the first memory location of ROM and continues in sequence to execute the program. Prepared By: SriKisna Khadka 2006 Batch

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Signal The variation of the dependent parameter with respect to the independent parameter is considered as a signal. In the alongside figure a kind of signal is varying its magnitude f(t) along Y - direction as a function of (t) which is along X-direction. Here the parameter (t) is considered as independent whereas the f(t) is depends upon the parameter (t). The variation of Current/Voltage against time or Displacement against force etc can be considered for example of such type of signal variation. General Types of Signal On the basis of the Analog & Digital Instrumentation System and the concept regarding the process of conversion of an analog signal into digital one and vice versa the signal can be categorized into following types: 1. 2. 3. 4.

Continuous Time Signal (Analog Signal) Continuous Time Quantized Signal Sampled Data Signal Digital Signal

1. Continuous Time Signal (Analog Signal)

It is defined over a continuous range of time i.e. it is a continuous function. In this type of signal the amplitude may be assumed to have a continuous value with time.

2. Continuous Time Quantized Signal

The continuous time signal being represented by a distinct set of value i.e. quantized value is referred as continuous time quantized signal. In this type of signal the amplitude is quantized with discrete value but the time is not being quantized. The range of magnitude is divided into a finite number of intervals which are not necessarily to be equal. Prepared By: SriKisna Khadka 2006 Batch

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3. Sampled Data Signal

The signal defined at discrete interval of time is known as discrete time signal. If the amplitude can take a continuous range of value then the signal is called sampled data signal. It can be generated by sampling an analog signal at discrete interval of time. Here also only the time is quantized but the magnitude is not.

4. Digital Signal

It is the discrete time signal with quantized magnitude. It is the signal quantized in both magnitude and time. The digital signal consists of number of discrete and discontinuous pulses whose time relationship contains information regarding magnitude or the nature of the quantity.


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General Types of Instrumentation System (a) Analog Instrumentation System (b) Digital Instrumentation System The components of both Analog & Digital Instrumentation System can be viewed as shown. (A) Components of Analog Instrumentation System Sensor Or Transducer

Signal Conditioning Equipments

Multiplexer

Display Or Storage

Amplifier

Legend: 1. 2. 3. 4. 5. 6.

Physical Variable – I/P to the Sensor/Transducer (Measurand). Electronic Signal – O/P from the Sensor/Transducer – I/P to the Signal Conditioning Equipments Conditioned Data/Information – O/P from SCE – I/P to the Multiplexer Multiplexed Data/Information - O/P from MUX – I/P to the Amplifier Amplified Data/Information - O/P form AMP – I/P to the Display/Storage (End Devices) Visual or Recorded O/P as a Result – To Observer.

(B) Components of Digital Instrumentation System Sensor Or Transducer

Signal Conditioning Equipments

Multiplexer

Display Or Storage

Analog to Digital Converter

Sampling & Holding Circuit

Legend: 1. 2. 3. 4. 5. 6. 7.

Physical Variable – I/P to the Sensor/Transducer (Measurand). Electronic Signal – O/P from the Sensor/Transducer – I/P to the Signal Conditioning Equipments Conditioned Data/Information – O/P from SCE – I/P to the Multiplexer Multiplexed Data/Information - O/P from MUX – I/P to the Sampling & Holding Circuit Sampled Data/Information - O/P form SHC – I/P to the Analog to Digital Converter Digital Data/Information – O/P from ADC – I/P to the Display/Storage (End Devices) Visual or Recorded O/P as a Result – To Observer. Prepared By: SriKisna Khadka 2006 Batch

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Instrumentation-I

HWHIC GSSE BLEX IV

Analog Instrumentation System (i)

Sensor/Transducer: It is low energy device, which when actuated by one form of energy is capable of converting it into another form of energy.

(ii)

Signal Conditioning Equipment: - It includes any equipment that assists in transforming the output of transducer to the desired magnitude or form required by next stage of instrumentation system.

(iii)

Multiplexer: Multiplexing is the process of sharing a signal channel with more than one output. Thus a multiplexer accepts multiple analog inputs and connects them sequentially to one measuring input.

(iv)

Amplifier: It amplifies or increases the amplitude or the strength of the input signal without varying it in any other way.

(v)

Visual Display/Analog Recorder: It results out the output either in visual form or recorded form and puts data/information on them in analog format, e.g. CRT, Tape, Chart Recorder etc.

Digital Instrumentation System

(i)

Sensor/Transducer: It is low energy device, which when actuated by one form of energy is capable of converting it into another form of energy.

(ii)

Signal Conditioning Equipment: - It includes any equipment that assists in transforming the output of transducer to the desired magnitude or form required by next stage of instrumentation system.

(iii)

Multiplexer: Multiplexing is the process of sharing a signal channel with more than one output. Thus a multiplexer accepts multiple analog inputs and connects them sequentially to one measuring input.

(iv)

Sampling & Holding Circuit: It translates the analog signal to a form acceptable by the analog to digital (A/D) converter.

(v)

A/D converter: It converts the analog signal to its equivalent digital form.

(vi)

Digital Recorder/Display: It records/displays information in digital form as in floppy, CD, DVD, Punched Cards etc or to the combination of these systems. Prepared By: SriKisna Khadka 2006 Batch

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HWHIC GSSE BLEX IV

Chapter 2 Measurements The measurement of given quantity is essentially the result of comparison between the quantity whose magnitude is known and a predefined standard. Since two quantities are compared the result is expressed in numerical value. Measurement is the process by which one can convert physical parameters into meaningful number. In measuring process the property of an object or system under measurement is compared to an accepted standard unit defined for that particular property. Units and Standards of Measurement To specify and perform calculation with physical quantity, the physical quantity must be defined both in kind and magnitude. The standard measure of each kind of physical quantity is the unit. Without any unit the number of measure has no physical meaning. A standard of measurement is physical representation of a unit of measurement.  International Standard: e.g. SI, CGS, FPS etc.  Primary Standard: e.g. National Standard  Secondary Standard: e.g. Industrial Measurement Lab  Working Standard: e.g. Quality Control Department Method of Measurement 1. Direct Method In this method the unknown quantity is directly compared against the standard. The result is expressed as a numerical value. This type of measurement is common for the measurement of physical quantities like length, mass and time. Measurements by direct method are not always possible, feasible and practical. This method in most of cases is inaccurate because they involved human factor. They are also less sensitive and rarely used in instrumentation system. 2. Indirect Method In this method unknown quantity is measured using measuring instrument. A measuring instrument provides information about the physical quantity of same variable being measured. Function of Measuring Instrument 1. 2. 3. 4.

Indicating e.g. Multimeter Recording e.g. Graph Plotter Integrating e.g. Meter Reader Controlling e.g. Relay

Characteristics of Measuring Instrument 1. Static Characteristics 2. Dynamic Characteristics Prepared By: SriKisna Khadka 2006 Batch

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1. Static Characteristics of Measuring instruments Measuring Instruments are those, which must be considered when the system or instrument is used to measure the quality and not varying with time. There are various elements contributing the static characteristics of measuring instrument. (a) Accuracy & Precision Accuracy is the degree of closeness with which an instrument reading approaches the true value of the quantity being measured. Accuracy of the measurement means conformity to the truth. True value of the quantity to be measured may be defined as the average of the infinite number of readings while the average deviations due to various contributing factors tend to be zero. Precision is the major of degree of agreement within a group of measurement. It consists of two characteristics, they are: (i) Conformity (ii) Significant Figure For example a resistor having true value of 1.485432 ohm is measured by an ohm-meter, which is repeatedly indicating 1.5 ohm. Although there is no deviation from the observed value, the error created by the limitation of the scale reading is precision. So conformity is necessary but not a sufficient condition for precision because of lack of significant figure obtained. Significant figure convey the actual information regarding the magnitude and the measurement precision of the quantity. The more significant figure means the greater precision of the measurement. Similarly, precision is necessary but not sufficient condition for the accuracy. (b) Sensitivity It is the ratio of the magnitude of the output signal to input of the quantity being measured. The sensitivity of the instrument can be defined as the slope of calibration curve. The sensitivity of the instrument should be high and therefore instrument should not have arranged greatly exceeding the value to be measured. Therefore, Sensitivity (θ) = Qo/Qi (c) Reproducibility It is the degree of closeness with which a given value may be repeatedly measured. It may be specified in terms of unit for given period of time. (d) Drift There are three types of drift. i. Zero Drift ii. Span Drift iii. Zonal Drift Prepared By: SriKisna Khadka 2006 Batch

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(i) Zero Drift: The whole calibration gradually shift due to slipping or permanent set. This can be prevented by zero setting. (ii) Span Drift: If there is proportional change in indication all along the upward scale, the drift is called expand drift or resistive drift. (iii) Zonal Drift: It occurs only over a portion of span of the instrument.

(e) Linearity

A straight line is drawn by using the techniques of least square method from given calibration data, which is known as idealized straight line. The linearity is simply a measure of mean deviation of any of the calibration point from idealized straight line. In figure: dm – Maximum Deviation

(f) Resolution If the input is slowly increased for some value which is not really equal to zero, it is found that output does not change at all until the certain increment is exceeded. The smallest increment in input quantity being measured, which can be detected with conformity by an instrument is known as its resolution. (g) Dead Zone It is defined as the largest change in input for which there is no increment in output. (h) Static Error It is the deviation from true value.


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2. Dynamic Characteristics of Measuring Instruments Some measurements are made under such condition that sufficient time is available for the measurement system to settle its final steady state condition. Under such condition study of behavior of system under transient state is not much important. Only the steady state condition of the measurement is considered. In some measurement it becomes necessary to study the response of the system under both transient and steady state condition.

Dynamic Characteristics of Measuring Instruments are as follows: (i) Speed of response (ii) Measuring Lag (iii) Fidelity (iv) Dynamic Error

Total Response f(t) = ft(t) + ftt(t)

(a) Speed of response It is defined as the rapidity with which the measurement system and instrument response to the change in measured quantity.

(b) Measuring Lag It is the delay in response of measurement system to change in the measured quantity. There are two types of measuring lags. (i) Retardation type measuring lag and (ii) Time delay type measuring lag

(c) Fidelity It is defined as the degree to which a measurement system indicates the change in measured quantity without any dynamic error.

(d) Dynamic Error It is the difference between the value of the quantity under measurement changing with time and the value indicated by the measurement system. If no static error is assumed, it is called measurement error.


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Wheat Stonebridge Measurement of Resistance with Wheat Stonebridge It is one of the accurate arrangements for measuring the resistance of a conductor. As shown in alongside figure, four resistances R1, R2, R3 & R4 are connected to form a quadrilateral. A galvanometer is connected between B & D while a battery is connected between points A & C. Usually, R1 & R2 called ratio arms are known resistances, R3 is a variable resistance (Resistance Box) and R4 is the unknown resistance. The value of resistance R3 is so adjusted that galvanometer does not give deflection i.e. points B & D are ate the same potential. In such a case, the bridge is said to be balanced and then, (R1/R2) = (R3/R4)

Proof: Let VA, VB, VC and VD be potentials of point A, B, C and D respectively. Let I be the current in the main circuit. If the main current branches into I1, I2, I3, I4 respectively to the four arms of the bridge, then …….. (i)

I1R1 = I2R2

On second case, when the bridge is in the balanced condition, current flowing through the galvanometer is zero, then I1 = I3 = V/(R1+R3) I2 = I4 = V/(R2+R4)

…….. (ii) …….. (iii)

From equations (ii) and (iii), putting the values of I1 and I2 in equation (i) then we get, R1/(R1+R3) = R2/(R2+R4) ………(iv) Or, (R1+R3)/R1 = (R2+R4)/R2 Or, 1 + R3/R1 = 1 + R4/R2 Or, R3/R1 = R4/R2 Or, R1/R2 = R3/R4 i.e.;

R4 = R3 (R2/R1)

Hence, using Wheat Stonebridge the value of an unknown resistor can be easily evaluated with the help of other known quantity. Here, the measurement of the unknown resistor R4 is independent of the characteristic or the calibration of the null detecting galvanometer, provided the null detector has sufficient sensitivity to indicate the balance position of the bridge with the required degree of precision. Prepared By: SriKisna Khadka 2006 Batch

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Sensitivity of the Wheat Stonebridge If the resistance R4 is incremented by small resistance ‘r’, so the bridge becomes unbalanced. Then from Thevenin’s Theorem, we have VO

=

[{R1/(R1+R3)} – {R2/(R2+R4+r)}]V

From equation (iv), we have R1/(R1+R3) = R2/(R2+R4) i.e.

VO

i.e.

VO

= = = ~

[{R2/(R2+R4)} – {R2/(R2+R4+r)}]V [(R22 + R2.R4 + R2.r - R22 – R2.R4)/{(R2+R4)(R2+R4+r)}]V r.[R2/{(R2+R4)(R2+R4+r)}]V r.[R2/{(R2+R4)2}]V ( r 10. For Q value less than 10, (1/Q)2 becomes important factor and cannot be negligible. In this case Maxwell’s bridge is more suitable.

Schearing Bridge This bridge is one of the most important ac bridges and it is widely used for the measurement of unknown capacitance.

C1 R2

For balanced condition Z1.Z4 = Z4 =

R1

C4

Z2.Z3 Z2.Z3.(1/ Z1) = Z2.Z3.Y1 ……….. (i)

Y1 = (1/R1) + jωC1, Z2 = R2 Z3 = 1/jωC3 Z4 = R4+1/jωC4 Putting all these values in equation …. (i), we get Where,

C3 R4

R4+1/jωC4 = (1/R1 + jωC1)R2/jωC3 R4 – j/ωC4 = C1R2/C3 – jR2/ωC3R1 ……………(ii)

i.e.

Now, equating the real and imaginary parts of the above equation, we get. R4

=

C1R2/C3

and

C4

=


R1C3/R2

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Example: Find the unknown impedance of the circuit given in the figure. Solution: We have given that

50 ohm

0.2µF

20 V 1KHz 300 ohm Z4

0.1 µF

Here, i.e.

C1 = 0.2 F R2 = 500  C3 = 0.1 F R3 = 300  Vs = 20 V fi = 1KHz Z4 = ?

Z1 = 1/jωC1 = 1/j2лfiC1 = 1/(j2л10000.210-6) Z1 = -j795.77 = 0 + (-j795.77) = Pol(0, -795.77) Z1= -795.77 -90o s

Similarly; Z2 = 500  0o But, Y3

= = = = =

1/R3 + 1/(1/jωC3) 1/300 + j(2л10000.110-6) 3.3310-3 + j(6.2810-4) Pol(3.3310-3, 6.2810-4) 3.3910-3 10.67o

Therefore Z3 = =

1/Y3 294.98 -10.67o

Finally, Z4

Z1. Z3

=

= = Hence, |Z4|=  =

Z2 (-795.77 -90o)(294.98 -10.67o) 500  0o 946.65 -100.67o 946.65 -100.67o


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Types of Error in Measurement No any measurement can be made with perfect accuracy, but it is important to find out what the accuracy is and how different errors have exerted into the measurement system. A study of error is the first step in finding the ways to reduce them. Error may come from different source and are mainly classified as:   

Gross Error Systematic Error Random Error

Gross Error This class of error mainly covers the case of mistaken in reading or in use of instruments made by human. Also in recording and calculating the measurement results human factors may involved. As long as human beings are involved, some gross errors will occurs. Although complete elimination of gross error is impossible, one should try to carry the correct decision. Some gross errors may early detect, while others may be very hard to detect. One common type of gross error frequently committed by beginners is in measurement work and also involves the improper use of instrument. In general, indicating instruments changes conditions to some extent, when connected into a complete circuit, so that measured quantity is changed by the method that has being employed, e.g. miss reading, improper selection of instrument, carelessness, bad handling etc.

Systematic Error This type of error is usually categorized into two types: they are  Instrumental Error, and  Environmental Error 1. Instrumental Error These types of errors are inherent in the measuring instrument because of their mechanical structure. It may be due to manufacturing faults, i.e. construction, calibration or operation of the instrument. There are many kinds of instrumental errors depending upon the kind of instruments used. This type of error may be reduced by:  Selecting a suitable instrument for the particular measurement application.  Applying correction factors determining the amount of instrumental error.  Calibrating the instrument against the standard. 2. Environmental Error It is due to the external condition of the measuring device including the surrounding condition of the instrument, e.g. change in temperature, humidity, pressure, magnetic or electrostatic fields etc. Prepared By: SriKisna Khadka 2006 Batch

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Random Error These errors are due toe the unknown cause and occurs even if all systematic errors are removed. Even in the well designed instruments, few random errors usually occur. These errors cannot be corrected by any methods of calibration or other known method of control. The only way to minimize these errors is by increasing the number of reading and using statistical means to obtain the best approximation of the true value of the quantity under measurement.

Mean: X

=

Deviation (δi)

=

Mean Deviation (D)

=

Standard Deviation (σ) I.e. Variance (σ2)

= =

X1+X2+X3+X4+X5+…….+Xn n Xi -X |δ1+δ2+δ3+δ4+δ5+…..+δn| n 2 2 √ {(δ1 +δ2 +δ32+δ42+δ52+…..+δn2)/n} (δ12+δ22+δ32+δ42+δ52+…..+δn2)/n

Example: Voltmeter No. of Reading(V) Readings(f) 99.7 1 99.8 4 99.9 12 100 19 100.1 10 100.2 3 100.3 1 I. Fig: Observation Table

19

100 II. Fig: Gaussian/Normal Distribution Curve

Normal Laws of Error (Gaussian Law): 1. All the observation includes small distribution effect called random error. 2. It can be positive or negative. 3. There is an equal probability of positive and negative random error. The possibilities as to the form of error distribution curve can be stated as follows. 1. Small errors are more probable than larger error. 2. Large errors are very improbable. 3. The probability of given error will be symmetrical about the true value. Prepared By: SriKisna Khadka 2006 Batch

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Probable Error: The area under normal distribution curve between limits + ∞ and - ∞ represents the total number of observation. Inc. Area Deviation Included Area 50% 1σ 68.28 % 2σ 95.46% 3σ 99.72% r 50% -∞ +∞ Where, r = 0.6745× σ -2σ -1σ 0 1σ 2σ Therefore, probable error is that error of measurement, which covers the 50% of readings among the total measurements. Example: Large numbers of 100Ω resistors are measured. Mean value = 100 Ω Standard Deviation (σ) = 0.2 Ω Which shows 68.2% of resistor lies in between the limits of (100±0.2) Ω Or, 95.46 % of resistors lies in between the limit of (100±0.4) Ω Therefore 50% of resistors lie in between the limits of (100±r) Ω Problem: A voltmeter, having sensitivity of 1 Ω/V, reads 100V on its 150V scale when connected across an unknown resistor in series with a mili-ammeter. When the mili-ammeter reads 5mA, calculate: (a) Apparent resistance of the unknown resistor. (b) The actual resistance of the unknown resistor. (c) The error due to the loading effect of voltmeter. Solution: (a) The total circuit resistance (RT) = 100V/5mA Neglecting the resistance of the mili-ammeter The value of unknown resistance (RX) = 20 KΩ.

=

20 K Ω

(b) The voltmeter resistance (RV) = 1000Ω/V × 150 = 150KΩ Since, the voltmeter is connected in parallel with the unknown resistance, So, we can write, RT = RX//RV = RX.RV (RX+RV) Therefore, RX = RT.RV = 20×150 = 23.08 KΩ. (RV-RT) 150-20 (c) % - Error = (Actual Reading – Apparent Reading) × 100% Actual Reading = (23.05-20) × 100% 23.05 Therefore, % - Error = 13.34 % Prepared By: SriKisna Khadka 2006 Batch

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Chapter 3 Variables & Transducers The physical quantity under measurement, called the measurand, makes its first contact with the primary sensing element of a measuring system. The measurand is always disturbed by the act of measurement, but good instruments are designed to minimize this effect. Primary sensing elements may have a non electrical input and output. In case of the primary sensing element having a non electrical input and output, then it is converted into an electrical signal by means of transducer. The transducer is defined as a device, which when actuated by one form of energy is capable of converting it into another form of energy. They can be classified as: 1. 2. 3. 4.

Primary and Secondary Transducers, Active and Passive Transducers, Analog and Digital Transducers, Transducers and Inverse Transducers.

On the basis of the principle of operation, transducers are further classified in following types. 1. 2. 3. 4. 5. 6. 7.

Resistive Transducers, Capacitive Transducers, Inductive Transducers, Piezoelectric Transducers, Thermoelectric Transducers, Electromagnetic Transducers, Optical Transducers.

Primary & Secondary Transducers On the basis of methods of applications, it may be classified into primary and secondary transducers. When the input signal is directly sensed by the transducer and physical phenomenon is converted into the electrical form directly then such a transducer is called primary transducer, e.g. thermistor, which senses the temperature directly and causes the change in resistance with the change in temperature. When the input signal is sensed first by some detector or sensor and then its output being of some form other than input signal is given as input to a transducer for conversion into electrical form, then such a transducer falls in the category of secondary transducers, e.g. in case of pressure measurement, bourden tube is a primary sensor which converts pressure first into displacement and displacement is then converted into and output voltage by an LVDT, in this case LVDT is secondary transducer. Prepared By: SriKisna Khadka 2006 Batch

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Active & Passive Transducers On the basis of methods of energy conversion, transducers may be classified into active and passive transducers. Self generating type transducers i.e. the transducers, which develop their output in the form of electrical voltage or current without any auxiliary source, are called the active transducers. Such transducers draw energy from the system under measurement, e.g. Tacho-generator for measurement of angular velocity, thermocouples for measurement for temperature etc. Transducers in which electrical parameters i.e. resistance, inductance or capacitance changes with the change in input signal are called the passive transducers. These transducers required the external power source of energy conversion. In such transducers electrical parameters i.e. resistance, capacitance, inductance causes a change in voltage, current or frequency of the external power source.

Analog & Digital Transducers Transducers on the basis of nature of output signal may be classified into analog and digital transducers. Analog transducers convert input signal into such a output signal, which is a continuous function of time such as thermistor, strain gauge, LVDT, thermocouple etc. Digital transducers convert input signal into the output signal of the form of pulse, e.g. it gives discrete output. The digital signal can be transmitted over a long distance without causing much distortion due to amplitude variation and phase shift.

Transducers & Inverse Transducers Since, transducers convert a non-electrical quantity into an electrical quantity, i.e. a transducer with associated circuit has a non electrical input and an electrical output, e.g. thermocouple, photo conductive cell, pressure gauge etc. An inverse transducer is a device that converts and electrical quantity into a non electrical quantity, e.g. a piezoelectric crystal and translational/angular moving coil elements can be employed as inverse transducer. An ammeter or voltmeter converts electric current or voltage into mechanical movement of the needle. A most useful application of inverse transducers is in feedback measuring systems.


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Resistive Transducers Resistive transducers are the one, in which the output terminal of a transducer gets varied according to the measurand. They are preferred over other transducers because dc and ac both are suitable for resistance measurement. Resistance of any metal conductor is given by the expression, (R) = ρ(L/A) Where, ρ = Resistivity of the metal conductor in ohm-meter (Ω-m) L = Length of the conductor in meter (m). A = Cross sectional area of the conductor in meter-square (m2)

Potentiometer A potentiometer is a resistive transducer, which converts linear or rotational displacement into voltage as an output. There are two types of potentiometer. 1. Translatory Potentiometer 2. Rotary Potentiometer In this chapter we only deal with the first type of potentiometer, i.e. Translatory Potentiometer.

Vin

Xt

Since, Mechanical device acts as a primary transducer. Let us take an example of simple potentiometer having following parameters. Xi = Displacement of wiper from its zero position. Xt = Total length of translation in meter. Rp = Total resistance of the potentiometer. And with input supply Vin and producing Vo as output.

Rp

Xi

Vo

If the distribution of resistances throughout the potentiometer is linear then the potentiometer is said to be linear of which the resistance per unit length will be equal to Rp/Xt.

For Ideal Condition: Vo/Vin (Rp/Xt).Xi Vo

=

× Vin Rp

Vo/Vin Xi/Xt

= = =


(Xi/Xt).Vin Xi/Xt K say (0≤K≤1)

29

Instrumentation-I

HWHIC GSSE BLEX IV

Let a voltmeter is connected to output terminal of the potentiometer whose internal resistance is Rm. Then output resistance is given by: Vin

Xt

Rp

Rout Xi

Rm

Vo

Or,

Rout

= = = =

{(Rp/Xt).Xi}//Rm {Rp(Xt/Xi)}//Rm (KRP)//Rm (KRP .Rm) (Rm+KRP)

= = =

Rout + (1-K)Rp {(KRP . Rm)/ (Rm+KRP)} + (1-K)Rp KRP.Rm + RP.Rm(1-K) + KRp2(1-K) (Rm+KRP) 2 Rm.Rp + KRp (1-K) (Rm+KRP)

Then, Total input resistance is given by: Rin

=

So, Current (i)

=

Vin/Rin

And, Output Voltage (VO)

=

Rout (Vin) Rin KRP.Rm × (Rm+KRP) KVin {1+K(1-K)Rp/Rm}

= =

Let, Rp/Rm Then, Vo

= =

1/α α.KVin α +K(1-K)

For: Rm → ∞, α → ∞ Then, Vo =

=

Vin(Rm+KRP) Rm.Rp + KRp2(1-K)

(Rm+KRP) Rm.Rp+KRp2(1-K)

……*

KVin Now From equation … * we can see that there is a non linear relationship between input and output Voltage as shown in the graph alongside.

Vo/Vin

Loading Error: Xi/Xt i t

 

Absoluter Loading Error:(εa) Relative Loading Error:(εr)

Where, (εa) = O/P Voltage at No load – O/P Voltage Under load (εr) = (O/P Voltage at No load – O/P Voltage Under load)/O/P Voltage at No load Prepared By: SriKisna Khadka 2006 Batch

30

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Therefore,

εa

εr

=

KVin -

α.KVin α + K(1-K)

KVin -

α.KVin α + K(1-K)

=

=

K2(1-K)Vin, α + K(1-K)

=

1

εr

=

α + K(1-K)

K(1-K) α + K(1-K)

The maximum error may occurs, for which:

i.e. i.e. i.e. i.e. i.e.

α

-

KVin i.e.

and

dεr dK

must be equal to zero.

d εr = 0 dK d/dK{(K-K2)/( α + K-K2)} = 0 {(α + K-K2)(1-2K)-(K-K2)(1-2K)}/( α + K-K2) (1-2K)( α + K-K2-K+K2) = 0 (1-2K)α = 0

=

0

Since, α ≠ 0, being a constant. Therefore, 1-2K = 0 i.e. K = ½

εr

εr, max

Hence, the error will be maximum when the wiper is at mid position of K

0

50%

the total length of the potentiometer. But in actual practice the error is maximum at 67% of displacement from initial zero position.


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HWHIC GSSE BLEX IV

Method of Reducing the Loading Error: 1. 2. 3. 4.

The loading error can be reduced by increasing ‘α’ i.e. internal resistance of output device. By using digital voltmeter instead of analog. By using buffer circuit. Using compensating resistor as shown in figure below.

Vo/Vin Rcom

Vin

Xt

1

3 2

Rp

Xi

Rm

LEGEND

Vo

Xi/Xt 0.5

Rcom = Compensating resistor 1= Linear Characteristics of PM 2= PM with internal resistance 3= PM with Rcom resistor

Advantages of Potentiometer:    

In expensive. Easy to handle and operate. Useful for measurement of large amplitude of displacement. High electrical efficiency.

Disadvantages of Potentiometer:   

Require large force to move their wiper. Sliding contact can be contaminated, so can be wear-out and also generate the noise. It has limited life time.


32

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Strain Gauge A strain gauge is basically a device used for measuring mechanical surface strain. It can detect and convert force or small mechanical displacement into electrical signal. Many other quantities like torque, weight, tension etc; which involves effect of force or displacement can also be measured by strain gauge. Working Principle: The working of strain gauge is based on the fact that, when stress is applied on the metal conductor its resistance changes with respect to the change in length and cross-sectional area of the conductor. Resistance of conductor under stress is also changed due to the change in Resistivity of the conductor. This property is called the piezo-resistive effect. That is why; strain gauges are also called the piezo-resistive strain gauges. Ta

A

Let us now consider a conductor of length ‘L’ and area of cross-section ‘A’ is subjected to axial tension, the resistance will change because of change in length, area of cross-section and Resistivity of the material as:

D L

R

=

ρ.(L/A)

…….. (i)

Where, R is the resistance of unstrained conductor. Let, under strained condition resistance of the conductor be changed by ∆R because of change in length by ∆L, cross-sectional area by ∆A. Now, equation (i) becomes, R+∆R = = = = R+∆R = R =

ρ.(L+∆L)/(A-∆A) ρL (1+∆L/L) A (1-∆A/A) R(1+∆L/L) (1- ∆D/D)2 (1+∆L/L) {1-2(∆D/D)+(∆D/D)2} Neglecting the higher (1+∆L/L) × {1+2(∆D/D)} order terms of ∆D. Since, {1-2(∆D/D)} {1+2(∆D/D)} it is very small. {1+∆L/L+2(∆D.∆L/∆L)+2(∆D/D)2} {1-4(∆D/D)2}

i.e. 1+∆R/R

=

1+∆L/L+2. ∆D+2(∆D/D)

i.e. ∆R/R

=

∆L/L+2∆D/D

i.e. (∆R/R) (∆L/L)

= =

1+2(∆D/D) (∆L/L)

Gf

=

1+ 2γ

i.e.

……. (ii)

…….(iii)


33

Instrumentation-I

Where;

Gf is known as Gauge Factor γ is known as Poisson’s Ratio

= =

HWHIC GSSE BLEX IV

(∆R/R)/ (∆L/L) (∆D/D)/ (∆L/L)

If piezo-resistive effect is also considered then equation … (ii) can be written as:

Where,

∆R/R = ∆ρ/ ρ =

∆L/L+2∆D/D+∆ρ/ρ …….. (iv) Piezo-resistive effect.

Example: A strain gauge is bounded to a steel beam of 10 cm long and has cross-sectional area of 4 cm2. Young’s modulus of steel is 207 GN/m2. The strain gauge has an unstrained resistance of 240 Ω and gauge factor of 2.2. When a load is applied, the resistance of the gauge is increased by 0.013 Ω. Calculate the change in length of steel beam and amount of force applied. Solution: Given,

L A E R Gf ∆L

= = = = = =

100cm 4 cm2 207 GN/m2 240 Ω 2.2 ? F

= = =

0.1 m 4×10-4 m2 207×109 N/m2

=

?

= = = = =

(∆R/R)/ (∆L/L) (∆R/R)×(L/Gf) (0.013×0.1)/(240×2.2) 2.46×10-6 m 2.46 µm

= = = = =

Stress/Strain (F/A)/( ∆L/L) EA×( ∆L/L) (207×109×4×10-4×2.46×10-6)/0.1 2.03 KN

As we know,

i.e;

Gf ∆L

i.e.

∆L

Again, E i.e.

F

i.e.

F


34

Instrumentation-I

HWHIC GSSE BLEX IV

Types of Strain Gauge: Mainly there are two types of strain gauge, they are: 1. Unbounded Wire Strain Gauge 2. Bounded Wire Strain Gauge. UNBOUNDED WIRE STRAIN GAUGE FORCE

1 4

2

MOVING FRAME

3

STATIONARY FRAME

In this type of strain gauge, strain is directly transferred to the resistance wire so that smaller force can be measured. The resistance wires are stretched between a stationary frame and movable frame. Generally four wire resistances are connected in four arms of Wheat Stonebridge as shown in above figure. At balanced condition, Vo = V1 – V2 = 0

Application of external force increases tension in two wires and decreases in other two wires. Due to this there

V1 R3

R1

is change in resistance of wire causing unbalance in

Vout R4

R2

bridge and gives output voltage proportional to the V2

external force.

V

BOUNDED WIRE STRAIN GAUGE C O N N E C T I N G

Resistance Wire

L E A D S

Carrier Base

R3

R1

V

Vout R2

R4

This type of strain gauge is used for both stress analyzing as well as transducer. In bound wire strain gauge a grid of fine resistance wire of diameter 0.025 mm or less is placed on a base known as carrier made up of thin sheet of paper or bakelite etc. The wire is covered on top with thin sheet of material. The bounded strain gauge is plastid with a special adhesive to the structure, where the strength is to be measured. The resistance of strain gauge is measured with Wheat Stonebridge, connecting it in one of the four arms, while remaining three arms have standard resistance of nearly equal to the value as that of gauge resistance at unstrained condition.


35

Instrumentation-I

HWHIC GSSE BLEX IV

Resistance temperature Detector (RTD) RTD operates upon the fact that almost pure metals have the property of varying their resistance with temperature. Change in resistance is almost directly proportional to the change in temperature. Electrical resistance with temperature for most metallic materials can be represented by an expression of the form: Rt

Ro(1+αt+βt2+γt3+…+ωtn)

=

….. (i)

Where, Ro is the resistance in ohm at reference temperature (usually at ice point, 0oC), Rt is resistance in ohm at temperature t, α is the temperature co-efficient of resistance in Ω/oC and β, γ, ω are co-efficient determined on the basis of two or more calibration points. For narrow range of operation, higher order co-efficients are negligible. So equation … (i) becomes Rt

Ro(1+αt)

=

…… (ii)

The requirements for the resistance material of RTDs are as follows  High temperature co-efficient of resistance.  High resistivity.  Linearity between resistance and temperature.  Stability of electrical characteristics.  Sufficient mechanical strength. The most common RTDs are made of platinum, nickel or nickel alloy. Material Platinum Copper Nickel Tungsten

α/oC 0.0039 0.0425 0.0066 0.0052

Resistivity (10-8) 9.83 1.56 6.38 -

Temperature Change (oC) -250 to 900 -200 to 150 -70 to 150 -200 to 1000

Melting Point(oC) 1775.5 1083 1455 -

Rt/Ro

6 5

Nickel

Copper

Platinum

4 3 2 1 0

400

600

800

1000

1200

Temperature 1400

Fig: Characteristics Curve for Different RTD’s Materials. Prepared By: SriKisna Khadka 2006 Batch

36

Instrumentation-I

HWHIC GSSE BLEX IV

Mounting Base

In RTD resistance element is mounted on one side of the thin pipe and the other side of pipe is mounted on a mounting base. The resistance can be connected in any one arm of the wheat stone bridge to measure the change in resistance o RTD. Range of RTD is 10 ohm to several kilo ohms. A typical type of resistance temperature detector is depicted alongside in the figure with its main components.

Resistance Element

Connecting Wires

Thermal Resistor (Thermistor) The name thermistor is derived from thermally sensitive resistors, as the resistance of a thermistor varies as a function of temperature. Thermistors are generally composed of semiconductor materials. Most of the thermistor has negative temperature co-efficient of resistance, i.e. resistance decreases with increase in temperature. Thermistor has high sensitivity to temperature change as compared to RTD and thermocouple. So they are used for precision measurement of temperature. Thermistors are widely used in the applications which involve the measurement of temperature in the range of -60oC to 15oC. The resistances of thermistor have a very non linear characteristic between resistance and temperature as given by the expression: R

=

αeβ/T ……… (i)

Where, α and β are constants depending upon the material and manufacturing techniques. The approximate relationship between R and T can be obtained by rewriting the equation (i), i.e. R

=

β(1/T1-1/To) Roe

…(ii)

Where, R1 and Ro are resistances in ohm at absolute temperatures T1 and To respectively and β is the thermistor constant. Thermistors are composed of metallic oxides such as Fe, Co, Ni, Cu etc. They are available in variety of shape and size. Glass Coated

( a ) Bead

( b ) Probe

Glass

Lead Wires

( c ) Rod Prepared By: SriKisna Khadka 2006 Batch

( d ) Washer 37

Instrumentation-I

HWHIC GSSE BLEX IV

Application of Thermistors       

Measurement of temperature Measurement of difference of two temperature Control of temperature Temperature compensation Thermal conductivity measurement Measurement of gas composition Measurement of flow

Characteristics of Thermistors There are three important characteristics of thermistor that make them extremely useful in measurement and control applications. They are:  Resistance-Temperature Characteristics  Voltage-Current Characteristics  Current-Time Characteristics Resistance-Temperature Characteristics Thermistors are essentially R e s I s t I v I t y

-200

102

semiconductor devices that

10

behave as resistors with

1

high negative temperature

10-2

10

-6

10

-8

-100

co-efficient

Thermistors of different materials

10-4

0.04/oC

Platinum

0

100

200

300

(usually at

-

room

temperature of about 25oC)

400

500

600

Figure: Resistance-TemperatureTemperature Characteristics of Thermistor (oC) The R-T characteristics of thermistor are determined by following relation. R

=

αeβ/T

R

=

Roeβ(1/T1-1/To)

α

=

(dR1/dt)/R1

Approximately, Where,


=

-β/T2

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Instrumentation-I

HWHIC GSSE BLEX IV

Voltage-Current Characteristics V

The voltage drop across a thermistor increases with the increase in current until it attains the peak value beyond which the voltage drop fall with the increase in current with the very small voltage applied to the thermistor, the resulting current doesn’t produce sufficient heat to raise the temperature of the thermistor above ambient and under this condition the thermistor obeys ohm’s law.

1000 V o 100 l t a 10 g e 1

0oC 25oC 60oC

0.01

0.1 1 Current (µA)

10

100

1000

Fig: Voltage-Current Characteristics of Thermistor Current-Time Characteristics mA 40 C u 30 r r 20 e n 10 t 1

60 V 50 V 40 V 30 V 20 V 0

1

2

3

4

5 6 Time

7

8

9

t

The current-time characteristics of a thermistor for various applied voltages are shown in above figure, which indicates that the time delays to reach maximum current as a function of the applied voltage. When the self heating effect occurs in a thermistor network a certain finite time is required for thermistor to heat and the current to build up to a maximum steady state value.

Figure: Current-Time Characteristics of Thermistor


39

Instrumentation-I

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Thermocouples Thermocouples are essentially consists of two dissimilar metal A and B, insulated from each other but welded or brazed together at their ends forming two junctions as shown in figure. When each end of wires A and B is connected to a measuring instrument, it becomes an accurate and sensitive temperature measuring device.

Metal A

T1

e2

e1

T2

Metal B

Operating Principle When two different metals having different work function are placed together a voltage is generated at the junction, which is directly proportional to the temperature difference. This operation principle is based on See beck Effect. The thermal emf developed in the circuit composed of two dissimilar metals with junction kept at absolute temperatures T1 and T2 may be written as: e = a (T1-T2)+b(T1-T2)2, (T1>T2); Where, a and b are constants, whose values depend upon the nature of metals used. On simplification it can be written as; e = a (T1-T2) = a∆T; 1. The thermoelectric emf depends on the difference of temperature between two junctions. 2. If third metal is connected between the junction whose junction temperature is same, then there will be no change in emf induced originally, e.g. use of voltmeter 3. If third metal is coupled at the junction with same temperature at its two ends there will be no change in induced emf originally, e.g. welding, soldering etc. 4. If e be the originally induced emf then e=e1 and e=e2.

e e2

e1

T1

e1

T1

T1

e2

T2

T2

T2

T1

Copper Wire

Metal A O/P to emf Measuring Device

Detecting Junction Metal B

Temperature Controlled Junction Box


40

Instrumentation-I

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Application of Thermocouples:    

Indication of rapidly changing temperature. To measure the resistance at a number of points. To localize the position of temperature. Measurement of surface temperature.

Merits of Using Thermocouples:     

Cheaper than RTD. Can withstand high shock. Simple in construction and made in very small sizes. Having small time lag. Suitable for recording rapid change in temperature.

Demerits of Using Thermocouples:     

Low accuracy than RTD. The circuitry is very complex for remote sensing devices. Need periodical checking. Need compensating lead. Reference junction compensation is required.

Example: Calculate the thermoelectric sensitivity of the device using Bismuth and Tellurium as the dissimilar metals. Estimate the maximum output voltage for 100oC temperature difference. The sensitivity of Bismuth is -72μV/oC and that of Tellurium is 500 µV/oC. Solution: Thermoelectric sensitivity of thermocouple is (ST) For 100oC temperature difference, O/P voltage (e)

= = = =


500-(-72) 572 µV/oC 572 × 100 57.2 mV. Ans

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Instrumentation-I

HWHIC GSSE BLEX IV

Capacitive Transducers The variable capacitance transducer comprises of a capacitor, the capacitance of which is varied by the non-electrical quantity being measured. The capacitance of a parallel plate capacitor, C is given by an expression, C

= =

Where, εo =

εr

= A = D =

Permittivity of free space

ε.A/d (Farad) εo.εr.A/d =

8.854 × 10-12 F/m

Relative permittivity of the dielectric material. Area of the plate in m2 Distance between the two plates in m.

Capacitive transducers are analog passive transducers. In such transducers capacitance of the capacitor is varied by any of the following three methods.   

By Varying Overlapping Area of Plates, A By Varying Distance Between Plates, d By Varying Relative Permittivity, εr

The above changes can be caused by physical variable like displacement, force or pressure. The change in capacitance may also be caused by change in permittivity as in the case of measurement of levels of liquids or gases.

1. Capacitive Transducers: By Variation of Overlapping Area of Plates. Such a transducers operates on the fact that capacitance of any capacitor is proportional to the overlapping area of plates. Let us consider a capacitive transducer having parallel plates of constant width ‘w’ as shown in alongside figure. In such a transducer capacitance is proportional to ‘l’, where ‘l’ is the length of the overlapping portion of plates and it varies according to the displacement under measurement. So any change in displacement causes change in capacitance.


Fixed Plate

w

Movable Plate Direction of Movement

l

42

Instrumentation-I

As, C = =

εo.εr.A/d ε.wl/d (ε = εo.εr)

HWHIC GSSE BLEX IV

C

A

Sensitivity, i.e.

S S

= = =

Output/Input δC/δl ε.w/d

Hence, sensitivity is constant and a curve drawn between the capacitance of the transducer and displacement is linear except the linear portion.

Another capacitive transducer, operating on the same principle as mentioned above is cylindrical capacitor, whose overlapping area is varied by varying the length of overlapping portion of the cylinder as shown. Where, C = 2π εo.εr (Farads) ln(D/d) So, Sensitivity = δC/δl = 2π ε F/m ln(D/d) Here, sensitivity is also constant.

The principle of variation of capacitance with change in area can also be used to measure the angular displacement. Let us consider a capacitive transducer having two parallel semi-circular plates; one fixed another movable as shown in figure below. C = εo.εr. r2.β (A= βr2/2) Movable Plate 2d r Where, r is the radius of movable plate in meter, ß d is the distance between two circular Fixed Plate parallel plates. So, Sensitivity i.e.

(S)

= =

δC/δr εo.εr. r2/2d

=

εr2/2d

C a p a c i t a n c e

A - Cmax B - Dmax

ew/d

B

D

Displacement (m)

Fixed Cylinder

D

Movable Cylinder

d

O/P

C

A C a p a c i t a n c e


A - Cmax B - ßmax

er2/2d

pi/2 Angular Displacement (m)

B pi

ß

43

Instrumentation-I

HWHIC GSSE BLEX IV

2. Capacitive Transducer: By Variation of distance between the plates. Such a capacitor operates upon the fact that the capacitance of any capacitor is inversely proportional to the distance between the plates. Such a capacitive transducer used for measurement of linear displacement as shown in the figure alongside.

Fixed Plate Movable Plate

Displacement x

C C A P A C I T A N C E

DISPLACEMENT

x

From figure it can be seen that the curve is non linear so the sensitivity of this transducer is high for the initial portion of the curve, therefore these transducers are used only for measuring extremely small displacement. Now, C Therefore, Sensitivity S i.e.

S

=

εo.εr A/x

= =

δC/δx δ/δx(εo.εr A/x)

=

-ε/x2, it is not a constant, so varies over the transducer range.

3. Capacitive Transducer: By Variation of the Permittivity of the

Dielectric Material Between the Plates. In such a transducer, capacitance is varied by varying the permittivity of the dielectric material used between two plates of a capacitor. In this arrangement, a dielectric material of relative permittivity εr, moves between the two fixed plates parallel to each other according to the displacement under measurement. The capacitance of the transducer is given by the expression, C = εo.εr A/d (Where, εo is the permittivity of air or vacuum.) Let us consider a dielectric material having cross-sectional dimension (w*d), placed between two parallel plates of a capacitor separated by a distance‘d’; Where ‘l’ is the length of the plates. Initially, the dielectric material is at l1 position from the right. The capacitance at this condition is now given by: C = εo.wl1/d + C = =

Fixed Plate w

x

Dielectric Material

d

Displacement

l1 l

εo.εr w(l-l1)/d εo.w/d {(l1 + εr(l-l1)} ……. (i) Prepared By: SriKisna Khadka 2006 Batch

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Now, If dielectric material moves out a distance x, then value of capacitance changes from C to C-∆C i.e. C-∆C = εo.w/d(l1 + x) + εo.εr w/d{ l-(l1+x)}

=

εo.w/d[l1 + x + εr{ l-(l1+x)}] εo.w/d{(l1 + x) + εr(l-l1)-εrx)} εo.w/d{l1 + εr(l-l1)-x(εr-1)} εo.w/d{l1 + εr(l-l1)}-εo.w/d{x(εr-1)} C - εo.w/d{x(εr-1)}

=

εo.w/d{x(εr-1)}

= =

= =

i.e.

∆C

So, change in capacitance is proportional to the displacement. This method can be used to measure the displacement from 1 µm to 10 mm.

Differential Arrangement In order to achieve linear characteristics, differential arrangement is used as shown in above figure, where P and Q are fixed plates whereas M is moveable plate to which displacement under measurement is applied. Thus we have two capacitors with different output. When the movable plate M is midway between fixed plates P & Q and distance d meters apart from them, the capacitance C1 and C2 are equal and each of then is equal to εo.εr A/d i.e. C1

=

C2

=

εo.εr A/d

P - Fixed Plate D I S P L A C E M E N T

C1, V1

d V M – Movable Plate d

C2, V2 Q - Fixed Plate

Now, the movable plate M is moved by distance x meters towards plate P Then, C1 = εo.εr A/(d-x) and C2 = εo.εr A/(d+x) If and alternating voltage V is applied across plates P and Q, then Voltage across C1 given by V1 = VC2 C1+C2 = εo.εr A/(d+x) ×V εo.εr A/(d-x) + εo.εr A/(d+x) V1

=

(d-x)V/2d Prepared By: SriKisna Khadka 2006 Batch

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Similarly, voltage across C2 is given by V2

= =

V2

=

VC1 C1+C2 εo.εr A/(d-x) ×V εo.εr A/(d-x) + εo.εr A/(d+x) (d+x)V/2d

Finally, The differential output voltage is given by ∆V i.e. ∆V

= = =

V2 -V1 (d-x)V/2d - (d+x)V/2d (x/d)V

Therefore, the output voltage varies linearly as the displacement x and sensitivity (∆V/x) ∆V is inversely proportional to the separation ‘d’ and directly proportional to the applied voltage. This method can be used for the measurement of linear displacement between 0.01 µm and 10 mm with an accuracy of ±0.1%. Merits of Using Capacitive Transducers:      

These transducers have very high impedance so; loading effects are minimized on the measuring circuits. They have excellent frequency response (as high as 40 KHz) and so can be used for measurement of both static and dynamic phenomena. They are not affected by stray magnetic field; i.e. why they are used for applications, where stray magnetic fields make the inductive transducers useless. These transducers are extremely sensitive. A resolution of order of 2.5 microns can be achieved with these transducers. They can be operated with very small forces so, they are very useful for small system and they need small power to operate.

Demerits of Using Capacitive Transducers:  

 

Output impedance of capacitive transducers is very high so its measuring circuit becomes very complicated. Insulation resistance of the system cannot be neglected because of high output impedance of the transducer so, it reduces its sensitivity. Moreover with change in physical conditions e.g. humidity, temperature, pressure etc. this resistance changes its value and so introduces error in measurements. Stray capacitance including due to cables etc; in parallel with the output impedance of the transducer also cause error and introduces non linearity. Electrostatic screening should be provided for capacitive transducers in order to avoid any pick up. Prepared By: SriKisna Khadka 2006 Batch

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The screened cable connector to the transducer can be a source of error because its capacitance varies with the movement between the cable conductors and cable dielectric. Capacitance of capacitive transducer changes with change in temperature or on account of presence of small external matter e.g. dusts particles and moisture etc. Hence error is introduced in measurement. Since, the displacement in general is small and a large sensitivity is usually needed so adequate design is required for accurate measurements.

Applications of Capacitive Transducers: 

   

They can be employed for both linear and angular displacement measurement. The capacitive transducers are highly sensitive and can be employed for measuring extremely small displacements, such as 0.01 micro meters. On the other hand they can be employed for measuring large distances up to about 30 m as in airplanes. They can be employed for measuring force and pressure, which are first converted into displacement and the displacement, make the capacitance to change. They can also be employed for measuring the pressure directly in all those cases in which permittivity of a medium changes with pressure, such as in case of Benzene e-varies by 0.5% in the pressure range of 1 to 1,000 times the atmospheric pressure. They can be employed for measuring humidity. Since, the permittivity of gases varies with the variation in humidity. Capacitive transducers can be employed for the measurement of density, volume, level of liquid, weight etc; but with mechanical modifiers.

Inductive Transducers These are analog passive transducers. These transducers operate generally upon one of the following three principles:   

Variation of self inductance of the coil. Variation of mutual inductance of the coil. Production of eddy currents.

1. Variation of Self Inductance of the Coil: The self inductance of a coil is given by the expression.

Where,

L

= = =

N2/( ℓ /μA) N2μ(A/ ℓ) N2μG

N = Number of turns of the coil. ℓ = Mean length of the magnetic path. A = Area of the cross-section of magnetic path. μ = Permeability of the magnetic material. G = A/ ℓ = Geometric form factor, Prepared By: SriKisna Khadka 2006 Batch

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Hence, from the above expression, the self inductance of a coil can be varied by varying the number of turns of the coil, permeability of the material and by changing the geometrical configuration of the magnetic circuit. These transducers are usually used for the measurement of linear as well as angular displacement. The displacement under measurement causes the change in self inductance of the coil (L) by (∆L) by varying any of the three variables viz. N, μ or G.

2. Variation of Mutual Inductance of the Coil: Such transducers operate on the fact that mutual inductance between the coils depend upon the self inductance of the coils and co-efficient of coupling between them as mutual inductance between two coils and is given by the expression: M = K√(L1L2) Where, K is the co-efficient of coupling and L1, L2 are self inductances of coils.

3. Production of Eddy Current: When a conduction plate is kept near a coil carrying alternating current, eddy current is induced in the current conduction plate, producing its own magnetic field in opposition to the main field created by the coil; which reduces the net flux linking with the coil. The higher is the induced eddy current, higher the reduction in the inductance of the coil. Thus the inductance of the coil changes with the movement of the plate.

Conducting Plate

Coil

O/P

Displacement

Coil Displacement

Short Circuit Sleeve

Fig: Inductive Transducers for Measurement of Linear Displacement. Sensitivity of this type of inductive transducers is usually low.


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Linear Variable Differential Transformer (LVDT) This is most widely used inductive transducer for translating the linear motion into an electrical signal. The basic construction of an LVDT is shown in figure below. Secondary Winding Primary Winding

Movable Magnetic Core

Arm

S1

P

S2

VO VI Differential O/P Voltage AC I/P Voltage

Fig: Basic Construction of LVDT (Cross Sectional View)

LVDT is a differential transformer consisting of one primary winding (P) and two secondary windings S1 and S2, wound over a hollow bobbin of nonmagnetic and insulating material. The secondary windings S1 and S2, which have equal number of turns are arranged concentrically and placed either side of the primary winding P. A soft iron core, attached to the sensing element of which displacement is to be measured in the shape of rod or cylinder slides freely in the hollow portion of the bobbin.

Primary Winding

Movable Magnetic Core

es1

es2

Vout

Primary winding is connected to an ac source of voltage varying from 5 to 25 V and of frequency ranging from 50 Hz to 20 KHz. When the core is moved inside the bobbin it varies coupling of primary winding to secondary windings S1 and S2. In null position of the core i.e. in central position coupling of primary winding to both of the secondary windings S1 and S2 is equal i.e. es1 = es2, so output voltage induced in secondary windings S1 and S2 are equal. As the core is moved towards left from its null position, the magnetic linkage to S1 increases whereas that of S2 decreases. Therefore output voltage induced in S1 increases whereas the output voltage induced in S2 decreases. The movement of the core to the right will have opposite effect. Since, S1 and S2 are connected in series opposition so that difference of output voltages of secondary windings gives the measurement of displacement. Prepared By: SriKisna Khadka 2006 Batch

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From the characteristics shown

Eo- O/P Voltage

in

alongside figure, LVDT is linear for limited range of displacement (say 5 mm either side from the

Residual Voltage B

null position) and beyond this range curve starts flattering

out

at

both

ends.

X-Displacement O/P Voltage out of phase with I/P primary Voltage

as

O/P Voltage in phase with I/P primary Voltage

curve

HWHIC GSSE BLEX IV

A

Merits of Using LVDTs           

LVDT has infinite resolution as it gives step less output. It ha almost linear characteristics within its prescribed range. It has high sensitivity (10 mV/mm – 40 mV/mm) Its output is very high. These devices consume very less power. It can be used on high frequencies up to 20 KHz. Output impedance of LVDT remains constant. LVDT is a more reliable device. It has very low hysteresis, so a good repeatability can be achieved with it. LVDTs are very rugged device in construction, so it can tolerate shock and vibration without any adverse effect. It is very stable and easy to align and maintain due to simplicity of construction.

Demerits of Using LVDTs      

These devices are sensitive to stray magnetic fields. Relatively large displacement is required for appreciable differentiable output. Sometime, the transducer performance can be affected by vibration. The receiving instrument must be selected on ac signal or a demodulator must be used if a dc output is required. The dynamic response is limited mechanically by the mass of the core and electrically by the frequency of applied voltage. Temperature affects the performance of the transducer.


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Application of LVDTs 



LVDTs are suitable for the application, where the displacement are too large for strain gauges to handle; e.g. LVDTs can be employed for measurement of displacement that ranges from a fraction of a mm to few cm. If LVDT is to be employed for measurement of mechanical displacement greater than 25 mm, an appropriate mechanical gearing must be used. LVDTs can also be connected to other transducers, whose outputs are mechanical displacement, so these are often employed together with other transducer for measurement of force, weight, pressure etc.

Piezo Electric Transducers Piezo electric material is one in which an electric potential appears across the opposite faces of the material as a result of dimensional changes when a mechanical force is applied to it. The potential is produced by the displacement of charge and this effect is reversible. Common piezoelectric materials are: Rochelle-Salts, Ammonium Di-Hydrogen-Phosphate, Lithium-Sulphate, Quartz etc

Force

t

Vout

Let ‘t’ be the thickness of piezo electric material, ‘A’ be the area of crystal, where force ‘F’ is applied and Q be the charge produced, then: Q α F i.e, Q = dF; Where ‘d’ is crystal charge sensitivity. Its unit is coulomb/Newton. Therefore, Vout = Q/C, where C = εo.εr A/t i.e;

Vout = Qt/(

i.e;

Vout = g.p.t

εo.εr A)

=

F.d.t/(εo.εr A)

=

(d/εo.εr).(F/A).t

Where, ‘g’ is the crystal voltage sensitivity (Vm/N) and p is the pressure applied (N/m2)

C

Q

C

R

Vout

Fig: Equivalent Current Source

Eo

R

Vout

Fig: Equivalent Voltage Source


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Advantages of Using Piezo-electric Transducers: 1. These transducers are generally small in size, light in weight & simple in construction. 2. Piezo-electric materials have high stability and they also have very good high frequency response. 3. They are self generating transducers as they do not need external power. 4. Their outputs are quite large (125 mV/Kpa for 2.5 mm).

Disadvantages of Using Piezo-electric Transducers: 1. The output voltage is affected by temperature variation of the crystal. 2. The leakage resistance gives reasonably low leakage to allow static measurement. 3. For a long life, it should be protected from moisture.

Hall Effect Transducers If a strip of conducting material carries current in the presence of a transverse magnetic field, an emf is produced between two edges of the conductor. The magnitude of voltage depends on the current flowing through conductor, flux density and the property of the conductor-called hall-effect co-efficient. Mathematically, Vout = KHI(B/t) Where; KH = Hall effect co-efficient (Vm3/Awp) I = Current flowing B = Magnetic flux density T = Thickness of conductor strip

(Volts) Vo t

Direction of Current

ut

Magnet ic Flux

Hall Effect emf is very small in conductor and is difficult to measure, but in semi-conductor like Germanium, the emf produces is sufficiently large.

Application:  

Hall-effect element can be used for measurement of current by the magnetic field produced due to flow of current. It may be used for measuring a linear displacement.

Advantages: 

The main advantage of Hall-effect transducers is that they are non-contact devices with small size and high resolution.

Disadvantages:  The main drawbacks of these transducers are high sensitivity to temperature changes and variation of hall co-efficient from plate to plate; thereby requires individual calibration in each case. Prepared By: SriKisna Khadka 2006 Batch

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Optical Transducers The primary types of optical transducers are; photo-conductive cell, photovoltaic cell, photodiode and photo-transmitter.

1. Photo Conductive Cell (Photo Resistor) LDR (Light Dependent Resistor) When light falls on photo conductive material. It release charge cannibal or free electrons due to which the resistance between two electrodes is decreased. When the cell is kept in dark, its resistance is called dark resistance and may be as high as 1013 ohms. If the cell is laminated its resistance decreases. The resistance depends on the physical character of the photo conductive layer as well as on the dimension of the cell and its geometric configuration. Material Cadmium Sulphite Cadmium Selenide Lead Sulphite Lead Selenide

Time Constant 100 ms 10 ms 400 μs 10 μs

Spectral Band 0.47-0.71 μm 0.6-0.77 μm 1-3 μm 1.5-4 μm

2. Photo Transistor: Vcc

It is a normal transistor in which the junction is transparent to allow light to fall on the base at any pn-junction hole, electrons pairs are generated when light falls on junction. So any light falling on the base-emitter R

junction produces a current which is amplified by transistor action.

3. Photo Voltaic Cell: The photo-voltaic cell converts electromagnetic energy in electrical energy. Photo-voltaic cell is a large diode consists of a pn-junction between two semiconductors. Photons striking the cell pass through the ptype upper layer and are absorbed by the electron in the lower n-type layer causing

Light PN Junction


P-Ty N-Ty

pe L ayer pe L ayer

R

Vout

Conduction Base

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Instrumentation-I

HWHIC GSSE BLEX IV

formation of conduction electrons. Then the depletion layer of pn-junction separates its conduction electrons and holes. Therefore a potential difference is developed across the junction. The open circuit voltage is given by: Vo

Where, Vc = Ve =

=

Vc. lnVe

Calibration Voltage Radiant Incidence Voltage (w/m2)

Photo Conductive Material Silicon (Si) Germanium (Ge)

Time Constant 20 μs 50 μs

Spectral Band 0.49 – 1 μm 0.79 – 1.8 μm

4. Photo Diodes: A photo diode is a silicon diode with an opening in its case containing a lens which focuses incident light on the pn junction. The photo diode with no bias operates as a photovoltaic device and with a reverse bias as a photoconductive device. A reverse bias semiconductor diode, when not exposed to light allows only a small leakage current to bias and pass but when exposed to light the current rises almost in direct proportion to light. The photodiodes leakage current is detected and amplified for providing a usable output.

V

Reverse Bias 0 0.1 W/m 1 W/m

2

2 2

10 W/m

i

L E C A U K R A R G E E N T

The photo diode has the most important advantage of much faster response over the photoconductive cell and so can be employed in applications involving light fluctuating occurring at high frequencies.


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Chapter 4 Signal Conditioning & Processing Introduction: The signal after being sensed may be in highly distorted form and the interfering sources must be removed. Certain operations are performed on the signal before further transmission. These process may be linear like amplification, integration, differentiation, addition, subtraction etc. some nonlinear process like modulation, detection, sampling, filtering, linearization, squaring etc; are also performed on the signal to bring it to the acceptable form. This process of conversion is called “Signal Conditioning”.

Importance of Signal Conditioning & Processing:    

It assists in transforming the output of the input stage to the desired magnitude or form acceptable to the output stage. Signal conditioning supply excitation to passive transducers and acts as an amplification system for active transducers. The transducer output is brought up to sufficient level to make it useful for conversion, processing, indication and recording. It performs various linear and nonlinear processes on the signal as described above.

The signal conditioning or data acquisition equipment in many a situation is an excitation and amplification system for passive transducers. It may be an amplification system for active transducers. In both the applications, the transducer output is brought up to a sufficient level to make it useful for conversion, processing, indication and recording. Excitation is needed for passive transducers because these transducers do not generate their own voltage or current. Therefore, passive transducers like strain gauges, potentiometers, and resistance thermometers, inductive and capacitive transducers require excitation from external sources. Active transducers like techno generators, thermocouples, inductive pick-ups and Piezo-electric crystals, on the other hand, do not require an external source of excitation since they produce their own electrical output on account of application of physical quantities. But these signals usually have a low voltage level and hence need amplification. The excitation sources may be an alternating or D.C. voltage source. Depending upon the excitation sources, the signal conditioning system can be classified as: 1. 2.

DC Signal Conditioning System AC Signal Conditioning System.


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DC Signal Conditioning System: -

-

Generally used for common resistance transducers like pots and resistance strain gauges. The desirable characteristics of a DC amplifier in DC signal conditioning systems are: 1. It may need balanced differential inputs giving a high common mode rejection ration (CMMR). 2. It should have extremely good thermal and long term stability. The advantages of DC amplifier in DC signal conditioning system are that: 1. It is easy to calibrate at low frequencies. 2. It is able to recover from an overload condition unlike its a.c. counterpart. DC EXCITATION SOURCE

TRANSDUCER

I/P

BRIDGE

POWER SUPPLY

CALIBRATION & ZEROING N/W

DC N/W

L.P.F

0/P

Fig: DC Signal Conditioning System

- But the greatest disadvantage of a DC amplifier in DC signal conditioning system is that if suffers from the problem of drift. Thus low frequency spurious signals come out as data information. For this reason special low drift DC amplifiers are used. The DC amplifier is followed by a low pass filter which is used to eliminate high frequency components or noise from the data signal.

AC Signal Conditioning System: -

Generally used for variable reactance transducers and for systems, where signal have to transmit via long cables to connect the transducers to the signal conditioning equipment. In order to overcome the problems that are encountered in DC system AC signal conditioning systems are used. In AC system, the carrier-type AC signal conditioning systems are used as shown in figure below DC EXCITATION SOURCE

TRANSDUCER

I/P

BRIDGE

POWER SUPPLY

CALIBRATION & ZEROING N/W

CARRIER OSCILLATOR

POWER SUPPLY

AC AMPLIFIER

PHASE SENSITIVE DEMODULATOR

0/P

L.P.F

Reference Fig: AC Signal Conditioning System

-

In this system amplifier drift and spurious signals are not of much importance unless they modulate the carrier. However, it is more difficult to achieve a stable carrier oscillator than a comparable DC stabilized source. In carrier systems, it is easy to obtain very high rejection of mains frequency pick up. Active filters can be used to reject this frequency and prevent overloading of AC amplifier. The phase-sensitive, demodulators filter out carrier frequency components of the data signal. Prepared By: SriKisna Khadka 2006 Batch

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-

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After the physical quantities like temperature, pressure, strain, acceleration etc. have been transduced into their analogous electrical form and amplified to sufficient current or voltage levels they are further processed by electronic circuits. In some applications the signal does not need any further processing and the amplified signal may be directly applied to indication or recording or control instruments. But many applications involve further processing or signals which involve linear and non linear operations.

Analogue to Digital Multiplexer

Analogous Signals from Signal Conditioning Equipment

Control Unit

Digital Output

Control Signal

Analogue Multiplexer Sample & Hold Circuits

Fig: Data acquisition and conversion system

-

The signal may be applied to: 1. Sample & Hold Circuit (S/H): The S/H units sample the different inputs at a specified time and then hold the voltage levels at their output. 2. Analog Multiplexer:  Time Division Multiplexing (TDM): It means that each input channel is sequentially connected to the multiplexer for a certain specified time. The input signals are not applied to the multiplexer continuously but are connected in turn to the multiplexer thereby sharing time. The timing of the various input channels is controlled by a control unit, which controls the S/H circuits, the multiplexer and the A/D converter. It may be controlled itself.  Frequency Division Multiplexing (FDM): In this case, the multiple data analog inputs can remain in analog form and re transmitted all at the same time, using frequency division multiplexing. The voltage input from the signal conditioning equipment is converted into frequency. Thus a change in voltage input of the measurand produces a corresponding change in frequency. 3. Analog to Digital Converter (A/D): Since, the most naturally occurring phenomena are analog in nature. Analog quantities are continuous functions with time and most transducers give an analog output. So, in order to introduce such analog inputs to digital devices like computer they need to be converted in digital form. Therefore A/D conversion devices are used in measurement and instrumentation systems.


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Operational Amplifier (Op-Amp) On the basis of amplification ICs are of two types, namely: - Linear ICs - Digital ICs An important application of linear ICs is operational amplifier commonly referred to as an Opamp. An operational amplifier is a direct coupled amplifier with two differential inputs and a single output. It is a versatile device used in almost all analog circuit. It provides very high open loop gain. It is a linear active device, which consists of different stages. It was originally designed for performing mathematical operation such as, summation, subtraction, multiplication, differentiation, integration, sigh changing etc. Now-a-days it has numerous usages e.g. scale changing analog computer operation, in instrumentation and control system and in various phase-shift and oscillator circuits. +Vcc

Inverting I /P Terminal V1

-

V1 Op-Amp

V2

OpAmp

Vout Output Terminal

V2

Vout

+

+

Non Inverting I /P Terminal

-Vcc

Fig: Circuit Symbol of Op-Amp

Fig: Power Supply Connections

Ideal Op-Amp The Op-amp is designed to sense and amplify the difference between the voltages signal applied at its two input terminals. The output of Op-amp is: Vo Where, A = V2 = V1 =

= A(V2-V1)

Open loop gain. Voltage between terminal 2 and ground, and Voltage between terminal 1 and ground.


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Characteristics of Ideal Op-Amp: 1. The input impedance of an ideal Op-amp is infinity, i.e.

V1

I1=0

-

the signal current into terminal one and two both are zero. Vout

2. The output impedance of an ideal Op-amp is zero, i.e. the V2

output voltage with respect to ground is always equal to

+

I2=0

VO = A(V2-V1) and is independent of the load. -

3. It has infinite common mode rejection, i.e. it ignores any signal common to both inputs.

I1=0

+ -

V1

4. Ideal Op-amp has infinite band width, i.e. it has gain ‘A’ that remains constant down to zero frequency up to

I2=0

Vo=A(V2-V1)

+

V2

infinite frequency.

Virtual Short Circuit & Virtual Ground: If the Op-amp has infinite open loop gain, i.e. A → ∞; and producing finite voltage at output, then voltage between the Op-amp input terminals should be negligibly constant as shown. VO = A(V2-V1) i.e. V2-V1 = VO/ A (i.e. finite/infinite) i.e. V2-V1 = 0 i.e. V2 = V1

V1

1 A

V2

2

Vout

+

This means that, Gain (A) → ∞; the voltage V1 → V2, we call this as two input terminal ‘Tracking Each Other in Potential’ or ‘Virtual Short Circuit’ exists between the two input terminals. A virtual short circuit means that whatever voltage is at terminal two, will automatically appear at terminal one because of infinite gain. If terminal two is grounded, voltage at terminal one is zero volts, so we call the terminal one as a virtual ground.


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Op-Amp Circuit 1. Inverting Configuration: R2 In this circuit input is supplied on the

i2

inverting terminal of the Op-amp, so called

R1

inverting configuration. R2 closes loop around the Op-amp, so acts as a negative feedback.

V1

1

-

i1

Vi

A

Calculation of Closed Loop Gain:

V2=0

2

Vo

+

Case I: If A → ∞; From short circuit theory, V2 = 0 =V1 As, (Vi – V1)/R1 = i.e. i1 = and also i1 =

i1 Vi/R1 ……….. (i) i2 ………..(ii)

Again, V1 – i2R2 – Vo i.e, Vo

=0 = V1 – i2R2 = -i1R2 = (-Vi/R1)R2

Therefore, Closed loop Gain (A)

i.e,

A

(from i and ii)

= Vo/Vi = -R2/R1

= -R2/R1

Case II: If A is finite, then: Vo = A(V2-V1) Since, V2 = 0, but V2≠V1 Therefore from calculation, it is observed that, Af

=


Vo/Vi =

- R2/R1 1 + 1/A(1+ R2/R1)

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2. Non inverting Configuration: R2

Here, input is fed into the non inverting terminal

-

2;

so

called

non-inverting

i2 R1

V1

configuration.

1

-

i1 A

Calculation of Closed Loop Gain: V2

Case I: If A → ∞;

2

Vo

+

Vi

V1 = Vi So; 0 – i1R1 - V1 = 0 i.e. V1 = -i1R1 i.e. i1 = -V1/R1 = Vi/R1 Also, i1 =i2 Therefore, i1 = i2 = -Vi/R1 Again, i.e.

V1 - i2R2 – Vo = 0 Vo = V1 – i2R2 = Vi + Vi.R2/R1

i.e. Vo/Vi = A = (1+R2/R1)

Case II: If A is finite, then: Vo = A(V2-V1) Then, Vo/Vi = A =

(1+R2/R1) (1+1/A +1/A.R2/R1)


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3. The Voltage Follower (Buffer Amplifier): The non inverting configuration has infinite input resistance. It enables using this

Vi = V1

1

circuit as a buffer amplifier to connect a

-

source with high impedance with low

A=1

Vo

impedance. Buffer amplifier has voltage gain of 1.

Vi

V2

2

+

4. Integrator: It consists of a capacitor-C in the

Vc(t)

feedback path of the inverting configuration. I2(t)

From the alongside figure, we have: i1 = =

1

Vi(t)

-

V1

{Vi(t) – V1}/R1 {Vi(t) – 0}/R1

R1 I1(t)

A=1

Vo(t)

(V2 = 0 = V1) V2 = 0 2

+

Therefore; i1 =

Vi(t)/R1 and i2 =i1

So, from loop equation, V1 – Vc(t) – Vo(t) = 0



i.e. V1 – 1/C i2(t)dt – Vo(t) = 0



i.e. 0 - 1/C i2(t)dt = Vo(t) Therefore,



Vo(t) = -1/C Vi(t)/R1dt



i.e. Vo(t) = -1/R1C Vi(t)/R1dt


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5. Differentiator: It consists of a capacitor in the inverting

R

terminal – 1 of the inverting configuration. In which V2 = 0 = V1.

I2(t)

Vc(t)

1

Vi(t)

-

V1 I1(t)

So, from alongside figure, we have:

A=1

Vo(t)

Vi(t) – Vc(t) – V1 = 0 V2 = 0 2

Therefore

+

Vi(t) = Vc(t) Since; i1(t) = C dVc(t)/dt i.e. i1(t) = C dVi(t)/dt

Again, V1 – i2(t)R – Vo(t) = 0 i.e.Vo(t)

=

- i2(t)R

i.e Vo(t)

=

-RC dVi(t)/dt

6. Adder: From the alongside figure: i1 = (Vi – V1)/R1 = V1/R1

V1 V2

Similarly; i2 = V1/R2, i3 = V2/R3,

V3 V4

R1

I1 Rf

R2

I2

R3

I3 o

R4

I4

i4 = V3/R4,

i V1

-

i Vo

V2 = 0

+

in = Vn/Rn,


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At junction o; i

=

i1 + i2 + i3 + … + in-1 + in

=

V1/R1 + V1/R2 + V2/R3 + … + Vn-1/Rn-1 + Vn/Rn

Again from loop equation. V1 – iRf – Vo = 0 i.e. Vo – iRf Therefore; Vo = -{ V1Rf/R1 + V1Rf/R2 + V2Rf/R3 + … + Vn-1Rf/Rn-1 + VnRf/Rn}

Where, Rf/R1, Rf/R2, Rf/R3 … Rf/Rn-1, Rf/Rn are known as the weights of V1, V2, V3 … Vn-1, Vn respectively. If R1 = R2 = R3 … Rn-1 = Rn, then Vo = -(V1 + V2 + V3 + … + Vn-1 + Vn)

Op-amp summing amplifier are also called mixers.

7. Subtractor: Op-amp

can

be

used

in

Rf

subtracting mode. The alongside i

figure shows a circuit that can provide the difference between two

R1

-

V1 i1

inputs. From figure, we have: V2

1

Vi1

=

R3  Vi2 (R2 + R3)

A=1 V2

Vi2

2 i2

Vo

+

R3

Since, V1 = V2; Therefore, V1 =

R3  Vi2 (R2 + R3) Prepared By: SriKisna Khadka 2006 Batch

64

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HWHIC GSSE BLEX IV

As; Vi1 – i1R1 – V1 = 0; i.e. i1 = (Vi1 – V1)/R1 and i1 = i2; So, from another loop equation; V1 – iRf – Vo = 0 i.e. Vo = V1 - iRf = R3  Vi2 ( R2 + R3) = R3  Vi2 ( R2 + R3)

-

(Vi1 – V1)  Rf R1 Vi1  Rf + R1

R3  Rf  Vi2 (R2 + R3) R1

For this case, we have: Rf/R1 = R3/R2 Therefore, Vo =

R3/R2 (1+R3/R2) Rf/R1 (1+Rf/R1) Rf (R1+Rf) R1Rf + Rf2 R1(R1+Rf) Rf(R1+Rf) R1(R1+Rf)

 Vi2

-

 Vi2

-

 Vi2

–

 Vi2

-

 Vi2

-

Rf  Vi1 R1 Rf  Vi1 R1 Rf  Vi1 R1 Rf  Vi1 R1 Rf  Vi1 R1

+ + +

R3/R2  Rf  Vi2 (1+R3/R2) R1 Rf/R1  Rf  Vi2 (1+Rf/R1) R1 Rf  Rf Vi2 (R1+Rf) R1

i.e. Vo = Rf/R1(Vi2 – Vi1) If Rf = R1, then Vo = Vi2 – Vi1

8. Comparator: -

Vin

Vo VR

+

Comparators are similar to Op-amp except that open loop gain is made longer by including positive feedback in the internal circuit. Due to very large open loop gain, output voltage essentially provides digital

Vo

operation. There are only two possible outputs, they are Vmax and

Vmax

Vmin. VR

Vin

When, Vin > VR then Vo = Vmax Vmin

Vin < VR then Vo = Vmin Prepared By: SriKisna Khadka 2006 Batch

65

Instrumentation-I

HWHIC GSSE BLEX IV

9. Instrumentation Amplifier: It

is

a

dedicated

differential

amplifier with extremely high input

+

impedance and its gain can be

-

R2

R4

1

controlled by a single internal or R1

external resistor. It consists of two stage amplifier. The first stage offers very high input impedance to both

Rg

Vo1

3

Vout

R1

input signals allows setting the gain with a resistor. The second stage is differential negative

amplifier feedback

with

output,

and

ground

R3

-

R5

2 +

connection for further amplification. Fig: Instrumentation Amplifier

Let; V2 > V1, then V2 – V1 = IgRg Therefore, Ig = (V2 – V1)/Rg

Now; Vo1 = Ig(2R1 + Rg) = (2R1+Rg) (V2 – V1)/Rg Therefore, Vo1 = (1-2R1/Rg)Vin

The gain of amplifier is constant but can be changed by varying the external resistance Rg. Op amp – 1 and op amp – 2 act as a buffer with unit gain for common mode signal and with a gain of (1+2R1/Rg) for differential input of V1 and V2. The circuit has high input impedance since op amp – 1 and op amp – 2 operate in non-inverting mode for common mode signal.


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HWHIC GSSE BLEX IV

Digital to Analog (D/A) Conversion Digital to analog conversion involves translation of digital information into equivalent analog information and this is accomplished by the use of digital to analog converter (DAC). DACs are used whenever the output of digital circuit has to provide an analog voltage or current to drive an analog device. For example: -

Adjusting the motor speed Temperature of furnace Controlling almost any physical variable.

DAC is often referred to as decoding device. Basically, D/A conversion is the process of taking a value represented in digital code and converting it into a voltage or current which is proportional to the digital value.

LSB D L O G I C

D3

20R

D2

21R

D1

22R

D0

23R

Precision Reference Supply I3 Rf

C B

I/P

MSB A

I2 I I1 I0

Op-amp

Vout Analog O/P

+ Fig: DAC Circuitry

The basic configuration of a simple DAC is shown in above figure, which consists of a precision resistor ladder network, a reference precision voltage supply, logic inputs, semiconductor switches and an operational amplifier. The inputs A, B, C, D are binary inputs, which are assumed to have values of either 0V (low) or 8V (high). When input  8V (high), the switches close the point and connects a precision reference supply to the input resistor. When input  0V (low), the switches are open. The reference voltage produces a very stable, precise voltage required for generating an accurate analog output. If all switches are closed: I

=

I0+ I1 + I2 + I3 ………….. (i)


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HWHIC GSSE BLEX IV

Therefore, Vout

=

-I  Rf

=

-Rf (I0+ I1 + I2 + I3)

=

-Rf[Vref(1/23R + 1/22R + 1/21R + 1/20R)]

=

-Vref. Rf(D0/23R + D1/22R + D2/21R + D3/20R)

=

-Vref. Rf (20D0 + 21D1 + 22D2 + 23D3) 23R

……… (ii)

Where, D0, D1, D2 & D3 are the position of switches. i.e. Low Input  OFF State High Input  ON State Therefore, for Rf = R; equation.. (ii) becomes: Vout

=

-Vref (20D0 + 21D1 + 22D2 + 23D3) 23

……… (ii)

Where, the equation … (ii) gives the analog output equivalent to digital inputs fed to the converter. This is an example of 4-bit D/A converter.

For n-bit D/A converter, the above equation becomes: Vout

=

-Vref (20D0 + 21D1 + 22D2 + 23D3 + ………..+ 2n-1Dn-1) 2n-1

In this converter, a summing amplifier is used to weigh the input voltage in digital form to produce the corresponding analog voltage. This approach is not satisfactory for large number of bits because it requires too much precision in the summing resistors. A 12-bit DAC of this type would require the largest weighted resistors to be 211 (2048 * Smallest register value). So this approach is impractical for large number of bits.


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R-2R Binary ladder Network A DAC using R-2R ladder network with 4-input voltages, representing 4-bits of digital data and dc voltage output is illustrated in the figure below.

L O G I C I N P U T S

LSB D 2R

I3

D3

C R

D2

B R A MSB

Rf

2R

I2

I

-

2R

I1

D1 R

2R

I0

Op-amp

Vout Analog Output

+ D0

R

Fig: R-2R Ladder Circuitry

The output current ‘I’ depends on the positions of the four switches and the digital inputs D0, D1, D2 and D3 control the states of the switches. The current is allowed to flow through an op-amp current-to-voltage converter to give Vout.

If all switches are closed, then I

=

I0+ I1 + I2 + I3 ………….. (i)

Vout

=

-I  Rf

=

-Rf (I0+ I1 + I2 + I3)

=

-Rf[Vref(1/24R + 1/23R + 1/22R + 1/21R)]

=

-Vref. Rf (1/23R + 1/22R + 1/21R + 1/20R) 2R

=

-Vref. Rf (D020 + D121 + D222 + D323)

Therefore,

…….. (ii)

24R Prepared By: SriKisna Khadka 2006 Batch

69

Instrumentation-I

HWHIC GSSE BLEX IV

Where, D0, D1, D2 & D3 are the position of switches. i.e. Low Input  OFF State High Input  ON State Therefore, for Rf = R; equation.. (ii) becomes: -Vref (D020 + D121 + D222 + D323) 24 For n-bit D/A converter of this type, the above equation becomes: Vout

=

Vout

=

-Vref (D020 + 21 + D1 22D2 + D323 + ………+ Dn-12n-1 + Dn2n) 24

Example: 1.

A D/A converter have 6 bits and a reference voltage of 10 V. Calculate the minimum value of R such that the maximum value of output current does not exceed 10 mA. Find also the smallest quantized value of output current. Solution: Since, the maximum output current Imax is given by: Imax = ER (2n-1) 2n-2 R The minimum value of R = ER (2n-1) 2n-2 Imax = 10 (26-1) (25×10 ×10-3) = 1969  = 2 K So, Current with LSB = ER/(2n-1R) = 10/(25×2000) = 156 A

2.

Consider a 6-bit D/A converter with a resistance of 320 K in LSB position. The converter is designed with weighted resistive network. The reference voltage is 10V. The output of the resistive network is connected to an op-amp with a feedback resistance of 5 K. What is the output voltage for a binary input of 111.010? Solution: Output Current (Io) = ER/R [dn-1 + (dn-2/2) + ……. + (d1/2n-2)+ (d0/2n-1)] Since, n = 6 Resistance in LSB = 2n-1R 320 K = 25R  R = 10 K Hence, the O/P current (Io) = 10/(10×103)[1×1 + 1×(1/2) + 1×(1/4) + 0×(1/8) + 1×(1/16) + 0×(1/32)] = 1.8125 mA Output Voltage (Eo) = -IoRf = -1.8125×10-35×55×103 = -9V Prepared By: SriKisna Khadka 2006 Batch

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HWHIC GSSE BLEX IV

Analog to Digital (A/D) Conversion The process of changing an analog signal to an equivalent digital signal is accomplished with the help of an analog-to-digital converter (ADC); e.g. and ADC is used to convert an analog signal from a transducer into an equivalent digital signal. Measuring some physical quantity such as temperature, pressure, position, rotational speed, or flow rate etc are usually found in analog form and they need to convert in digital form for the shake of simplicity. ADC is often referred to as an encoding device, as it is employed for encoding signals for entry into a digital system. The A/D conversion is a process of converting an analog input voltage into an equivalent digital signal. Hence the maximum permissible rate of change of analog voltage and maximum permissible frequency of analog voltage should be fed to ADC.

As, V So, dV/dt

= =

Vm sinωt ωVmsinωt

For t  0; dV/dt

=

maximum

=

ωVm =

i.e. dV dt max

2лfVm

If Vmax is full scale range of converter and Tcon be the conversion time of ADC then for the error, we have no more than one LSB. i.e. dV dt max

≤

Vmax 2nTcon

i.e. 2лfVm

≤

Vmax 2nTcon

Now, For Vm = Vmax

i..e.

f

≤ 2

n+1

1 лTcon


71

Instrumentation-I

HWHIC GSSE BLEX IV

Sampling The operation that transforms continuous time signal into discrete time signal is known as the sampling process. The main purpose of signal sampling is efficient use of data processing and data transmission unit. In sampling process, the continuous time signal is multiplied by a train of pulse of unit magnitude. Once the continuous time signal is converted into discrete time signal, there is no record of what the signal was doing in between the sample points. For sufficiently low frequency, signal can be assumed that missing data falls on straight lines between two known sample points.

Analog Signal

Unit Train Pulse

Discrete Signal

In order not to lose the identity of the continuous time signal, when it is sampled, the sampling theorem states that, “If the highest frequency content in the input signal is fn in Hz, then the input signal can be recovered without distortion, if it is sampled at the rate of 2fn sample per second.” This rate is known as Nyquiest Rate, i.e.; fs ≥ 2fn. If the sampling frequency is smaller compared to frequency of input signal then the reconstructed signal wave form is different than the original signal.

Sample & Hold Circuit A sampler is a digital system which converts a continuous time signal into a discrete time signal. The hold circuit holds the value of sampled pulse over a specified period of time. Sample and hold circuit is necessary in ADC to produce a number that accurately represents the input signal ate the sampling instant. Fig: Sampling CIrcuit -

Hold Drop

Vout Sample & Hold Effect

+ Vin

+ Pulse Width

Sampler Fig: Sample & Hold Effect in O/P


Aperture time

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Instrumentation-I

HWHIC GSSE BLEX IV

Quantization The main functions involved in ADC are sampling, holding, quantizing and coding. When the value of any sampled signals falls between two permitted output states, it must be road on the permitted state nearest the actual value of the input signal. The process of representing a continuous or analog signal by finite number of discrete state is called quantization. The standard number system used for processing the digital signal is binary number system. In this system, the code group consists of n-pulses, each indicating 0 or 1. The quantization level (Q) is the range between adjacent decision points and is given by: Q = Full Scale Range 2n Where, LSB of digital signal is quantization level. v +Q/2

0 Q t

-Q/2

Fig: Quantization Level

Fig: Quantization Error

Quantization Error: When the input to the quanitzer is moved through its full scale range and subtracted from the discrete output levels, the error signal is obtained as shown in figure known as quantization error. The rms value of quantization error is given by: Eq = Q/2√3 Quantization error is due to the fact that bits in the digital world are finite. ADC results in finite resolution the analog signal must be rounded off to a quantization level. The error varies from 0 to ±Q/2; no matter how many bits are used there is always some quantization error in ADC. Aperture Time: In order to perform the operation of quantizing and coding a signal, and A/D converter requires an aperture time. The use of a sample and hold circuit provides a very small time for taking a very rapid sample of signal and then holding its value till it is converted. Prepared By: SriKisna Khadka 2006 Batch

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Instrumentation-I

HWHIC GSSE BLEX IV

Types of Analog-to-Digital Converter: Out of many other methods of analog-to-digital conversion, we will discuss the following types: -

Successive Approximation ADC Digital Ramp ADC Dual Ramp ADC Flash Type ADC

Successive Approximation ADC This is one of the most widely used methods of A/D conversion. Though it ahs complex circuitry, it has much shorter conversion time. This type of ADC makes direct comparison between and unknown input signal and a reference signal. The basic arrangement of a successive approximation ADC is shown in figure below. It can be employed at conversion speeds of up to about 1,00,000 samples per second at resolution of up to 16-bits. Start Clear Bits

Comparator

Register

+ Sample Pulse

Start at MSB

Clock Logic Circuit

-

M S B

Bit = 1

L S B

Go to Next Bit

VD Reference Voltage

If Vb > V a

Yes

Clear Bit to 0

DAC

Fig: Basic Diagram of Successive Approximation ADC

Fig: Flow - Diagram


If All Bits are Checked

Stop

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Instrumentation-I

HWHIC GSSE BLEX IV

Working Principle:

A generalized block diagram and flow chart of successive approximation ADC are shown in above figure. - First of all, both the control and the distribution register are set with 1 in the MSB and 0 in all bits. - Distribution register indicates the starting of a cycle in first stage. - The control register shows 1000, which causes an output voltage at the DAC one half of the reference supply. - At the same time, a pulse enters the time delay circuitry. - By the time that the DAC and Comparator have settled, this delayed pulse is gated with the comparator output. - When the next MSB is set in control register, the MSB remains in 1 state or it is reset to 0 depending upon the comparator output. - The procedure repeats itself until the final approximation has been corrected and the distribution register indicates the end of the conversion.

Digital Ramp ADC A digital ramp ADC is shown in figure below. It consists of a digital counter, a DAC, an analog comparator and a control AND gate. The digital counter advances from a zero count while the reference voltage VD-output of DAC driven by the counter, increases on voltage increment for each count step. A comparator circuit receiving both DAC’s output and analog input voltage VA provides a signal to stop the count when VD rises above VA. The counter value ate this time is the digital output. VA Analog Sample

Clock

VD < VA = 1 VD > VA = 0

+ -

Reference Ramp Signal VD Reset Analog Input Voltage VA VD Reference Voltage

DAC

Count Pulse

Digital Counter

Count Start

Count Stop

Count Interval MSB

Digital Output

LSB

Fig: Logic Diagram of Digital Ramp ADC


Fig: Output Wave Form

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Instrumentation-I

HWHIC GSSE BLEX IV

Dual Ramp ADC This is a popular method of converting an analog voltage into a digital value. The block diagram and wave diagram of a basic dual-ramp ADC are shown in figure below. VO

VA

i ii iii

Integrator

Input Sample

1 2 3

Comparator

A

B

C

a Fixed Time Interval

VO

b

t c

Legend: I: Larger I/P Voltage II: Normal I/P Voltage III: Smaller I/P Voltage

VD

Control Logic

Reference Input

Clock

Digital Counter

A: Smaller Digital Count B: Normal Digital Count C: Larger Digital Count 1,2,3: Fixed Discharge Rate a, b, c, are count intervals correspond to A, B & C respectively

Fig: Logic Diagram of Dual Ramp ADC

The analog voltage to be converted into a digital signal is applied through an electronic switch to an integrator or ramp generator circuit, which essentially a constant current is charging a capacitor to give a linear-ramp voltage. The counter operated during both positive and negative slope intervals to the integrator gives the digital output Working Principle:

-

-

The reference voltage and the analog input voltage must be of opposite polarity. The input voltage is integrated for a fixed input sample time. It is then discharged ate a fixed rate and the time required is measured by a counter. The control logic gives (i) Reset and (ii) Convert command to the counter. If a convert command is received by counter, it resets to all zeros and the switch connects the input voltage to the integrator. The output from the comparator is designed so that ate this time it will permit the counter to count up for an output from the integrator. On the next count after the converter has counted all 1s (i.e. the next count will cause it to go all zeros and start over again), the switch changes its position and connects the reference voltage to the integrator. The integrator now integrates the opposite polarity voltage, which causes the output to decrease towards zero voltage. In the mean time, the counter is counting up from zero again. When the output of the integrator goes to zero, it causes the comparator to switch its output, thereby stopping the counter via control logic. The binary number in the counter at this time is proportional to the time taken to integrate down from its starting point to zero. Therefore, the binary count is proportional to the input voltage. Prepared By: SriKisna Khadka 76 2006 Batch

Instrumentation-I

HWHIC GSSE BLEX IV

Summary

For a fixed time interval (usually the full count range of the counter), the analog input voltage connected to the integrator raises the voltage in the comparator to some positive level as shown in characteristic curve. It is obvious that at the end of fixed time interval the voltage from the integrator is greater for greater input voltages. Ate the end of the fixed count interval, the count is set to zero and the electronic switch connects the integrator to a reference or fixed input. The integrator output or input to the comparator then decreases at a fixed rate as shown in the same figure. The counter advances this time. The integrator output voltage decreases at a fixed rate until it drops below the comparator reference voltage, ate which the control logic receives a signal to stop the count. The count shown by the counter at this time represents the digital output of the ADC.

Flash Type ADC The resistor net and comparators provide an input to the combinational logic circuit, so the conversion time is just he propagation delay through the network. It is not limited by the clock rate or some convergence sequence. It is the fastest type of ADC available but requires a comparator for each value of output (63 for 6-bit, 255 for 8-bit etc). Such ADCs are available in IC form up to 8-bit and 10-bit flash ADCs (1023 comparators) are planned. The encoder logic executes a truth table to convert the ladder of inputs to the binary number output. Vref Vin

1k

Thermometric Code +

7 -

1k

-

1k

6

+

-

1k

E N C O D E R

+

5

+

4

MSB

-

1k

L O G I C

+

3 -

1k

+

-

1k

2

LSB

D I G I T I L O/P

+

-

1

Comparators Fig: Flash Type ADC


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Instrumentation-I

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Example: 1. Find the successive approximation A/D output for a 4 bit converter to a 8.217 V input if the reference is 5 V. Solution: Let the 4-bit A/D converter has its bit element given by d3d2d1d0 (i) Setting d3 = 1 Output = 5/21 = 2.5 V Since, 3.217 > 2.5  Setting d3 = 1 (ii) Setting d2 = 1 Since, 3.217 < 3.75

Output = 2.5 + 5/22 = 3.75  Setting d2 = 0

(iii) Setting d1 = 1  Output = 2.5 + 0 + 5/23 = 3.125 Since, 3.125 < 3.217  Setting d1 = 1 (iv) Setting d0 = 1  Output = 3.125 + 5/24 = 3.4375 Since, 3.4375 > 3.217  Setting d0 = 0 Thus output of 4-bit SAR converter is: 1010 2. A 5-bit converter is used for a d.c. voltage range of 0 – 10 V. Find the weight of MSB and LSB. Also the exact range of the converter and the error. Find the error if a 10 bit converter is used. Solution: Range of MSB = ½ × Range of Converter = ½ × 10 = 5 V Range of LSB = (½)5× Range of Converter = ½ × 10 = 0.3125 V So, the exact range of the converter is given by: Eo = ER (dn-1×2-1 + dn-2×2-2 + ……. + d1×2-n-1 + d0×2-n) = 10 (1×2-1 + 1×2-2 + 1×2-3 + 1×2-4 + 1×2-5) = 9.6875 V Error = = =

10 – 9.6875 0.3125 3.215 %

Again, the exact range of the converter when 10 bits are used is: = 10 (1×2-1 + 1×2-2 + 1×2-3 + 1×2-4 + 1×2-5 + 1×2-6 + 1×2-7 + 1×2-8 + 1×2-9 + 1×2-10) = 9.99 V Error = 10 – 9.99 = 0.01 = 0.1% Thus if a large number of bits are used, the error reduces considerably. But the use of converter with a large number of bits results in higher cost of the converter itself and also of the system where it is used. Also, a higher number of bits add to the complexity of the system. Prepared By: SriKisna Khadka 2006 Batch

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Grounding & Shielding A. Grounding: Grounding provides safety and signal reference. The principle of grounding is to minimize the voltage differential between the instrument and a reference point. The following figure shows grounding and illustrates two different configurations. Circuit A

Circuit B

 V=0

Ground Current

Ground Structure + Ground Potential not equal to zero Fig: Single Point Ground

Circuit A

Circuit B dV=0

Low Impedance

Ground Plate -

+

Ground Potential = 0 Fig: Multi Point Ground with Low Impedance Ground Structure

Safety grounding seeks to reduce the voltage differential between exposed conducting surfaces, while signal referencing seeks to reduce the voltage differential between reference points. Obviously a dynamic tension exists between these concerns. Safety grounding should have many connections between exposed conducting surfaces and signal referencing should have one connection between reference points at low frequency.


79

Instrumentation-I

Power Supply

HWHIC GSSE BLEX IV

+ -

Circuit A

Circuit B

Circuit C

Fig: Series Return Connection

Power Supply

+ -

Circuit A

Circuit B

Circuit C

Single Point Return Fig: Series Return Connection

Bus Bar of Return Plane

Power Supply

+ -

Circuit A

Circuit B

Circuit C

Fig: Multi Point Return

Ground and Return Symbol: Safety Ground

Symbol

A connection to an electrical ground structure like building steel or an isolated ground wire. Signal Ground

Symbol

A connection to a chassis that does not normally conduct current.

Signal Ground

Symbol

A conductor that sustains return current for signal and power.


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B. Shielding: Shielding either prevents noise energy from coupling between circuits or suppresses it. The energy coupling may be through magnetic flux; electric field or electromagnetic wave propagation. Because prevention is cheaper and effective than suppression, shielding also prevents noise coupling. Types: - Inductive Shielding - Capacitive Shielding - Electromagnetic Shielding B.1 Inductive Shielding: It is concerned with self-inductance and mutual-inductance. It reduces noise coupling by reducing or recording magnetic flux. Magnetic noise coupling depends on the loop area and current within both the emitting and receiving circuits. The most effective inductive shielding minimizes loop area. The cost of manufacturing makes magnetically permeable enclosure an even less desirable solution for inductive shielding. Twisting the signal and return conductors in a cable reduces the mutual inductance and improves the shunt capacitance.

Twisted Pair Cable

+

Signal Source

Ic -

Stray Capacitance

Loop Area

Earth Ground

Fig: Inductive Shielding

Twisting the wire and running it close to the ground will reduce the common-mode current Ic by reducing the loop area for inductive coupling. B.2 Capacitive Shielding: It reduces noise coupling by reducing or rerouting the electrical charge in an electrical field. Capacitive shields shunt to ground charge that is capacitively coupled as shown in figure. At low frequencies less than 1 MHz, we should connect a capacitive shield at one point if the signal circuit is grounded. Multiple connections can form ground loops. Furthermore we can improve capacitive shielding by reducing the following: Prepared By: SriKisna Khadka 2006 Batch

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- Noise Voltage & Frequency - Signal Impedance - Floating Metal Surfaces

Stray Capacitive Coupling

Susceptible Circuit

Noise Source

Faraday Shield

Susceptible Circuit

Noise Source

Noise Source

Driven Shield for Noise Sensitive Electronics

A Single Point Connection

Fig: Different Cases of Capacitive Shielding


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B.3 Electromagnetic Shielding: It reduces emission and reception. Emission sources include lightening, discharges, radio and television transmitters and high frequency circuits. Electromagnetic interference (EMI) always begins as conductive, becomes radiative and ends as conductive as given in figure below: Complete 360o Seal Circuit Enclosure A

Circuit Enclosure B Cable Shield Fig: Electromagnetic Shield

Several techniques can reduce EMI. -

Reduced bandwidth (Longer wavelength) Good layout and signal routine Shielded enclosures

C. Filtering: Filtering reduces conductive noise coupling. A filter can either block or pass energy by three criteria. - Frequency - Mode (Common or Differential) - Amplitude (Surge Suppression) C.1 Frequency: A low pass filter passes low frequency energy and rejects high frequency while a high pass filter passes high frequency energy and rejects low frequency. Time average and time synchronization filters are frequency selective as well. C.2 Mode: Common mode noise injects current in the same direction in both the signal and return lines. Differential mode noise injects current in opposite direction in the signal and return lines. Prepared By: SriKisna Khadka 2006 Batch

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Ic

Id

Common Mode

Differential Mode

Signal Source

Load

Fig: Common Mode Filter

+ Vdm/2 - Signal Sources + Vdm/2 Icm

Load

Vdm +

-

Fig: Differential Mode Filter

C.3 Amplitude: An amplitude-selective filter generally removes large transients or spikes of noise energy from a signal line. Surge suppressors that are built into ac power strip are amplitude-selective filters to protect sensitive equipments.


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Chapter 5 Signal Transmission Transmission Media: The transmission media or channel is a physical medium used to pass the signal from transmitter to receiver. Essential features of the transmission media is that it introduces multiplicative (multipath fading) and additive (natural & manmade) noise to the signal picked up by the receiver. Transmission media may be wire line or wireless. A. Wire line Channels: For landline telemetry wire line channel are used. This type of channel is extensively used in telephony, computer networks as a link between the transmitter and antenna in wireless communication etc. this channel uses a pair of wires, co-axial cables or optical fibers as the medium. In order to select the transmission media following points may be considerable. - Low attenuation - Impedance matching - High SNR - Not susceptible to radio frequency interference (RFI) and electromagnetic interference (EMI); such that less number of repeaters are required. - High data rate and high bandwidth. A.1 Co-axial Cable: Mainly co-axial cables are of two types; - Thick Co-axial Cable - Thin Co-axial Cable

PVC Jacket Aluminum Sleeve Copper Center Conductor

Conductor Insulator

Characteristics of Thick Co-axial Cable (10Base5):

-

Device attachment possible at every 2.5 m. Maximum cable length is 500 m. Maximum cable length with repeater is 2500 m. Transmission rate is 10 Mbps. Support base band transmission. Maximum delay per segment is 2156 nsec. Uses 50 ohms terminators.

Characteristics of Thin Co-axial Cable (10Base2):

-

Construction is similar to that of thick co-axial cable. Device attachment possible at every 0.5 m. Maximum cable length is 85 m. Data transmission rate is 10 Mbps. Support base band transmission. Maximum delay per segment is 950 nsec. Uses 50 ohms connectors. Prepared By: SriKisna Khadka 2006 Batch

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A.2 Twisted Pair Cable: Characteristics

-

Maximum cable length: 100 m. Transmission rate: 10 to 100 Mbps. Support base band transmission. Maximum delay per segment: 1000 nsec. No external terminators.

Twisted Pair Cables

PVC Jacket

A.3 Optical Fiber Channel: Protective Layer Cladding (100-150µm) Core (3-50µm)

A portion of fiber is shown in alongside figure and a general optical fiber communication system is given below.

Information Source

Electrical Transmit

Optical Source

Optical Fiber Cable

Optical Detector

Electrical Recieve

Destination

Optical Fiber Communication System

The information source provides and electrical signal, which drives an optical source to give modulation of the light wave carrier. The optical source (LED or LASER) provides the electrical to optical conversion. The transmission medium is and optical fiber cable. The optical detector (APD or PIN Photodiode) demodulates the optical carrier. Basis Of Light Propagation In Optical Fiber: ?

?

1

Fig: I

2

?

?

2

1

Fig: II


?

1

?

2

Fig: III

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When light propagation from denser medium with refractive index η1 incidents on a rarer medium with refractive index η2; (η 1 > η 2) it bends away from the normal, then according to Snell’s law:

i.e.

η1sinФ1 = sinФ1/ sinФ2 =

η2sinФ2 η2/η1 ……….. (i)

The corresponding angle of incidence in the denser medium for which the angle of refraction is 90o is called critical angle (Фc). When the angle of incidence is greater than the critical angle, almost all incident light (99.9%) reflects back to the denser medium. This phenomenon is called the total internal reflection. Cladding (? 2)

Then, equation (i) becomes: sinФC/sin90o = η2/η1

Air

i.e. sinФC = η2/η1 …….. (ii)

Air Core (? 2) Cladding (? 2)

In case of optical fiber cable the refractive index of core (η1) is greater than that of cladding (η2). The light entering from air is incident on the core-cladding interface as an angle greater than the critical angle. Hence the light is propagated down the fiber with low loss. B. Wireless Channels: B.1 Radio channels: Where longer distances greater than 1 km, are involved or where measurements have to made in a missile or moving vehicle, it may be necessary to be radio frequency (RF) techniques to transmit the signals. -

Radio waves are easy to generate, can travel distances and penetrate building easily. Widely used for data transmission both indoors and outdoors. Radio waves are omni directional, so that Tx and Rx does not have to be carefully aligned physically. Radio waves frequency generally ranges from 104 Hz to 106Hz. Radio links are used for radio (Short Wave, FM) and television (VHF, UHF) broadcasting. It is commonly deployed with air borne instrumentated flight vehicles, rockets, unmanned space crafts etc. Frequency 104 106 108 1010 1012 1014 Waves Radio Infrared µ - Wave

Visible Light


1016 1018 1022 1024 UV Rays X - Rays Gamma Rays

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B.2 Microwave Channels: This is a special case of radio transmission, employ high frequencies several bands of 890 MHz to 30 GHz, and have been allocated for microwave transmission. Use of microwave media has increased due to heavy requirement of chemicals in industries like power and gas types of microwave. (a) Terrestrial Microwave (b) Satellite Microwave

(a) Terrestrial Microwaves: -

Usually operate in low GHz range (typically between 4 to 6 and 21 to 30 GHz). Typical data rate for a single-frequency varying from (1 to 10 Mbps). Microwave links are susceptible to extend interference, jamming, attenuated by rain and fog.

(b) Satellite Microwaves: -

Usually operate between 11 to 14 GHz. Maximum capacity depends upon the bands used (less than or equal to 45 Mbps). it is subjected to a propagation delay ranging from 500 msec to more than 5 seconds. Also susceptible to external interference and affected by rain and fog.

Transmission Schemes The data on the signal may be retained in an analog form during transmission or they may be converted to digital before being to its destination.

A. Analog Transmission Scheme: Analog signal can be sent directly from the transducer to the measuring/recording instruments without any prior conditioning (amplification, filtering). This transmission method is the simplest but is quite limited in its application. If the signal source and measuring instruments are very close (within 1-2 meters) and the signal levels are not too small (greater than 100 mV), the technique may be sufficiently effective to yield satisfactory results. However, if the signal levels are small (less than 100 mV) and if the instrument must be located at some distance from the measuring point (greater than 5 meters), the other two data transmission methods are usually employed. They are: 1. 2.

Analog Voltage Transmission. Analog Current Transmission.


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A.1 Analog Voltage Transmission:

IA

Slider

Channel

V End Device Receiving Terminal Bourden Gauge Tube Transmitting Terminal

-

-

This is popular techniques if the distances are less than 30 meters. This is less expensive than analog current method as long as the distance limitation is not exceeded. The low level signal from the source is amplified by an instrumentation amplifier (IA) placed close to signal source. The output of the IA is a high level analog voltage signal of 0-5 V or 0-10 V. Since, they possess substantially large amplitudes in systems that are well designed against external noise pickup. Such high level voltage signals don’t suffer much degradation during transmission. For greater distances, cable resistance, grounding problems etc; reduce the effectiveness of these type techniques.

A.2 Analog Current Transmission:

-

-

DC Power Supply 24V/48V

Process Transmitter

Measurand

Sensor

End Device

This method uses an analog dc current signal with a value of 4 mA corresponding to zero signals and 20 mA representing full scale. The current signal can be transmitted for distances up to 2 miles and this allows measurements of parameters like temperature, pressure etc to be brought into control room from remote plant locations. Different loads can be connected to the transmitting circuit because the circuits are designed to work into any load from 0 ohm to 1000 ohms. Since, the current in a series circuit is constant everywhere along the path; there is no degradation of the signal with distance as there is when transmitting voltage signals.


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B. Digital Transmission Scheme: Analog data transmission system suffers from three basic demerits, they are: 1. Limited distance (30 m in analog voltage transmission and 3000 m in analog current transmission scheme). 2. Prone to degradation by interference signal. 3. Must be converted to digital form fro digital computers and records to handle the data. Measurand data can also be converted to and transmitted in digital form. By using various transmission techniques, digital data can be sent to he destination points of virtually unlimited distance. Data transmission can be performed in a highly efficient and virtually errorless manner; elimination the problem of reduced accuracy that results from interference. Finally digital data can be transmitted in the format required by the receiving digital computers or display device. There are mainly five types of standard interface which are most commonly encountered when transmitting digital data between instruments and other digital devices. They are: (i) (ii) (iii) (iv) (v)

Parallel Interface Binary Coded Decimal (BCD) Interface IEEE-488 Bus Interface CAMAC Interface Serial, Asynchronous Interface.

B.1 Parallel Interface: -

This is general interface method. Digital data transmitted along paths that may physically consists of wires, microwaves, radio waves etc.

-

Such paths (data buses) usually consists of not only lines for carrying measured data but also additional lines whose function is to carry out the control signals between instruments and digital devices.

Data Bits T R A N S M I T T E R

Control Lines

R E C E I V E R

Fig: Parallel Interface

-

The digital data that are carried on such buses are encoded in a digital format (BCD, 8-Bit Word or ASCII).

-

If all the bits that make up a digital word are transmitted simultaneously, this is known as ‘Parallel Transmission’. In this system, each bit of the data-word requires its own data lines and together with control lines appears as the interface shown in above figure. Parallel transmission can be either synchronous or asynchronous. Prepared By: SriKisna Khadka 2006 Batch

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1. Synchronous System: In this system a clock pulse is also transmitted in parallel with the data. The rate of parallel synchronous can be very high. The distance of transmission is limited to about 12 ft; and synchronization is costly and complex to implement. It is employed for data transfer within computers and from computer to computer. 2. Asynchronous System: It is performed without the use of synchronizing clock pulses. It requires handshake signal (‘Data Ready’) between the transmitting and receiving devices to ensure that valid data are transferred. B.2 Binary Coded Decimal (BCD) Interface: -

-

The BCD interface is a parallel asynchronous interface that originated when attempts were made to connect digital instruments to other digital devices. In this system of interface the output of ADC is in the instrument is fed to a series of 4-Bit Counters, which encode the digital data into BCD words. The output of counter together with control and handshake forms the BCD interface. The main disadvantage of this system is that for each bit of added resolution, 4-parallel lines must be added. The second disadvantage is that the computer needs to convert the BCD data to ASCII data before processing it. It is designed only to send data in uni-direction. Seven Segment Displays

Measurand

ADC

Analog Signal

BCD Counter

BCD Counter

Control Circuit

BCD Counter M S B

B C D

L S B

I N T E R F A C E

Fig: Binary Coded Decimal Interface


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B.3 IEEE-488 Bus Interface: -

-

The IEEE - 488 standards defines a byte-serial, 8-bit parallel, asynchronous type instrument interface. The IEEE - 488 standards is a document that describes the rules, specifications, timing relationships, physical characteristics etc of an interfacing technique that allows digital instruments and devices to be interconnected. It is a hardware (wires, connectors etc) that is used to implement the standard. Sixteen signals line comprise the complete IEEE – 488 bus structure as shown below. 1 2 3 4 5 6 7 8

D A T A L I N E S

1 2 3 4 5 6 7 8

Hand-Shake Lines 1 1 DAV 2 2 NRFD 3 3 NDAC Bus Management Lines 4 5 6 7 8

IFC ATN REN SRQ EOI

4 5 6 7 8

Fig: IEEE – 488 Interface

Legend: Bus Management Lines EOI – End or Identity SRQ – Service Request REN – Remote Enable ATN – Attention IFC – Interface Clear Hand-Shake Lines NDAC – Not Data Accepted NRFD – Not Ready For Data DAV – Data Valid Since, it is not guaranteed by the standard that instruments will send information coded in this suggested manner, two IEEE – 488 interconnected instruments may always be able to talk to each other, but they may not always be able to understand each other. Prepared By: SriKisna Khadka 2006 Batch

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B.4 CAMAC Interface: -

It can be used to transmit data in parallel, serial or byte-serial manner. It was originally designed to meet the requirements of nuclear instrumentation labs. The basic word length in CAMAC system is 24 – bits. But when all control lines are added, a parallel CAMAC requires a 66 – wires interface. When data are transmitted by as serial CAMAC interface just two data lines are required and only a nine-wire cable is needed. CAMAC I/O boxes are called CAMAC CRATES. The crate contains a power supply and up to 25 – plugs in modules. The fastest data transmission rates in CAMAC systems are achieved using parallel interfaces. Longer distance transmission up to 300 ft. ate equally high speeds can be performed using the Parallel CAMAC Highway (66 – wire cable). For further longer distance transmission, date rates up to 5 Mbps can be achieved by using either of the two serial transmission options (CAMAC – Serial Highway).

B.5 Serial Interface: -

Transmission of data over long distances becomes expensive if done in parallel fashion. If the data are transmitted serially, only one path is required, since the data are sent only on bit at a time. Single serial data pack requires just two wires, only one transmitting processor to log the data out and one receiving processor to log it in. Serial transmission interfaces operate either in simplex, half duplex or full-duplex modes.

Transmitter

Receiver Fig: Serial Data Transmission

-

Serial transmission methods are characterized by how many bits per second they can transmit, i.e. 1 bit/sec = 1 baud. Most serial interfacing in instrumentation system is done in an asynchronous manner rater than a synchronous one. Although serial synchronous, transmission rates can be higher (9600 bauds) than asynchronous serial rates, it has greater system complexity. Serial asynchronous methods are usually adequate for most instrumentation applications. Serial asynchronous are relatively slow because they require a handshake for each character of data transfer.


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General Telemetry System The signal or data must often be transmitted from the point of measurement to some other point in the instrumentation system. For example, those measured data may need to be sent to display devices, recording devices, computers or other processes controllers. In many systems the destination may be quite far from the measurement point. The data must be transmitted ate the required rate while preserving the desired accuracy. Telemetry is the science of signal transmission and refers to the process by which signal from transducer and signal conditioning equipments is transferred to a remote location. A general telemetry system is shown in the figure below and consists of three basic components: transmitter, channel and receiver.

Meaurand

Sensor OR Transducer

Transmitter

Channel

Receiver

End Devices

Fig: General Telemetry System

Telemetry may be defined as measurement at a distance. It is a technology, which enables a user to collect data from several measurement points at inaccessible or inconvenient locations; transmit that data to a convenient location and to present the several individual measurements in a usable form. -

The primary detector (Sensor/Transducer) and the end device have the same position and functional roles as in a generalized measurement system. The function of telemetry transmitter is to convert the output of a primary sensing element into an electrical form and to transmit I over a telemetry channel. The signal is received by a receiver placed at a remote location. This signal is converted into a usable form by the receiver and is indicated or recorded by an end device, which is graduated in terms of the measurand.

Types: -

Land Line Telemetry Radio Frequency Telemetry


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A. Land Line Telemetry System: A land line telemetry system requires a telemeter channel which is a physical link between the telemeter transmitter and receiver. This physical link may be a cable, a specially laid out wire, existing telephone and telegraph cables or power line carriers. It is in fact, a direct transmission of information through cables and transmission lines. Direct transmission via cables employs current, voltage, frequency, position or impulses to convey information. The land line telemetry systems can be classified as: -

Voltage telemetry systems Current telemetry system Position telemetry system.

A.1 Position Telemetry System: A position telemetry system transmits and reproduces the measured value of variable by positioning variable resistors or other electrical components in a bridge circuit form so as to produce proportional changes at both the transmitter and the receiver ends. This is known as bridge type telemetry system. -

-

Figure shows two potentiometers, one at transmitting end and other at the receiving end. Two potentiometers are energized by a common power supply. The sliding contact at the transmitting end is positioned by the bourden tube as pressure is applied to the latter. If the sliding contact at the receiving end is positioned until the centre zero, galvanometer indicates zero, the position of the contact will assume the same position as the contact of the transmitter. The receiving contact moves the pointer which indicates on the scale, the pressure which is being measured (the scale is directly calibrated in terms of pressure). Principle – Same as that of wheat Stonebridge.

Telemetry Channel Sliding Contact

V

Bourden Tube

Centre Zero Galvanometer

Scale in KN/m2 Potentiometer Transmitting Terminal Receiving Terminal Fig: Position Telemetry System


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B. Radio Frequency Telemetry System: -

-

-

-

RF telemetry is used in applications where there is no physical linked between the transmitting and receiving stations. The link between the transmission station and the receiving station can only be established through radio links. The rocket or unmanned space craft presents more obvious need for radio link based telemetry. The vehicle in this case is too small to carry even one person, much less the entire team of engineers and also a computer. Here RF telemetry monitors all information which enables the team of engineers to evaluate performance of the test vehicle with the help of computer, while the flight is in progress. RF telemetry is usually more suitable if the data is to be transmitted over distance greater than 1 km. Certain parts of RF spectrum have been allocated for telemetry and micro wave links above 4 MHz. radio waves at these frequencies tend to travel in straight line requiring repeater stations with disc like antennas on high building and towers ever 30 to 60 km. The modulation methods used for transmission in RF telemetry are: (i) Amplitude Modulation (ii) Frequency Modulation (iii) Phase Modulations

-

Modulation is a process by which some low frequency signal is impressed on high frequency monochromatic carrier signal. The low frequency signal usually the information bearing signal and is called modulating or message signal.

A: 2.1 Amplitude Modulation (AM): In amplitude modulation the amplitude of high frequency monochromatic carrier signal c(t) is varied according to the rate of change of modulating signal m(t). In other words, in this modulation technique the amplitude of a carrier signal is varied by a modulating voltage signal whose frequency is much lower than that of the carrier. Formally, AM is defined as system of modulation in which the amplitude of the carrier is proportional to the instantaneous amplitude of the modulating signal whereas the modulating signal is the output voltage of a transducer which is generated on Emax account of application of the measurand.

m(t)

t

Message Signal c(t)

t

Carrier Signal

Emin

t

The modulation index is the term that defines the depth of modulation. Amplitude Modulated Signal

i.e. M.I. =

(Emax - Emin) (Emax + Emin) Prepared By: SriKisna Khadka 2006 Batch

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A: 2.2 Frequency Modulation (FM):

HWHIC GSSE BLEX IV m(t)

In frequency modulation the frequency of the t

carrier signal is varied in accordance to that of modulating signal. In frequency modulation, the frequency deviation in the carrier signal is directly

Message Signal c(t)

proportional to the modulation signal m(t). t

In other words, frequency modulation is Carrier Signal

a system in which the amplitude of modulated carrier is kept constant, while its frequency is varied t

by the modulating signal. The general equation of an unmodualted wave,

Frequency Modulated Signal

or carrier, can be written as: x = A sin (t+) Where,

x – instantaneous value of current/voltage A - amplitude of current/voltage  - angular frequency, rad/sec  - phase angle, rad

If any of these three parameters is varied in accordance with another signal, normally or a lower frequency, then the second signal is called modulating signal, and the first is modulated by the second. Amplitude modulation, already discussed, is achieved when amplitude A is varied, alteration of phase angle f will yield, phase modulation. Finally, if the frequency of the carrier is made to vary, frequency modulated waves are obtained. The modulation index for FM is defined as:

M.I.

=

Maximum frequency deviation () Modulating frequency (fs)


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Unguided Media For unguided media, transmission and reception are achieved by means of an antenna. For transmission antenna radiates electromagnetic energy into the medium usually air and for reception antenna picks up electromagnetic wave from the surrounding media. There are basically two types of configuration for wireless transmission. -

Directional, and Omni Directional

For directional configuration the transmitting antenna puts out a focused electromagnetic beam; the transmitter and receiver antenna must therefore be carefully aligned. In omni directional case, the transmitted signal spread out in all directional and can be received by many antennas. Frequency range of 30 MHz to 1 GHz is suitable for omni directional application and microwave frequency range of 2 GHz to 40 GHz is suitable for point to point (directional) transmission. A. Microwave Link: A microwave link performs the same function as co-axial by using point to point microwave transmission between repeaters. Microwave links require less number of power amplifier or repeater than the co-axial cable over the same distance. Microwave link is commonly used for both voice and data transmission. Common frequencies used for transmission are in the range of 2 - 40 GHz. The higher the frequency used, the higher the potential bandwidth and therefore higher the potential data rate.

As with any data transmission system the main source of loss is attenuation. For microwave link the loss can be expressed as:

PL

=

10 log (4πd/λ) 2

Where; d – Distance between the transmitter and receiver antenna.

λ – Wave length In microwave links, transmitter and receiver are placed about every 50 km.


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Receiving Antenna

Transmitting Antenna

Receiver Protection Circuit

Power Amplifier

Receiver Mixer

IF Amplifier & AGC

Band Pass Filter

Band Pass Filter

Amplifier Limiter

Mixer

25 %

Shift Oscillator

Transmitter Mixer

Power Splitter

Band Pass Filter

75 %

µ – Wave Generator

Fig: Simplified Block Diagram of Microwave Link Carrier Chain

Legend: IF – Intermediate Frequency AGC – Automatic Gate Controller


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B. FM/FM Radio Telemetry: The term FM/FM refers to the fact that two FM processes are employed. In the first process analog signals are converted to propagation frequency by using voltage-to-frequency converter. Low frequency range of 400 MHz – 70 GHz cannot be practically transmitted by radio propagation since they would require antenna of very large size; because the size of the antenna must be in the order of wave length to be transmitted so there is an additional FM to boost all the frequencies into the radio frequency range.

1

400 Hz

Sub Carrier Oscillation FM Receiver

Sum 2

560 Hz

Band Pass 400 Hz

FM Demodulator

560 Hz

Low Pass 6 Hz Filter Cut-Off

Modulator

Data

RF Oscillator

Frequency Multiplier

18

70KHz

Power Amplifier 70KHz

Fig: FM/FM Radio Telemetry System


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Chapter 6 Output Devices Output consists of the last stage of a measurement system. This stage consists of display devices and recorders. The result of any measurement system must be displayed for instant observation or for storage for further study or analysis. The output devices are also called data presentation devices. The output devices may also be used as control devices using inverse transducers. The choice between the display devices and recorders depends upon  The expected use of the output  The information content of output

A. Indicating Instruments: The electrical indicating instruments are used extensively for measurement of current voltage resistance and power. They are classified as:  

Analog Instruments Digital Instruments.

Analog Instruments: It deals with the measurement of information in analog form. These instruments generally make use of a dial and a pointer for this purpose; e.g. ammeter, voltmeter and wattmeter belong to this category. Depending upon the principle of operation analog instrument is categorized as: -

Magnetic Effect (Dynamometer type) Heating Effect Electrostatic Effect (Voltmeter type) Electromagnetic Effect (Wattmeter, Energy meters) Hall Effect (Flux meters, ammeters etc.)

Digital Instruments: These instruments indicate the value of the measurand in the form of a decimal number. The digital meters work on the principle of quantization. The analog measurand is first subdivided or quantized into a number of small intervals up to many decimal places. They are: -

Segmental Display Dot Matrices Rear Projection Display Nixie Tube etc. Prepared By: SriKisna Khadka 2006 Batch

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Advantages of Digital Instruments: -

-

The display is directly in decimal numbers and therefore human errors are eliminated. The readings may be carried to any number of significant figures. The output is in digital form and can be directly fed into memory. Low power requirements.

Advantages of Analog Instruments: -

-

They are cheap and simple Commonly used for ordinary purpose.

Comparison between Digital & Analog Instruments: 1. Accuracy: Best analog instruments rated 10.1% of full scale. Much greater accuracy can be achieved with digital instruments. 2. Environmental Reaction: Analog meter movements operate under a wide range of environments. Digital instruments are relatively complex and have large number of parts, which react to change in temperature and humidity. 3. Resolution: In analog instruments the limit is one part in several hundreds. In digital instruments it is one part in several thousands. 4. Power Requirements: Digital instruments draw negligible power whereas analog instruments may load the circuit under measurement. 5. Cost & Probability: Analog instruments are low in cost and are extremely portable. On the other hand digital instruments are not easily portable and require an external power source. However the development of VLSI and nano-technology, digital instruments are more portable and low in cost. 6. Range & Polarity: Most digital instruments are dc instruments and measures up to 100 V and 1000 V by mean of the range attenuator. Many digital instruments have automatic polarity section and auto ranging facilities. 7. Freedom from Observational Errors: The digital instruments are free from observational errors like parallax and approximation errors. Analog instruments have a scale, which give considerable observational errors.


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B. Data Recording System (Recorders) A recorder records electrical and non-electrical quantities as a function of time. This record may be written or printed which can be later examined and analyzed for better understanding and control of the processes; e.g. flow, pressure, temperature, current, voltage etc. Current and voltage can be recorded directly while the non-electrical quantities are recorded indirectly by first converting them to equivalent currents or voltages with the help of sensors or transducers. Types of Recorder 1. Graphic Recorder 2. Magnetic Tape Recorder 3. Oscillographic Recorder

1. Graphic Recorder: Graphic recorders are the devices, which display and store a pen-and-ink record of the history of some physical event. There are two types of graphic recorder. - Strip Chart Recorder - X-Y Recorder

Strip Chart Recorder Figure below shows a mechanism of a strip-chart recorder system. It records one or more variables with respect to time. It is also called X-t recorder. Indicating Scale Stylus Drive System

CHART

To Control Circuit Chart Speed Selector

Range Selector

Information to be Recorded

Fig: Strip-Chart Recorder


Paper Drive Mechanism

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A range selector switch is used so that input to the recorder drive system is written within the acceptable level. Most recorders use a pointer attached to the stylus. This pointer moves over a calibrated scale thus showing the instantaneous value of the quantity being measured and external control circuit for the stylus may be used. The stylus is filled with ink (usually red) by gravity or capillary actions.

X – Y Recorder Since, a strip chart recorder records the variation of a quantity with respect to time while an X-Y recorder is an instrument, which gives a graphic record of the relationship between two variables. In X-Y recorder an emf is plotted as a function of another emf. Y - Channel

Reference Source

Y- I/P

Attenuator

Balance Circuit

Pen Driving Motor

Y Amplifier

Y - Dir

Pen

X - Direction

X- I/P

Attenuator

Balance Circuit

Arm Driving Motor

Y Amplifier

Reference Source

X - Channel

Fig: X – Y Recorder

An X-Y Recorder consist of:  A pair of servo systems, driving a recording pen in two axes through a proper sliding pen and moving arm arrangement with reference to a stationary paper chart.  Attenuators are used to bring the input signals to the levels acceptable by the recorders.


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The above figure shows a block diagram of a type of X-Y recorder. A signal enters each of the two channels. The signal after passing through attenuator (0.5 mV) passes to a balance circuit where it is compared with and internal reference voltage. The error signal (i.e. the difference between two voltages) is fed to the chopper, which converts dc signal to ac signal. The signal is amplified in order to actuate a servomotor, which is used to balance the system and hold it in balance as the value of the quantity being recorded changes. An X-Y recorder may have: -

A sensitivity of 10 µV/mm. A slowing speed of 1.5 m/s. Frequency response of 6 Hz for both axes. Chart size of 250 × 180 mm, and an accuracy of about ±0.3 %

Uses: -

Speed torque characteristics of motors. Lift drag wind tunnel tests Plotting of characteristics of vacuum tubes, zener diodes, rectifiers, transistors etc.

Magnetic Tape Recorder Magnetic tape recorder is necessary to record data in such a way that they can be retrieved or reproduced in electrical form again. The most common and useful way is magnetic tape recording. Advantages:      

They have wide range of frequency from dc to several MHz. They have low distortion. The magnitude of the electrical input signal is stored in magnetic memory and this signal can be reproduced whenever desired. The recorded signal is immediately available, with no time lost in processing; playback or reproduced many times without loss of signal. Tape can be erased and reused to record new data. Data may be recorded at very fast speeds (1.52 or 3.05 m/s) and played back at relatively slow speeds (4.76 or 2.38 cm/s), which can be recorded with low frequency recorders like graphic recorder.


105

Instrumentation-I

HWHIC GSSE BLEX IV

Principle: When a magnetic tape is passed through a recording head, any signal recorded on the tape appears as magnetic pattern dispersed in space along the tape. The same tape when passed through a reproduce (playback) head produces variations in the reluctance of the winding thereby inducing a voltage in the winding dependent upon the direction of the magnetization and its magnitude on the magnetic tape. The induced voltage is proportional to the rate of change of flux linkages. Therefore the emf induced in the winding of reproducing head is proportional to the rate of change of the level of magnetization on the tape.

Recording Current

Magnetic Oxide

Magnetic tape

Plastic Base

Non Magnetic Gap

Tape Motion

Fig: Magnetic Tape Recording Head

i.e;

erep

α

Supply Reel

N(dФ/dt)

Take Reel

Let, the original signal be : Asinωt The current in the recording head winding and the flux produced will be proportional to this voltage. Ф = K1Asinωt

Inertia Roller

Pinch Roller

( K1 – Constant)

The voltage induced in the reproduce head winding.

Tension Arm Recording Tape Reproduce Heads Heads

erep

= = =

N(dФ/dt) K1NAωcosωt K2Aωcosωt

Fig: Tape Transport Mechanism

Thus the output signal is a derivative of the input signal. The output signal is proportional to the flux recorded as well as the frequency of recording signal.


106

A Notebook on Instrumentation System I

A Notebook on Instrumentation System I

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