Lectures in Electronic Devices (3rd Year, Course 1)

Lectures in Electronic Devices (3rd Year, Course 1)

Assistant Professor Dr. Hamad Rahman Jappor Department of Physics University of Babylon October, 2016

‫محاضرات في االلكترونيات (النبائط االلكترونية)‬ ‫)المرحلة الثالثة‪ ،‬الكورس االول(‬

‫اعداد‬ ‫األستاذ مساعد الدكتور حمد رحمن جبر‬ ‫قسم الفيزياء‬ ‫جامعة بابل‬ ‫تشرين األول‪2016 ،‬‬

Contents Chapter 1: Semiconductor Material The atom, materials used in electronics, current in semiconductors, N-type and P-type semiconductors, PN junction, Energy Diagrams of PN Junction. Chapter 2: Diodes and applications Diode operation, voltage-current characteristics, diode models, half-wave rectifiers, full-wave rectifiers, diode limiters and clampers, voltage multipliers. Chapter 3: Special-Purpose Diodes Zener diodes, Zener diode applications, Varactor diodes, optical diodes. Chapter 4: Bipolar Junction Transistors (BJTs) Bipolar junction transistor (BJT) structure, basic BJT operation, BJT characteristics and parameters, the BJT as an amplifier, the BJT as a switch, The DC operating point, voltage-divider bias, other bias methods. Chapter 5: BJT Amplifiers Amplifier operation, linear amplifier, transistor ac models, the commonemitter amplifier, the common-collector amplifier, the common-base amplifier, transistors as a small signal amplifier, gain. Chapter 6: Field-effect transistors (FETs) The JFET, JFET characteristics and parameters, JFET biasing, the MOSFET, MOSFET characteristics and parameters, MOSFET biasing. Chapter 7: FET Amplifiers FET amplification, common-source amplifiers, common-drain amplifiers common-gate amplifiers, the class D amplifier, MOSFET analog switching. Chapter 8: Amplifier Frequency Response Effect of coupling capacitors, miller’s theorem, the decibel, low-frequency amplifier response, high-frequency amplifier response, total amplifier frequency response. Chapter 9: Thyristors The four-layer diode, the silicon-controlled rectifier (SCR), SCR applications, the diac and triac, the silicon-controlled switch, the unijunction transistor, the programmable unijunction transistor.

Chapter 10: The Operational Amplifier Introduction to operational amplifiers, op-amp input modes and parameters negative feedback, op-amps with negative feedback, effects of negative feedback on op-amp impedances, bias current and offset voltage, compensation, open-loop response. Chapter 11: Basic Op-Amp Circuits Comparators, summing amplifiers, integrators, differentiators, instrumentation amplifiers, isolation amplifiers, operational transconductance amplifiers, log and antilog amplifiers, converters and other op-amp circuits. Chapter 12: Active Filters Basic filter responses, filter response characteristics, active low-pass filters, active high-pass, filters active, band-pass filters, active band-stop filters, filter response measurements. Chapter 13: Oscillator The oscillator, feedback oscillator, positive feedback, conditions of oscillation, the Wien-Bridge oscillator, relaxation oscillators, noise, thermal noise, shot noise, flicker noise, burst noise, avalanche noise Chapter 14: Voltage Regulators: Voltage regulation, basic linear series regulator, basic linear shunt regulators, basic switching regulator, integrated circuit voltage regulators integrated circuit voltage regulator. Textbook: Thomas L. Floyd, Electronic Devices: Electron Flow Version, 9th edition Pearson Education Inc., Upper Saddle River, New Jersey, 2012. References: 1- R. Boylestad., and L. Nashelsky, Electronic Devices and Circuit Theory. 10th edition, Pearson Education International, 2008. 2- Horowitz and Hill, The Art of Electronics, 2nd edition, Cambridge University Press, 1989. 3- A. Malvino, and D. J. Bates, Electronic principle, McGraw Hill, 7th edition, 2005.

Chapter 1: Semiconductor Material Electronics Electronics is the branch of physics that deals with the emission and effects of electrons; and the use of electronic devices, i.e., science of the motion of charges in a gas, vacuum or semiconductor. An electronic building block packaged in a discrete form with two or more connecting leads or metallic pads. Components are connected together to create an electronic circuit with a particular function, e.g.: an amplifier radio receiver or oscillator. Active components are sometimes called devices. Composed of subsystems or electronic circuits, which may include amplifiers signal sources, power supplies etc…, e.g.: Laptop, DVD players, iPod, mobile phones, PDA (Personal Digital Assistant). Atomic structure All matters on earth made of atoms (made up of elements or combination of elements); all atoms consist of electrons, protons, and neutrons except normal hydrogen, which does not have a neutron. An atom is the smallest particle of an element that retains the characteristics of that element. According to Bohr, atoms have a planetary orbits structure that consists of a central nucleus, surround by orbiting electrons (Figure 1). Nucleus contains protons and neutrons, similar to the way planets orbit the sun in our solar system. Each type of atom has a certain number of electrons and protons that distinguishes it from atoms of other elements. Each electron has its own orbit that corresponds to different energy levels. In an atom, orbits are grouped into energy bands known as shells. Each shell has a fixed maximum number of electrons at allowed energy levels. The maximum number of electrons (Ne) that can exist in each shell can be calculated as, Ne = 2n2 Figure (1) where n is the number of the shell. Electrons that are in orbits farther from the nucleus have higher energy and are less tightly bound to the atom than those closer to the nucleus. Electrons with the highest energy exist in the outermost shell of an atom and are relatively loosely bound to the atom. This outermost shell is known as the valence shell and electrons in this shell are called valence 1

Assist. Prof. Dr. Hamad Rahman

electrons. Valence electrons contribute to chemical reactions and bonding within the structure of a material and determine its electrical properties.

Figure 2: Illustration of the Bohr model of the silicon atom.

Maximum number of valence electron is 8. An atom is stable if it has 8 valence electrons. The number of valence electrons determines the ability of material to conduct current. Materials Classification (Insulators, Conductors, and Semiconductor) In terms of their electrical properties, materials can be classified into three groups: conductors, semiconductors, and insulators. Insulators: An insulator is a material that does not conduct electrical current under normal conditions. Valence electrons are tightly bound to the atoms; therefore, there are very few free electrons in an insulator. Energy gap in an insulator is very wide (≥6eV). Valence electron requires a large electric field to gain enough energy to jump into conduction band. Examples of insulators are rubber, plastics, glass, mica, and quartz. Conductors: A conductor is a material that easily conducts electrical current. Most metals are good conductors. The best conductors are (with one valence electron) e.g.: copper (Cu), silver (Ag), gold (Au), and aluminum (Al), which are characterized by atoms with only one valence electron very loosely bound to the atom. In a conductor, the valence band and the conductor band overlaps (≤ 0.01 eV). Only a little energy or voltage is needed for the electron to jump into conduction band. Semiconductors: A semiconductor is a material that is between conductors and insulators in its ability to conduct electrical current. A semiconductor in its pure (intrinsic) state is neither a good conductor nor a good insulator. Single-element semiconductors are silicon (Si), and germanium (Ge), antimony (Sb), arsenic (As), astatine (At), boron (B), polonium (Po), and tellurium (Te), these semiconductor characterized by atoms with four valence electrons. Compound semiconductors such as gallium arsenide, indium phosphide, gallium nitride, silicon carbide, and silicon germanium are also commonly used. Silicon is the most commonly used semiconductor. 2


Silicon is a semiconductor and copper is a conductor. Bohr diagrams of the silicon atom and the copper atom are shown in following Figure 3. A Silicon atom has 4 electrons in its valence ring. This makes it a semiconductor. A Copper atom has only 1 electron in its valence ring. This makes it good conductor.

Figure 3: Diagrams of the silicon and copper atoms. Silicon and Germanium The atomic structures of silicon and germanium are compared in Figure 4, both silicon and germanium have the characteristic four valence electrons. The valence electrons in germanium are in the fourth shell while those in silicon are in the third shell, closer to the nucleus. This means that the germanium valence electrons are at higher energy levels than those in silicon and, therefore, require a smaller amount of additional energy to escape from the atom. This property makes germanium more unstable at high temperatures and results in excessive reverse current. This is why silicon is a more widely used semiconductive material. Figure 4 Energy Gap Energy in an electron is of two types – kinetic (energy of motion) and potential (energy of position). Each material has its own set of permissible energy levels for the electrons in its atomic structure. Energy level in an atom is measured in electron volt (eV) = 1.602× 10-19 J Electrons that orbits within an energy level will have similar amount of energy. When an electron acquires sufficient additional energy, it can leave the valence shell and become a free electron and exists in the condition band. The energy difference between the valence band and conduction band is called the energy gap. Energy gap: the amount of energy that 3


a valence electron must have to jump into the conduction band. Figure 5 shows energy diagrams for insulators, semiconductors, and conductors. The gap for insulators can be crossed only when breakdown conditions occur. In semiconductors, the band gap is smaller, allowing an electron in the valence band to jump into the conduction band if it absorbs a photon. The band gap depends on the semiconductor material. In conductors, the conduction band and valence band overlap, so there is no gap. This means that electrons in the valence band move freely into the conduction band, so there are always electrons available as free electrons.

Figure 5: Energy diagrams for insulators, semiconductors, and conductors. Covalent Bonds Figure 6 shows how each silicon atom positions itself with four adjacent silicon atoms to form a silicon crystal. A silicon (Si) atom with its four valence electrons shares an electron with each of its four neighbors. This creates eight shared valence electrons for each atom and produces a state of chemical stability. Also, this sharing of valence electrons produces the covalent bonds that hold the atoms together. Covalent bonding in an intrinsic silicon crystal is shown in Figure 6c. An intrinsic crystal is one that has no impurities. Covalent bonding for germanium is similar because it also has four valence electrons.

(c) Figure 6: Illustration of covalent bonds in silicon.

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Conduction Electrons and Holes When an intrinsic silicon crystal gains sufficient heat (thermal energy), some valence electrons could break their covalent bonds to jump the gap into conduction band, becoming free electrons. Free electrons are also called conduction electrons, (negative charge). This is illustrated in Figure 7. The vacancy in the valence band is called a hole (positive charge). For every electron raised to the conduction band there is 1 hole in the valence band creating–electron-hole pair. There is an equal number of holes in the valence band created when these electrons jump into the conduction band, this is illustrated in Figure 8. When a conduction-band electron loses energy and falls back into a hole, this is called recombination.

Figure 7: Creation of electron-hole pairs in a silicon crystal.

Figure 8: Free electrons are being generated continuously while some recombine with holes.

Electron and Hole Current In conduction band, when a voltage is applied across a piece of intrinsic silicon, as shown in Figure 9, the thermally generated free electrons in the conduction band, are now easily attracted toward the positive end. This movement of free electrons is one type of current in a semiconductive material and is called electron current.

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Figure 8

In valance band, in valance band holes generated due to free electrons. Electrons in the valance band are although still attached with atom and not free to move, however they can move into nearby hole with a little change in energy, thus leaving another hole where it came from. Effectively the hole has moved from one place to another in the crystal structure, as illustrated in Figure 9. Although current in the valence band is produced by valence electrons, it is called hole current to distinguish it from electron current in the conduction band.

Figure 9

Doping Since semiconductors are generally poor conductors, their conductivity can be increased by the controlled addition of impurities to the intrinsic (pure) semiconductive material. This process, called doping, increases the number of current carriers (electrons or holes). Two types of semiconductor material that are subjected to doping process, which are N-type and P-type. Two types of elements used doping: Trivalent element – with 3 valence electrons and Pentavalent element – with 5 valence electrons. N-type semiconductors In order for our silicon crystal to conduct electricity, we need to introduce an impurity atom such as Arsenic (As), phosphorus (P), bismuth (Bi), or Antimony (Sb) into the crystalline structure making it extrinsic (impurities are added). These atoms have five outer electrons 6


in their outermost covalent bond to share with other atoms and are commonly called "Pentavalent" impurities. This allows four of the five electrons to bond with its neighbouring silicon atoms leaving one "free electron" to move about when an electrical voltage is applied (electron flow). As each impurity atom "donates" one electron, pentavalent atoms are generally known as "donors". In n-type material electrons are majority carrier, and holes the minority carrier.

Figure 10: An antimony (Sb) impurity atom is shown in the center. The extra electron from the Sb atom becomes a free electron. P-type semiconductors Trivalent (with 3 valence electrons) impurity atoms are added – Aluminum (Al), boron (B), indium (In), gallium (Ga), trivalent also known as a acceptor atom since they accept electrons. When a trivalent atom is added to an intrinsic, it will readily accept free electron, as a result –becomes p-type extrinsic semiconductor. Each trivalent atom forms covalent bond with 4 adjacent Si atom. Since 4 electrons are needed to form a covalent bond causes an existence of hole in the covalent bonding. It also causes a lack of valence electrons in the B atoms. In p-type material holes are majority carrier, and electron the minority carrier

Figure 11: Trivalent impurity atom in a silicon crystal structure. A boron (B) impurity atom is shown in the center. 7


The PN Junction The PN Junction is formed when p‐type region is joined with the n‐type region. This is a basic structure forms a semiconductor diode. The n‐type region has many free electrons (majority carriers) and only a few thermally generated holes. The p‐type region has many holes (majority carriers) and only a few thermally generated free electrons (minority carriers). The free electrons in the n region are randomly drifting in all directions. The basic silicon structure at the instant of junction formation showing only the majority and minority carriers. Free electrons in the n region near the pn junction begin to diffuse across the junction and fall into holes near the junction in the p region, as shown in Figure 12(a).

(a)

(b)

Figure 12:

When the pn junction is formed, the n region loses free electrons as they diffuse across the junction. This creates a layer of positive charges (pentavalent ions) near the junction. As the electrons move across the junction, the p region loses holes as the electrons and holes combine. This creates a layer of negative charges (trivalent ions) near the junction. These two layers of positive and negative charges form the depletion region, as shown in Figure 12(b). The term depletion refers to the fact that the region near the pn junction is depleted of charge carriers (electrons and holes) due to diffusion across the junction. Keep in mind that the depletion region is very thin compared to the n region and p region. The potential difference of the electric field across the depletion region is the amount of voltage required to move electrons through the electric field. This potential difference is called the barrier potential and is expressed in volts. Stated another way, a certain amount of voltage equal to the barrier potential and with the proper polarity must be applied across a pn junction before electrons will begin to flow across the junction. The potential barrier is approximately 0.7V for a silicon PN junction and 0.3V for germanium PN junction. The distance from one side of the barrier to the other side is called the width of the barrier, which depends on the nature of the material. 8


Energy Diagrams of the PN Junction An energy diagram for a pn junction at the instant of formation is shown in Figure 13(a). As you can see, the valence and conduction bands in the n region are at lower energy levels than those in the p region. The trivalent impurities (in p-type) exert lower forces on the outer-shell electrons than the pentavalent impurities (in n-type). The lower forces in ptype materials mean that the electron orbits are slightly larger and hence have greater energy than the electron orbits in the n-type materials. As the diffusion continues, the depletion region begins to form and the energy level of the n-region conduction band decreases. The decrease in the energy level of the conduction band in the n region is due to the loss of the higher-energy electrons that have diffused across the junction to the p region. Shortly, there are no electrons left in the n-region conduction band with enough energy to get across the junction to the p-region conduction band, as in Figure 13(b). At this point, the junction is at equilibrium; and the depletion region is complete because diffusion has stopped. There is an energy gradient across the depletion region that acts as an “energy hill” that an n-region electron must climb to get to the p region.

Figure 13: Energy diagrams illustrating the formation of the pn junction and depletion region.

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Chapter 2: Diode and Application Diode A diode is a semiconductor device, made from a small piece of semiconductor material, such as silicon, in which half is doped as a p region and half is doped as an n region with a pn junction and depletion region in between. The p region is called the anode and n region is called the cathode. It conducts current in one direction and offers high resistance in other direction. The basic diode structure and symbol are shown in Fig.1.

Figure 1. Forward Bias Bias is the application of a dc voltage to a diode to make it either conduct or block current. Forward bias is the condition that allows current through the pn junction. This external bias voltage is designated as VBIAS. The resistor limits the forward current to a value that will not damage the diode. In the forward bias, the negative side of VBIAS is connected to the n region of the diode and the positive side is connected to the p region. The bias voltage VBIAS, must be greater than the barrier potential; bias must be greater than 0.3V for germanium or 0.7V for silicon diodes.

Figure 2: A diode connected for forward bias. Negative side of bias voltage ‘pushes’ free electrons towards pn junction. The negative side of the source also provides a continuous flow of electrons through the external connection (conductor) and into the n region as shown in Figure 3. The bias-voltage source imparts sufficient energy to the free electrons for them to overcome the barrier potential of the depletion region and move on through into the p region. Since unlike charges attract, the positive side of the bias-voltage source attracts the valence electrons 10

toward the left end of the p region. The holes in the p region provide the medium for these valence electrons to move through the p region. The holes, (majority in p region), move to the right toward the junction. As the electrons flow out of the p region through the external connection (conductor), these electrons become conduction electrons in the metal conductor. As more electrons move into the depletion region, the number of positive ions is reduced. As more holes flow into the depletion region on the other side of the pn junction, the number of negative ions is reduced. This reduction in positive and negative ions causes the depletion region to narrow.

Figure 3: A forward-biased diode showing the flow of majority carriers and the voltage due to the barrier potential across the depletion region. Reverse Bias Reverse bias is the condition that essentially prevents current through the diode. Figure 4 shows a dc voltage source connected across a diode in the direction to produce reverse bias. The positive side of VBIAS is connected to the n region of the diode and the negative side is connected to the p region. Also, note that the depletion region is shown much wider than in forward bias or equilibrium. The positive side of the bias-voltage source pulls the free electrons, (majority in n region), away from the pn junction. As electrons move away from junction, more positive ions are created. This results in a widening of the depletion region and a depletion of majority carriers.

Figure 4 In p region, electrons from negative side of battery enter as valence electrons. It moves from hole to hole toward the depletion region, creating more negative ions. This can be viewed as holes being pulled towards the negative side. The electric field increases in strength until the potential across depletion region equals the bias voltage. At this point, very small reverse current exist that can usually be neglected. 11

Reverse Breakdown Normally, the reverse current is so small that it can be neglected. If the external reversebias voltage is increased to a value called the breakdown voltage, the reverse current will drastically increase. The high reverse-bias voltage imparts energy to the free minority electrons so that as they speed through the p region, they collide with atoms with enough energy to knock valence electrons out of orbit and into the conduction band. The newly created conduction electrons have high energy, and repeat the process, they quickly multiply. They have high energy to move though pn junction, and not combine with holes. The multiplication of conduction electrons just discussed is known as the avalanche effect. Voltage-Current (V-I) Characteristic of A Diode V-I Characteristic for Forward Bias The current in forward biased called forward current and is designated If. At 0V (Vbias) across the diode, there is no forward current. Figure 5 illustrates what happens as the forward-bias voltage is increased positively from 0 V. The resistor is used to limit the forward current to a value that will not overheat the diode and cause damage. With gradual increase of Vbias, the forward voltage and forward current increases. A portion of forward-bias voltage (Vf) drops across the limiting resistor. Continuing increase of Vf causes rapid increase of forward current but the voltage across the diode increases only gradually above 0.7V. The resistance of the forward-biased diode is not constant but it changes over the entire curve. Therefore, it is called dynamic resistance.

Figure 5: Relationship of voltage and current in a forward-biased diode. V-I Characteristic for Reverse Bias With 0V reverse voltage there is no reverse current. There is only a small current through the junction as the reverse voltage increases. At a point, reverse current shoots up with the breakdown of diode. The voltage called breakdown voltage. This is not 12


normal mode of operation. After this point the reverse voltage remains at approximately VBR but IR increase very rapidly. Break down voltage depends on doping level, set by manufacturer. Combine the curves for both forward bias and reverse bias, and you have the complete V-I characteristic curve for a diode, as shown in Figure 6.

Figure 6

Diode models The Ideal Diode Mode When the diode is forward-biased, it ideally acts like a closed (on) switch, as shown in Figure 7. When the diode is reverse-biased, it ideally acts like an open (off) switch, as shown in part (b). The barrier potential, the forward dynamic resistance, and the reverse current are all neglected. In Figure 7c, the ideal V-I characteristic curve graphically depicts the ideal diode operation.

Figure 7

The Practical Diode Model The practical model includes the barrier potential. The characteristic curve for the practical diode model is shown in Figure 8c. Since the barrier potential is included and the dynamic resistance is neglected, the diode is assumed to have a voltage across it when forward-biased, as indicated by the curve to the right of the origin. The practical model is useful in lower-voltage circuits and in designing basic diode circuits. The forward current is determined using first Kirchhoff’s voltage law to Figure 8a: 13


VBIAS − VF − VRLIMIT = 0 VRLIMIT = 𝐼𝐹 𝑅𝐿𝐼𝑀𝐼𝑇 Substituting and solving for IF VBIAS − VF 𝐼F = 𝑅𝐿𝐼𝑀𝐼𝑇 The diode is assumed to have zero reverse current, VF=0.7V , VR=VBIAS , IR= 0A

Figure 8

The Complete Diode Model The complete model of a diode includes the barrier potential, the small forward dynamic resistance (𝑟́𝑑 ) and the large internal reverse resistance (𝑟́𝑅 ). The reverse resistance is taken into account because it provides a path for the reverse current, which is included in this diode model.

Figure 9

Example 1: (a) Determine the forward voltage and forward current for the diode in Figure 10(a) for each of ideal and practical diode models. Also, find the voltage across the limiting resistor in each case. (b) Determine the reverse voltage and reverse current for the diode in Figure 10(b) for each of the diode models. Also, find the voltage across the limiting resistor in each case. Assume IR = 1μA. (H.W.) 14


Figure 10

Solution:

The DC power supply A power supply is an essential part of each electronic system from the simplest to the most complex. A basic block diagram of the complete power supply is shown in Figure 11. The transformer changes ac voltages based on the turns ratio between the primary and secondary. The rectifier converts the ac input voltage to dc voltage. The filter eliminates the fluctuations in the rectified voltage and produces a relatively smooth dc voltage. The regulator is a circuit that maintains a constant dc voltage for variations in the input line voltage or in the load.

Figure 11

Half-Wave Rectifiers Because of their ability to conduct current in one direction and block current in the other direction, diodes are used in circuits called rectifiers that convert ac voltage into dc voltage. Rectifiers are found in all dc power supplies that operate from an ac voltage source. When connected with ac voltage, diode only allows half cycle passing through it 15


and hence convert ac into dc. As the half of the wave get rectified, the process called half-wave rectification. The output frequency is the same as the input.

Figure 12

The average value (VAVG) of half-wave rectified voltage if its peak amplitude is 50 V is VAVG = VP/π=50/3.14=15.9V

,

VAVG is approximately 31.8% of Vp

PIV= Vp(in) PIV: Peak inverse voltage=is the maximum voltage occurs at the peak of each half-cycle of the input voltage when the diode is reverse-biased. The diode must be capable of withstanding this amount voltage.

Figure 13

Full wave rectifiers Although half-wave rectifiers have some applications, the full-wave rectifier is the most commonly used type in dc power supplies. A full-wave rectifier allows unidirectional (one-way) current through the load during the entire of the input cycle, whereas a halfwave rectifier allows current through the load only during one-half of the cycle. The output voltage have twice the input frequency. VAVG = 2VP/π=

VAVG is approximately 63. 7% of Vp

Figure 14

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Center-Tapped Full-Wave Rectifier Operation A center-tapped rectifier is used two diodes that connected to the secondary of a centertapped transformer, as shown in Figure 14.

Figure 15

Figure 16: Basic operation of a center-tapped full-wave rectifier. The Bridge Full-wave rectifiers The Bridge Full-Wave rectifier uses four diodes connected across the entire secondary as shown in Figure 16.

Figure 17: Operation of a Bridge rectifier

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Diode Limiters Diode circuits, called limiters or clippers, are used to clip off portions of signal voltages above or below certain levels. Point A is limited to +0.7V when the input voltage exceeds this value (Figure 18(a)). If the diode is turned around, as in Figure 18(b), the negative part of the input voltage is clipped off. When the diode is forward-biased during the negative part of the input voltage, point A is held at -0.7V by the diode drop.

Figure 18: Examples of diode limiters (clippers). The desired amount of limitation can be attained by a power supply or voltage divider. The amount clipped can be adjusted with different levels of VBIAS. The peak output voltage across RL is determine by the following equation: 𝑉𝑜𝑢𝑡 = (

𝑅𝐿 )𝑉 𝑅1 + 𝑅𝐿 𝑖𝑛

Example 2: What would you expect to see displayed on an oscilloscope connected across RL in the limiter shown in following Figure.

Solution: The diode is forward-biased and conducts when the input voltage goes below -0.7V. So, for the negative limiter, determine the peak output voltage across RL by: 𝑉𝑜𝑢𝑡 = (

𝑅𝐿 100kΩ ) 𝑉𝑖𝑛 = ( ) 10V = 9.09V 𝑅1 + 𝑅𝐿 110kΩ 18


The scope will display an output waveform as shown in following Figure

Diode Clampers Another type of diode circuit, called a clamper, is used to add or restore a dc level to an electrical signal. The capacitor charges to the peak of the supply minus the diode drop. Once charged the capacitor acts like a battery in series with the input voltage. The AC voltage will “ride” along with the DC voltage. The polarity arrangement of the diode determines whether the DC voltage is negative or positive.

Figure 19: Positive clamper operation. Voltage multiplier Voltage multipliers use clamping action to increase peak rectified voltages without the necessity of increasing the transformer’s voltage rating. Multiplication factors of two, three, and four are common. Voltage multipliers are used in high-voltage, low-current applications such as cathode-ray tubes (CRTs) and particle accelerators. In the Figure 20 a half-wave voltage doubler, a voltage doubler is a voltage multiplier with a multiplication factor of two. Once C1 and C2 charges to the peak voltage they act like two batteries in series, effectively doubling the voltage output. The current capacity for voltage multipliers is low.

Figure 20: Half-wave voltage doubler operation. 19


The full-wave voltage doubler arrangement of diodes and capacitors takes advantage of both positive and negative peaks to charge the capacitors giving it more current capacity. Voltage triplers and quadruplers utilize three and four diode-capacitor arrangements, respectively.

Figure 21: Full-wave voltage doubler operation.

Typical diode packages with terminal identification. The letter K is used for cathode to avoid confusion with certain electrical quantities that are represented by C. Case type numbers are indicated for each diode.

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Chapter 3: Special-Purpose Diodes The Zener Diode A major application for zener diodes is as a type of voltage regulator for providing stable reference voltages for use in power supplies, voltmeters, and other instruments. The symbol for a zener diode is shown in Figure 1. A zener diode is a silicon pn junction device that is designed for operation in the reverse-breakdown region. When a diode reaches reverse breakdown, its voltage remains almost constant even though the current changes drastically, and this is key to the zener diode operation. Cathode (K)

Anode (A)

Figure 1: Zener diode symbol.

Figure 2: General zener diode V-I characteristic.

Zener diodes with breakdown voltages of less than approximately 5V operate in zener breakdown. Those with breakdown voltages greater than approximately 5V operate mostly in avalanche breakdown. Both types, however, are called zener diodes. Zeners are available with breakdown voltages from less than 1V to more than 250V. As the reverse voltage (VR) increases, the reverse current (IR) remains extremely small up to the knee of the curve. Reverse current is also called zener current (Iz). At knee point the breakdown effect begins, the internal zener resistance (ZZ) begins to decrease. The reverse current increase rapidly. The zener breakdown (VZ) voltage remains nearly constant. Figure 3: Reverse characteristic of a zener diode. VZ is usually specified at a value of the zener current known as the test current. The zener impedance, ZZ, is the ratio of a change in voltage in the breakdown region to the corresponding change in current: Δ𝑉𝑍 𝑍𝑍 = Δ𝐼𝑍 21


Figure 4 Example 1: What is the zener impedance if the zener diode voltage changes from 4.79 V to 4.94 V when the current changes from 5.00 mA to 10.0 mA? Answer: 30 Zener Diode Applications Zener Regulation with a Variable Input Voltage The zener diode can be used as a type of voltage regulator for providing stable reference voltages as in Figure 5. The ability to keep reverse voltage constant across its terminal is the key feature of the zener diode. It maintains constant voltage over a range of reverse current values. A minimum reverse current IZK must be maintained in order to keep diode in regulation mode. Voltage decreases drastically if the current is reduced below the knee of the curve. Above IZM, max current, the zener may get damaged permanently.

Figure 5: Zener regulation of a varying input voltage. 22


To illustrate regulation, let us use the ideal model of the 1N4740A zener diode (ignoring the zener resistance) in the circuit of Figure 6. • Ideal model of IN4047A • IZK = 0.25mA • VZ = 10V • PD(max) = 1W Figure 6 For the minimum zener current, the voltage across the 220Ω resistor is VR = IZKR = (0.25 mA)(220Ω) = 55mV, Since VIN =VR+VZ, VIN(min) = VR + VZ = 55mV+10V= 10.055V For the maximum zener current, the voltage across the 220Ω resistor is VR = IZMR = (100 mA)(220Ω) = 22V Therefore, VIN(max) = 22V+ 10V = 32V This shows that this zener diode can ideally regulate an input voltage from 10.055 to 32V and maintain an approximate 10V output. Zener Regulation with variable load Figure 7 shows a zener voltage regulator with a variable load resistor across the terminals. The zener diode maintains a nearly constant voltage across RL as long as the zener current is greater than IZK and less than IZM.

Figure 7: Zener regulation with a variable load. When RL=∞ (open cct), load current is zero and all of the current pass through zener diode. When RL is connected, current is divided between zener diode and RL. The total current through R remains constant as long as the zener is regulating. As RL decreases, IL increase and IZ decreases. The zener continues to regulate the voltage until IZ reaches its minimum value. Now, the load current is maximum, and a full-load condition exists. Example: Determine the minimum and the maximum load currents for which the zener diode in Figure 8 will maintain regulation. What is the minimum value of RL that can be used? VZ=12V, IZK=1mA, and IZM =50mA. Assume an ideal zener diode where ZZ=0Ω and VZ remains a constant 12V over the range of current values. 23


Figure 8 Solution When IL=0, (RL=∞), IZ=Izmax=IT IZ(max) = IT =

VIN − VZ 24 − 12 = = 25.5mA R 470

This value is less than 50mA, RL can be removed without disturbing regulation. IL(min) = 0A IL(max) occurs when IZ is minimum (IZ = IZK) IL(max) = IT−Iz(min)= 25.5mA −1mA = 24.5mA Minimum value of RL is 12V = 𝟒𝟗𝟎𝛀 IL(max) 24.5mA Regulation is maintained for any value of RL between 490 Ω and infinity. R L(min) =

VZ

=

Zener Limiter Zener diodes can be used as limiters. Figure 9 shows three basic ways the limiting action of a zener diode can be used. During the negative alternation, the zener acts as a forward-biased diode and limits the negative voltage to-0.7V as in part (A). When the zener is turned around, as in part (b), the negative peak is limited by zener action and the positive voltage is limited to +0.7V. Two back-to-back zeners limit both peaks to the zener voltage ± 0.7V as shown in part (c).

Figure 9: Basic zener limiting action with a sinusoidal input voltage. 24


Varactor Diode Varactor diode is a special purpose diode operated in reverse-bias to form a voltagecontrolled capacitor rather than traditional diodes. The applied voltage controls the capacitance and hence the resonant frequency. The width of the depletion region increases with reverse-bias. These devices are commonly used in communication systems. Varactor diodes are also referred to as tuning diodes.

Figure 10: The reverse-biased varactor diode acts as a variable capacitor. Optical Diodes In this section, three types of optoelectronic devices are introduced: the light-emitting diode, quantum dots, and the photodiode. The Light-Emitting Diode (LED) Light Emitting Diodes (LEDs), diodes can be made to emit light electroluminescence or sense light. When the device is forward-biased, electrons cross the pn junction from the n-type material and recombine with holes in the p-type material. The free electrons are in the conduction band and at a higher energy than the holes in the valence band. The difference in energy between the electrons and the holes corresponds to the energy of visible light. When recombination takes place, the recombining electrons release energy in the form of photons. The emitted light tends to be monochromatic (one color) that depends on the band gap (and other factors). A large exposed surface area on one layer of the semiconductive material permits the photons to be emitted as visible light. This process, called electroluminescence, is illustrated in Figure 12. LEDs vary widely in size and brightness–from small indicating lights and displays to high-intensity LEDs that are used in traffic signals, outdoor signs, and general illumination.

Figure 11: Symbol for an LED. When forward-biased, it emits light. 25


Figure12: Electroluminescence in a forward-biased LED.

The Photodiode The photodiode is a device that operates in reverse bias, as shown in Figure 13, where is Iλ the reverse light current. The photodiode has a small transparent window that allows light to strike the pn junction. A photodiode differs from a rectifier diode in that when its pn junction is exposed to light, the reverse current increases with the light intensity. When there is no incident light, the reverse current, Iλ, is almost negligible and is called the dark current.

Figure 13:Photodiode. Several types of diodes that you are less likely to encounter as a technician. Among these are the laser diode, the Schottky diode, the pin diode, the step-recovery diode, the tunnel diode, and the current regulator diode. The Laser Diode Laser light is monochromatic, which means that it consists of a single color and not a mixture of colors as compared to incoherent light, which consists of a wide band of wavelengths. The laser diode normally emits coherent light, whereas the LED emits incoherent light. The symbols are the same as shown in Figure 14.

Figure 14: Symbol for a Laser Diode. 26


Chapter 4: Bipolar Junction Transistors (BJTs) Bipolar Junction Transistor (BJT) Structure The BJT is constructed with three doped semiconductor regions separated by two pn junctions, as in Figure 1(a). The three regions are called emitter, base, and collector. Physical representations of the two types of BJTs are shown in Figure 1(b) and (c). One type consists of two n regions separated by a p region (npn), and the other type consists of two p regions separated by an n region (pnp). The term bipolar refers to the use of both holes and electrons as current carriers in the transistor structure. This mode of operation is contrasted with unipolar transistors, such as field-effect transistors, in which only one carrier type is employed (electron or hole, ex: diode).

Figure1: Basic BJT construction. The pn junction joining the base region and the emitter region is called the base-emitter junction. The pn junction joining the base region and the collector region is called the base-collector junction. A wire lead connects to each of the three regions. These leads are labeled E for emitter, B for base and C for collector. The base region is lightly doped and very thin compared to the heavily doped emitter and the moderately doped collector regions. Figure 2 shows the symbols for the npn and pnp bipolar junction transistors.

Figure 2: Standard BJT symbols. BJT Biasing In order for a BJT to operate properly as an amplifier, the two pn junctions must be correctly biased with external dc voltages. Figure 3 shows a bias arrangement for both npn and pnp BJTs for operation as an amplifier. In both cases, the base-emitter (BE) 27


junction is forward-biased and the base-collector (BC) junction is reverse-biased. This condition is called forward-reverse bias. For the npn type shown, the collector is more positive than the base, which is more positive than the emitter. For the pnp type, the voltages are reversed to maintain the forward-reverse bias.

Figure 3: Forward-reverse bias of a BJT. The heavily doped n-type emitter region has a very high density of conduction-band (free) electrons as indicated in Figure 4. These free electrons easily diffuse through the forward biased BE junction into the lightly doped and very thin p-type base region. The base has a low density of holes, which are the majority carriers, as represented by the white circles.

Figure 4: BJT operation showing electron flow.

A very little free electron recombine with holes in base and move as valence electrons through the base region and into the emitter region as hole current. The valence electrons leave the crystalline structure of the base, become free electrons in the metallic 28


base lead, and produce the external base current. Majority of free electrons move toward the reverse-biased BC junction and swept across into the collector region by the attraction of the positive collector supply voltage. The free electrons move through the collector region, into the external circuit, and then return into the emitter region along with the base current. Transistor Currents The conventional current flows in the direction of the arrow on the emitter terminal. The emitter current (IE) is the sum of the collector current (IC) and the small base current (IB). That is, IE = IC + IB IB is very small compared to IE or IC. The capital-letter subscripts indicate dc values. The voltage drop between base and emitter is VBE whereas the voltage drop between collector and base is called VCB.

. Figure 5: Transistor currents. BJT Characteristics and Parameters Two important parameters, βDC (dc current gain) and αDC are used to analyze a BJT circuit. When a transistor is connected to dc bias voltages, as shown in Figure 6 for both npn and pnp types, VBB forward-biases the base-emitter junction, and VCC reverse-biases the base-collector junction.

Figure 6: Transistor dc bias circuits. 29


The collector current is directly proportional to the base current. IC ∝ IB The βDC of a transistor is the ratio of the dc collector current (IC) to the dc base current (IB). IC βDC = IB This equation explains amplification of current. The ratio of the dc collector current (IC) to the dc emitter current (IE) is the (αDC). αDC =

IC IE

αDC is always less than 1 Example: Determine the dc current gain βDC and the emitter current IE for a transistor where IB=50μA and IC= 3.65 mA. Solution 𝐼𝐶 3.65 mA 𝛽𝐷𝐶 = = = 𝟕𝟑 𝐼𝐵 50 μA IE= IC + IB = 3.65 mA + 50μA = 3.70 mA BJT Circuit Analysis Consider the basic transistor bias circuit configuration in Figure 7. Three transistor dc currents and three dc voltages can be identified. IB: dc base current IE: dc emitter current IC: dc collector current VBE: dc voltage across base-emitter junction VCE: dc voltage across collector-emitter junction VCB: dc voltage across collector-base junction

Figure 7: Transistor currents and voltages. 30


When the base-emitter junction is forward-biased, it is like a forward-biased diode and has a forward voltage drop of 𝐕𝐁𝐄 ≅ 𝟎. 𝟕 𝐕 The voltage at the collector with respect to the grounded emitter is VCE=VCC – ICRC (ICRC=VRC ) The current across IB is VBB – VBE IB = (IB R B = 𝑉𝑅𝐵 ) RB The voltage across the reverse-biased collector-base junction is VCB=VCE – VBE Example: Determine IB, IC, IE, VBE, VCE, and VCB in the circuit of following Figure. The transistor has a βDC = 150.

Solution: 𝑉𝐵𝐸 ≅ 0.7 𝑉, Calculate the base, collector, and emitter currents as follows:

Since the collector is at a higher voltage than the base, the CB junction is reverse-biased. Collector Characteristic Curves The collector characteristic curves shows three mode of operations of transistor with the variation of collector current IC varies with the VCE for a specified value of base current IB. Assume that VBB is set to produce a certain value of IB and VCC is zero and VCE is zero. As VCE is increased, IC increases until B. When both BE and BC junctions are forward biased and the transistor is in saturation region. In saturation, an increase of base current has no effect on the collector current and the relation IC=βDCIB is no longer valid. 31


IC(SAT) =

VCC – VCE(SAT) RC

Figure 8: Collector characteristic curves. At this point, the transistor current is maximum and voltage across collector is minimum, for a given load.

Figure 9: Base-emitter and base-collector junctions are forward-biased. When VCE is increased furthers and exceeds 0.7V, the base-collector junction becomes reverse-biased and the transistor goes into the active, or linear, region of its operation. IC levels off and remains essentially constant for a given value of I B as VCE continues to increase. The value of IC is determined only by the relationship expressed as IC=βDCIB. A family of collector characteristic curves is produced when I C versus VCE is plotted for several values of IB, as illustrated in Figure 8(b). It can be read from the curves. The value of βDC is nearly the same wherever it is read in active region. In a BJT, cutoff is the condition in which there is no base current (IB=0), which results in only an extremely small leakage current (ICEO) in the collector circuit. The subscript CEO represents collector to-emitter with the base open. For practical work, this current is assumed to be zero. In cutoff, neither the BE junction, nor the BC junction are forward-biased. 32


Figure 10: Cutoff: Base-emitter and base-collector junctions are reverse-biased. Example: Determine whether or not the transistor in following figure is in saturation. Assume VCE(sat)= 0.2V.

Solution:

This shows that with the specified βDC, this base current is capable of producing an IC greater than IC(sat). Therefore, the transistor is saturated. The BJT as a Switch A BJT can be used as a switching device in logic circuits to turn on or off current to a load. As a switch, the transistor is normally in either cutoff (load is OFF) or saturation (load is ON).

Figure 11: Switching action of an ideal transistor. 33


DC Load Line Figure 12 shows a dc load line the cutoff point and the saturation point. The bottom of the load line is at ideal cutoff where IC=0 and VCE=VCC. The top of the load line is at saturation where IC=IC(sat) and VCE=VCE(sat). In between cutoff and saturation along the load line is the active region of the transistor’s operation

Figure 12. The BJT as an Amplifier Amplification is the process of increasing the power, voltage, or current by electronic means and is one of the major properties of a transistor. As you learned, a BJT exhibits current gain (called β). When a BJT is biased in the active (or linear) region, the BE junction has a low resistance due to forward bias and the BC junction has a high resistance due to reverse bias. The DC Operating Point Bias establishes the operating point (Q-point) of a transistor amplifier; the ac signal moves above and below this point. If an amplifier is not biased with correct dc voltages on the input and output, it can go into saturation or cutoff when an input signal is applied. Improper biasing can cause distortion in the output signal.

Figure 13: Examples of linear and nonlinear operation of an inverting amplifier. 34


The point at which the load line intersects a characteristic curve represents the Q-point for that particular value of IB. The region along the load line including all points between saturation and cutoff is known as the linear region of the transistor’s operation; the transistor is operated in this region.

Figure 14: Variations in IC and VCE as a result of a variation in base current. Point A, Q, B represents the Q-point for IB 400μA, 300μA and 200 μA, respectively. Assume sinusoidal voltage, Vin, is superimposed on VBB varying between 100μA to 300μA. It makes the collector current varies between 10 mA and 30 mA. As a result of the variation in IC, the VCE varies between 2.2V and 3.4V. Under certain input signal conditions the location of the Q-point on the load line can cause one peak of the Vce waveform to be limited or clipped, as shown Figure 15. For example, the bias has established a low Q- point. As a result, the signal is will be clipped because it is too close to cutoff.

Figure 15: Graphical load line illustration of a transistor being driven into cutoff. Voltage-Divider Bias A practical way to establish a Q-point is to form a voltage-divider from VCC. This is the most widely used biasing method. A dc bias voltage at the base of the transistor can be 35


developed by a resistive voltage divider that consists of R1 and R2, as in Figure 16. R1 and R2 are selected to establish VB. If the divider is stiff, IB is small compared to I2.

Figure 16: Voltage-divider bias. To analyze a voltage-divider circuit in which IB is small compared to I2, first calculate the voltage on the base: R2 VB ≅ ( )V R1 + 𝑅2 CC Once you know the base voltage, you can find the voltages and currents in the circuit, as follows: VE= VB-VBE And VE IC ≅ I E = RE Then VC=VCC- ICRC Once you know VC and VE, you can determine VCE. VCE= VC-VE A practical biasing technique that utilize single biasing sources instead of separate V CC and VBB. A dc bias voltage at the base of the transistor can be developed by a resistive voltage divider that consists of R1 and R2. H.W: Determine VCE and IC in the stiff voltage-divider biased transistor circuit of the following figure if βDC=100. Answer: IC=5.16mA, VCE=1.95V

36


Chapter 5: BJT Amplifiers Amplifier Operation DC Quantities use upper case roman subscripts. Example: VCE (The second letter in the subscript indicates the reference point). AC Quantities and time varying signals use lower case subscripts. Example: Vce. Instantaneous quantities are represented by both lowercase letters and subscripts such as ic, ie, ib, and vce. Internal transistor resistances are indicated as lower case quantities with a prime and an appropriate subscript. An example is the internal ac emitter resistance, 𝑟́𝑒 . External resistances are indicated as capital R with either a capital or lower case subscript depending on if it is a dc or ac resistance. Examples: RC and Rc. The Figure 1 shows an example of a specific waveform for the collector emitter voltage.

Figure 1 Linear Amplifier A linear amplifier provides amplification of a signal without any distortion so that the output signal is an exact amplified replica of the input signal. A voltage-divider biased transistor with a sinusoidal ac source capacitively coupled to the base through C1 and a load capacitively coupled to the collector through C2 is shown in Figure 2.

Figure 2 37


For the amplifier shown, notice that the voltage waveform is inverted between the input and output but has the same shape. Transistor Ac Models To visualize the operation of a transistor in an amplifier circuit, it is often useful to represent the device by a model circuit. A transistor model circuit uses various internal transistor parameters to represent its operation. Transistor models are described in this section based on resistance or r parameters. Another system of parameters, called h parameters. The five r parameters commonly used for BJTs are given in the following Table 1. The lowercase letter r with a prime denotes resistances internal to the transistor. r parameter αac βac 𝑟́𝑒 𝑟́𝑏 𝑟́𝑐

Description ac alpha (Ic/Ie) ac beta (Ic/Ib) ac emitter resistance ac base resistance ac collector resistance

The interpretation of this model circuit in terms of a transistor’s ac operation is as follows: A resistance (𝑟́𝑒 ) appears between the emitter and base terminals. This is the resistance “seen” looking into the emitter of a forward-biased transistor. The collector effectively acts as a dependent current source of αacIe or, equivalently, βacIb, represented by the diamond-shaped symbol, these factors are shown in Figure 3.

Figure 3: Relation of transistor symbol to r-parameter model. It is also temperature dependent and is based on an ambient temperature of 20°C. 𝑟́𝑒 ≅

24𝑚𝑉 𝐼𝐸

H.W: Determine the 𝑟́𝑒 of a transistor that is operating with a dc emitter current of 2mA. H.W:What is IE if 𝑟́𝑒 = 8Ω? 38


The Common-Emitter Amplifier Three amplifier configurations are the common-emitter, the common-base, and the common-collector. In the common-emitter (CE) amplifier, the input signal is applied to the base and the inverted output is taken from the collector. The emitter is common to ac signals. Figure 4 shows a common-emitter amplifier with voltage-divider bias and coupling capacitors C1 and C3 on the input and output and a bypass capacitor, C2, from emitter to ground. The input signal, Vin, is capacitively coupled to the base terminal, the output signal, Vout, is capacitively coupled from the collector to the load. A CE amplifier has high voltage, current, and power gains, but a relatively low input resistance.

Figure 4: A common-emitter amplifier. The Common-Collector Amplifier The common-collector (CC) amplifier is known as an emitter-follower (EF). In the common-collector (CC) amplifier, the input signal is applied to the base and the output is taken from the emitter. The collector is common to ac signals. A common-collector amplifier has high input resistance and high current gain, but its voltage gain is approximately 1.

Figure 5: A common-collector amplifier. 39


The Common-Base Amplifier The common-base (CB) amplifier provides high voltage gain with a maximum current gain of 1. Since it has a low input resistance, the CB amplifier is the most appropriate type for certain applications where sources tend to have very low-resistance outputs.

Figure 6: Common-base amplifier with voltage-divider bias. Capacitors in Amplifier Coupling capacitors are used to transmit an ac signal from one node to another. Coupling capacitors provide dc isolation between two nodes. Bypass capacitor is used to short circuit ac signals to ground (while not affecting the dc operation of the circuit). The value of the bypass capacitor must be large enough so that its reactance over the frequency range of the amplifier is very small (ideally) compared to R E. The capacitive reactance, XC, of the bypass capacitor should be at least 10 times smaller than RE at the minimum frequency for which the amplifier must operate (10XC ≤ RE).

Figure 7 Transistors as a Small Signal Amplifier There are 2 analysis; DC Analysis and AC Analysis. The purpose of DC analysis is to determine the initial operating values of IC, IB and VCE (Q-point). The goal is to set the Q-point such that it does not go into saturation or cutoff when an ac signal is applied. If 40


the Q-point is in active region, the transistor can operate as an amplifier. The purpose of AC analysis is to obtain the gain. An amplifier is a system that has a gaining ability to amplify where a small electrical signal will be converted into a strong one. Amplifiers are classified as small signal amplifiers (preamplifiers) and strong signal amplifiers (power amplifiers). Amplifiers are able to amplify current, voltage and/or power. In other words, only amplifiers are able to produce power gain where as other devices such as transformer are only able to produce voltage and current gain. Small signal amplification causes small current changes and small output voltage change surrounding operation point (Q-point from DC analysis). These small changes are small enough for us to disregard any influence it may have on the transistor’s parameter values such as α and β. There are 4 basic categories of small signal amplifiers: – Voltage amplifier. – Current Amplifier – Trans-conductance Amplifier (converts voltage to current) – Trans-resistance Amplifier (converts current to voltage) Gain The gain of an amplifier is the ratio of an output parameter to an input parameter. An amplifier with a current gain of 100–during normal use, the output current is a hundred times greater that the input current. There are three types of gain: Current gain

Ai =

Voltage gain

Av =

Power gain

Ap =

io ii vo vi Po Pi

= Av Ai

41


Chapter 6: Field-Effect Transistors (FETs) The Field-Effect Transistor The field-effect transistor (FET) is a semiconductor device, which depends for its operation on the control of current by an electric field. Today FETs are the most widely used components in integrated circuits. There are two of field effect transistors: 1. JFET (Junction Field-Effect Transistor). 2. MOSFET (Metal Oxide Semiconductor Field Effect Transistor). The FET has several advantages over conventional transistor. 1. In a conventional transistor, the operation depends upon the flow of majority and minority carriers. That is why it is called bipolar transistor. In FET the operation depends upon the flow of majority carriers only. It is called unipolar device. 2. The input to conventional transistor amplifier involves a forward biased PN junction with its inherently low dynamic impedance. The input to FET involves a reverse biased PN junction hence the high input impedance of the order of M ohm. 3. It is less noisy than a bipolar transistor. 4. It exhibits no offset voltage at zero drain current. 5. It has thermal stability. 6. It is relatively immune to radiation. The main disadvantage is its relatively small gain bandwidth product in comparison with conventional transistor. Junction Field-Effect Transistor The JFET is a type of FET that operates with a reverse-biased pn junction to control current in a channel. Depending on their structure, JFETs fall into either of two categories, n channel or p channel.

Figure 1: A representation of the basic structure of the two types of JFET. Figure 1(a) shows the basic structure of an n-channel JFET. Wire leads are connected to each end of the n-channel; the drain is at the upper end (analogous to the collector of 42


a BJT), and the source is at the lower end. Two p-type regions are diffused in the n-type material to form a channel, and both p-type regions are connected to the gate (analogous to the base of a BJT) lead. For simplicity, the gate lead is shown connected to only one of the p regions. Operation of JFET To illustrate the operation of a JFET, Figure 2 shows dc bias voltages applied to an nchannel device, when the drain is positive with respect to the source and there is no gatesource voltage, there is current in the channel. When a negative gate voltage is applied to the FET, the electric field causes the channel to narrow, which in turn causes current to decrease.

Figure 2: A biased n-channel JFET. The symbol for an n-channel JFET is shown, along with the proper polarities of the applied dc voltages. For an n-channel device, the gate is always operated with a negative (or zero) voltage with respect to the source.

Figure 3: JFET schematic symbols. JFET characteristics and parameters There are three regions in the characteristic curve for a JFET as illustrated for the case when VGS=0V. Between A and B is the Ohmic region, where current and voltage are related by Ohm’s law. From B to C is the active (constant-current) region where current is essentially independent of VDS. Beyond C is the breakdown region. Operation here can damage the FET. 43


Figure 4: The drain characteristic curve of a JFET for VGS=0. When VGS is set to different values, the relationship between VDS and ID develops a family of characteristic curves for the device. An n-channel characteristic is illustrated Figure 5. Notice that Vp is positive and has the same magnitude as VGS(off).

Figure 5: Family of drain characteristic curves. JFET Universal Transfer Characteristic A plot of VGS to ID is called the transfer or transconductance curve. The transfer curve is a is a plot of the output current (ID) to the input voltage (VGS).

Figure 6: JFET universal transfer characteristic curve (n-channel). 44


The transfer curve is based on the equation ID = IDSS (1 −

VGS

2

) VGS(off) By substitution, you can find other points on the curve for plotting the universal curve.

Figure 7: gm varies depending on the bias point (VGS). The transconductance (transfer conductance), gm, is the ratio of a change in output current (ΔID) to a change in the input voltage (ΔVGS). This definition is ∆𝐼𝐷 gm = ∆𝑉𝐺𝑆 The following approximate formula is useful for calculating gm if you know gm0. VGS g m = g m 0 (1 − ) VGS(off) The value of gm0 can be found from 2IDSS g m0 = |VGS(off) | Because the slope changes at every point along the curve, the transconductance is not constant, but depends on where it is measured. The input resistance of a JFET is given by: VGS R IN = | | IGSS where IGSS is the current into the reverse biased gate. JFETs have very high input resistance, but it drops when the temperature increases. Example: A certain JFET has an IGSS of -2nA for VGS=-20V. Determine the input resistance. Solution: R IN = |

VGS IGSS

|=

20V 2nA

= 10GΩ 45


JFET Biasing Just as with the BJT, the purpose of biasing is to select the proper dc gate-to-source voltage to establish a desired value of drain current and, thus, a proper Q-point. Three types of bias are self-bias, voltage-divider bias, and current-source bias. Self-bias Self-bias is simple and effective, so it is the most common biasing method for JFETs. The JFET must be operated such that the gate-source junction is always reverse-biased. This condition requires a negative VGS for an n-channel JFET and a positive VGS for a pchannel JFET. This can be achieved using the self-bias arrangements shown in Figure 8. The gate resistor (RG) does not affect the bias because it has essentially no voltage drop across it; and therefore the gate remains at 0V. R G is necessary only to force the gate to be at 0V and to isolate an ac signal from ground in amplifier applications.

Figure 8: Self-biased JFETs (IS= ID in all FETs). For the n-channel JFET in Figure 8(a), IS produces a voltage drop across RS and makes the source positive with respect to ground. Since I S=ID and VG=0, then VS=IDRS. The gate-to-source voltage is VGS=VG-VS = 0 - IDRS= - IDRS Thus, VGS = -IDRS For the p-channel JFET shown in Figure 8(b), the current through RS produces a negative voltage at the source, making the gate positive with respect to the source. Therefore, since IS =ID, VGS = +IDRS Keep in mind that analysis of the p-channel JFET is the same except for oppositepolarity voltages. The drain voltage with respect to ground is determined as follows: VD = VDD - IDRD Since VS=IDRS, the drain-to-source voltage is VDS =VD-VS =VDD - ID(RD+RS) 46


Example: For the JFET in the following Figure, the drain current (ID) is approximately 5 mA. Determine VDS and VGS. Solution: VS=IDRS= (5mA)(220Ω)=1.1V VD = VDD-IDRD=15V-(5mA)(1.0kΩ) =15V - 5V=10V Therefore, VDS= VD - VS = 10 V - 1.1 V = 8.9 V Since VG=0 V, VGS = VG - VS = 0 V - 1.1 V = -1.1 V Voltage-Divider Bias Voltage-divider biasing is a combination of a voltage-divider and a source resistor to keep the source more positive than the gate. VG is set by the voltage-divider and is independent of VS. VS must be larger than VG in order to maintain the gate at a negative voltage with respect to the source. Voltage-divider bias helps stabilize the bias for variations between transistors.

Figure 9: An n-channel JFET with voltage-divider bias (IS=ID). Current-Source Bias An even more stable form of bias is current-source bias. The current-source can be either a BJT or another FET. With current-source biasing, the drain current is essentially independent of VGS.

Figure 10: Current-source bias. 47


In this circuit, Q2 serves as a current source for Q1. An advantage to this particular circuit is that the output can be adjusted (using RS2) for 0 V DC. Example: A current-source bias circuit has the following values: VDD= 9V, VEE=-6V, and RG=10MΩ. To produce a 10 mA drain current and a 5V drain voltage, determine the values of RE and RD. Solution: VEE 6V RE = = = 600Ω ID 10mA VDD − VD 9V − 5V RD = = = 400Ω ID 10mA JFET Ohmic Region As described before, the ohmic region is between the origin and the active region. A JFET operated in this region can act as a variable resistor. Data from an actual FET is shown. The slopes (which represent conductance) of successive VGS lines are different in the ohmic region. JFETs are often biased in the ohmic region for use as a voltage controlled variable resistor. The control voltage is VGS, and it determines the resistance by varying the Q-point.

Figure 11: The ohmic region is the shaded area. THE MOSFET The MOSFET (metal oxide semiconductor field-effect transistor) is another category of field-effect transistor. The n-channel MOSFET (Figure 12) has only a single p region (called the substrate), one side of which acts as a conducting channel. A metallic gate is separated from the conducting channel by an insulating metal oxide (usually SiO2). The p-channel MOSFET, formed by interchanging p and n semiconductor materials, is described by complementary voltages and currents. The MOSFET, different from the JFET, has no pn junction structure. The two basic types of MOSFETs are enhancement and depletion. Because of the insulated gate, MOSFETs are sometimes called IGFETs. 48


Enhancement MOSFET (E-MOSFET) The E-MOSFET operates only in the enhancement mode and has no depletion mode. It differs in construction from the D-MOSFET, in that it has no structural channel, and the substrate extends completely to the SiO2 layer as shown in Figure 12(a). For an nchannel device, A channel is induced by applying a VGS greater than the threshold value, VGS(th), by creating a thin layer of negative charges in the substrate region adjacent to the SiO2 layer, as shown in Figure 12(b). The positive gate voltage attracts electron from the substrate to the region along the insulating layer. If the gate is made sufficiently positive, enough electrons will be pulled up from the substrate, an n-channel starts to form. The channel does not form uniformly but rather begins to form on the drain side. As the gate voltage increases, the channel length also increases. Finally, the gate voltage increases to the point (VGS(th)) where the channel reaches the source, and conduction begins. The conductivity of the channel is enhanced by increasing the VGS

Figure 12: The basic E-MOSFET construction and operation (n-channel). E-MOSFET Transfer Characteristic The transfer curve for a MOSFET is has the same parabolic shape as the JFET but the position is shifted along the x-axis. The transfer curve for p-channel and n-channel EMOSFET is entirely in the first quadrant as shown. The curve is on the enhancement region, ID = 0A when VGS = 0V and ID = 0A until VGS reaches the threshold value.

Figure 13: E-MOSFET general transfer characteristic curves. 49


The curve starts at VGS(th), which is a nonzero voltage that is required to have channel conduction. The equation for the drain current is ID= K(VGS-VGS(th))2

where K is constant is given by:

𝐊=

𝐈𝐃(𝐨𝐧) (𝐕𝐆𝐒 −𝐕𝐆𝐒(𝐭𝐡) )𝟐

Depletion MOSFET (D-MOSFET) The D-MOSFET has a channel that can is controlled by the gate voltage. For an nchannel type, a negative voltage depletes the channel; and a positive voltage enhances the channel. The D-MOSFET can be operated in either of two modes—the depletion mode or the enhancement mode, depending on the gate voltage, and is sometimes called a depletion/enhancement MOSFET. The n-channel MOSFET operates in the depletion mode when a negative gate-to-source voltage (VGS) is applied and in the enhancement mode when a positive gate-to-source voltage (VGS) is applied. D-MOSFET are generally operated in the depletion mode.

Figure 14: The basic structure of D-MOSFETs. Depletion Mode: with a negative VGS, the electric field produces in the channel drives electrons away from a portion of the channel near the SiO2 layer. This portion is depleted of carriers and the channel width is effectively narrowed. The channel conductivity is decreased. Further increasing the negative voltage at the gate pushes even more electrons away, narrowing the channel and decreasing the current (Figure 15)

Figure 15: Operation of n-channel D-MOSFET. 50


Enhancement Mode: VGS can be made positive without any concern for the consequences of forward biasing a junction. With a positive VGG, more conduction electrons are attracted into the channel. The channel conductivity is enhanced (increased), as shown in Figure 15 (b). D-MOSFET Transfer Characteristic Recall that the D-MOSFET can be operated in either mode. This is indicated on the general transfer characteristic curves in Figure 16 for both n-channel and p-channel MOSFETs. For the region VGS < 0V operation is in depletion mode, in the region VGS > 0V operation in enhancement mode. As with the JFET, The point on the curves where VGS=0 corresponds to IDSS. The equation for drain current is ID = IDSS (1 −

VGS VGS(off)

2

)

Figure 16: D-MOSFET general transfer characteristic curves. MOSFET Symbols The symbols for the n-channel and p-channel MOSFETs are shown in Figure 17. Notice the broken line representing the E-MOSFET that has an induced channel. An inwardpointing substrate arrow is for n-channel, and an outward-pointing arrow is for pchannel.

Figure 17: (a) E-MOSFET schematic symbols 51

(b) D-MOSFET schematic symbols. Assist. Prof. Dr. Hamad Rahman

MOSFET Biasing E-MOSFETs can be biased using bias methods like the BJT methods studied earlier. Voltage-divider bias and drain-feedback bias are illustrated for n-channel devices.

Biasing Figure 18: Common E-MOSFET biasing arrangements. The simplest way to bias a D-MOSFET is with zero bias. This works because the device can operate in either depletion or enhancement mode, so the gate can go above or below 0 V.

Figure 19: A zero-biased D-MOSFET. The drain-to-source voltage is expressed as follows: VDS = VDD - IDSSRD The purpose of RG is to accommodate an ac signal input by isolating it from ground, as shown in Figure 19(b). Since there is no dc gate current, RG does not affect the zero gate-to-source bias. Example: The datasheet for a 2N7002 E-MOSFET gives ID(on)=500 mA (minimum) at VGS=10 V and VGS(th)=1 V. Determine the drain current for VGS = 5V. Solution: First, solve for K 52


K=

ID(on) 500mA = = 6.17mA/V 2 2 2 (VGS − VGS(th) ) (10V − 1V)

Next, using the value of K, calculate ID for VGS=5 V. ID= K(VGS-VGS(th))2=(6.17mA/V2)(5V-1V)2=98.7mA Example: For a certain D-MOSFET, IDSS=10 mA and VGS(off) = -8V. (a) Is this an n-channel or a p-channel? (b) Calculate ID at VGS = -3 V. (c) Calculate ID at VGS =+3 V. Solution: (a) The device has a negative VGS(off); therefore, it is an n-channel MOSFET. (b) ID = IDSS (1 −

2

VGS VGS(off)

(c) ID = 10 mA (1 −

−3V 2

) = 10 mA (1 − −8V) = 𝟑. 𝟗𝟏𝐦𝐀

+3V 2 −8V

) = 𝟏𝟖. 𝟗𝐦𝐀

JFET vs MOSFET 1. The gate and channel in a JFET are separated by a pn junction 2. The channel width is controlled by the size of the depletion region of a pn junction

1. The gate of a MOSFET is insulated from the channel by a SiO2 layer 2. The channel width is controlled by the action of the electric field 3. Operates in depletion and enhancement modes

3. Operates in depletion mode

53


Chapter 7: FET Amplifiers Switching and Circuits The Common-Source Amplifier In a common-source (CS) amplifier, the input signal is applied to the gate and the output signal is taken from the drain. The amplifier has higher input resistance and lower gain than the equivalent CE amplifier.

Figure 1: JFET common-source amplifier. The ac voltage gain of this circuit is Vout=Vin, where Vin=Vgs and Vout=Vds. The voltage gain expression is, therefore, Vds Av = Vgs From the equivalent circuit, Vds=IdRd and from the definition of transconductance, gm=Id/Vgs, Substituting the two preceding expressions into the equation for voltage gain yields Av=gm Rd You can estimate what the transfer characteristic looks like from values on the specification sheet, but keep in mind that large variations are common with JFETs.

Figure 2

54


To analyze the CS amplifier, you need to start with dc values. It is useful to estimate ID based on typical values; specific circuits will vary from this estimate. The gain is reduced when a load is connected to the amplifier because the total ac drain resistance (Rd) is reduced Example: Determine the drain current for a typical 2N5458 JFET amplifier which shown in the following Figure. VDD +12 V RD 2.7 kW Vout

C1 0.1 mF Vin 100 mV

RG 10 MW

RS 470 W

C2 10 mF

Solution: From the specification sheet, the typical IDSS = 6.0 mA and VGS(off) = -4 V. These values can be plotted along with the load line to obtain a graphical solution. A graphical solution is illustrated. On the transconductance curve, plot the load line for the source resistor. Then read the current and voltage at the Q-point. ID = 2.8 mA and VGS = -1.3 V Alternatively, you can obtain ID using Equation 2

ID R S ID = IDSS (1 − ) VGS(off)

Example: Assume IDSS is 6.0 mA, VGS(off) is -4 V, and VGS = -1.3 V as found previously. What is the expected gain? Solution:

Av = gmRD = (2.02 mS)(2.7 kΩ) = 5.45 55


Example: How does the addition of the 10kΩ load affect the gain? Solution:

VDD +12 V RD 2.7 kW Vout

C1 0.1 mF Vin 100 mV

Av = gmRd = (2.02 mS)(2.13 kΩ) = 4.29

RG 10 MW

RS 470 W

C2 10 mF

RL 10 kW

D-MOSFET Amplifier Operation In operation, the D-MOSFET has the unique property in that it can be operated with zero bias, allowing the signal to swing above and below ground. This means that it can operate in either D-mode or E-mode. +VDD RD C2

Vout

C1 RL Vin

RG

Figure 3: (a) Zero-biased D-MOSFET common-source amplifier.

(b) Depletion-enhancement operation D-MOSFET shown on transfer characteristic curve.

E-MOSFET Amplifier Operation The E-MOSFET is a normally off device. The n-channel device is biased on by making the gate positive with respect to the source. A voltage-divider biased E-MOSFET amplifier is shown in Figure 4.

Figure 4: (a) Common-source E-MOSFET amplifier with voltage-divider bias.

(b) E-MOSFET (n-channel) operation shown on transfer characteristic curve.

56


The Common-Drain (CD) Amplifier In a CD amplifier, the input signal is applied to the gate and the output signal is taken from the source. There is no drain resistor, because it is common to the input and output signals.

Figure 5: JFET common-drain amplifier (source-follower). The voltage gain is given by the equation gmRS Av = 1 + gmRS The voltage gain is always slightly < 1. If gmRs>>1, then a good approximation is 𝐴𝑣 ≅ 1. Common-Gate Amplifier Operation A self-biased common-gate amplifier is shown in Figure 6. The gate is connected directly to ground. The input signal is applied at the source terminal through C1. The output is coupled through C2 from the drain terminal.

Figure 6: JFET common-gate amplifier. The Class-D Amplifier MOSFETs are useful as class-D amplifiers, which are very efficient because they operate as switching amplifiers. They use pulse- width modulation (PWM), a process in which the input signal is converted to a series of pulses. The pulse width varies proportionally to the amplitude of the input signal. 57


The modulated signal is amplified by class-B complementary MOSFET transistors. The output is filtered by a low-pass filter to recover the original signal and remove the higher modulation frequency. PWM is also useful in control applications such as motor controllers. MOSFETs are widely used in these applications because of fast switching time and low on-state resistance. +VDD

Q1 Modulated input

Low-pass filter RL Q2

–VDD

Figure 7: Complementary MOSFETs operating as switches to amplify power. MOSFET Switching Operation MOSFETs are also used as analog switches to connect or disconnect an analog signal. Analog switches are available in IC form. The configuration shown allows signals to be passed in either direction. Advantages of MOSFETs are that they have relatively low onstate resistance and they can be used at high frequencies, such as found in video applications. A basic n-channel MOSFET analog switch is shown in Figure 8. The signal at the drain is connected to the source when the MOSFET is turned on by a positive VGS and is disconnected when VGS is 0, as indicated.

Figure 9: Operation of an n-channel MOSFET analog switch.

Basic class D audio amplifier 58


Chapter 8: Amplifier Frequency Response Effect of Coupling Capacitors Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier

Figure 1: Examples of capacitively coupled BJT and FET amplifiers. For the circuit shown in Figure 1(a), the equivalent circuit for C1 is a high-pass filter, C3 and (RC + RL) form another high-pass filter. With FETs, the input coupling capacitor is usually smaller because of the high input resistance. The output capacitor may be smaller or larger depending on the drain and load resistor size. For the circuit shown in Figure 1(b), the equivalent low-pass filter for the input is simply C1 in series with RG because the gate input resistance is so high. Effect of Bypass Capacitors A bypass capacitor causes reduced gain at low-frequencies and has a high-pass filter response. The resistors “seen” by the bypass capacitor include RE, ré , and the bias resistors. For example, when the frequency is sufficiently high XC ≅ 0Ω and the voltage gain of the CE amplifier is Av = R c /ré . At lower frequencies, XC ≫ 0Ω and the voltage gain Av = R c /(ré + Ze ).

Figure 2: Nonzero reactance of the bypass capacitor in parallel with RE creates an emitter impedance (Ze), which reduces the voltage gain. 59


Internal Capacitances The high-frequency response of an amplifier is determined by internal junction capacitances. These capacitances form low-pass filters with the external resistors. Sometimes a designer will add an external parallel capacitor to deliberately reduce the high frequency response.

Figure 3: Internal transistor capacitances. Miller’s Theorem Miller’s theorem states that, for inverting amplifiers, the capacitance between the input and output is equivalent to separate input and output capacitances to ground.

Figure 4: General case of Miller input and output capacitances, C represents Cbc or Cgd. Av is the absolute value of the gain. For the input capacitance, the gain has a large effect on the equivalent capacitance, which is an important consideration when using inverting amplifiers. Notice that the effect of Miller’s theorem is an equivalent capacitance to ground, which shunts high frequencies to ground and reduces the gain as frequency is increased.

Figure 5: Amplifier ac equivalent circuits showing internal and effective Miller capacitances.

60


Example: What is the input capacitance for a 2N3904 inverting amplifier with a gain of 25? Assume the values of Cbc= 4pF and Cbe= 6pF. Solution: Cin = Cbc(Av + 1) + Cbe Cin = 4 pF(25 + 1) + 6 pF=110 pF The Decibel The decibel is a logarithmic ratio of two power levels and is used in electronics work in gain or attenuation measurements. Decibels can be expressed as a voltage ratio when the voltages are measured in the same impedance. To express power gain in decibels, the formula is Ap(dB)=10 log Ap Sometimes, 0 dB is assigned as a convenient reference level for comparison. Then, other power or voltage levels are shown with respect to 0 dB. Low-Frequency Response In capacitively coupled amplifiers, the coupling and bypass capacitors affect the low frequency cutoff. These capacitors form a high-pass filter with circuit resistances. A typical BJT amplifier has three high-pass filters. For example, the input coupling capacitor forms a high-pass filter with the input resistance of the amplifier:

Figure 6: A capacitively coupled BJT amplifier. The input RC circuit for the BJT amplifier in Figure 6 is formed by C 1 and the amplifier’s input resistance and is shown in Figure 7. The total input resistance is expressed by the following formula: 𝐑 𝐢𝐧(𝐭𝐨𝐭) = 𝐑 𝟏 ‖𝐑 𝟐 ‖ 𝐑 𝐢𝐧(𝐛𝐚𝐬𝐞)

61


Figure 7: Input RC circuit formed by the input coupling capacitor and the amplifier’s input resistance. The output RC circuit is composed of the series combination of the collector and load resistors with the output capacitor. The cutoff frequency due to the output circuit is 𝑓c =

1 2π(R C + 𝑅𝐿 )C3

Example: For the circuit in the following Figure, calculate the lower critical frequency due to the input RC circuit. Assumed ré = 9.6Ω and β=200. Notice that a swamping resistor, RE1, is used.

Solution: The input resistance is R in = R1 ‖R 2 ‖(β(ŕ e + R E1 )) = 68Ω‖22Ω‖(200(9.6Ω + 33Ω)) = 5.63kΩ The lower critical frequency is 1 1 𝑓cl(input) = = = 282Hz 2πR in C1 2π(5.63kΩ)(0.1μF) The Bode plot The Bode plot is a plot of decibel voltage gain verses frequency. The frequency axis is logarithmic; the decibel gain is plotted on a linear scale. The -3dB point is the critical frequency.

62


Figure 8: Bode plot. (Blue is ideal; red is actual.) The Bypass RC Circuit The bypass RC circuit response can be found by observing the charge/discharge paths. For this circuit, there is one path through RE2. A second path goes through RE1, 𝑟́𝑒 , and the parallel combination of bias and source resistances (source resistance not shown). The lower critical frequency for this equivalent bypass RC circuit is 𝑓cl(bypass) =

1 2π(𝑅𝑖𝑛(𝑒𝑚𝑖𝑡𝑡𝑒𝑟) ∥ 𝑅𝐸2 )C2

Rth is an equivalent resistance, the resistance in the emitter Rin(emitter) bypass circuit is 𝑅𝑡ℎ R in(emitter) = ŕ e + R E1 + 𝛽𝑎𝑐 Example: For the circuit in the following Figure, calculate the lower critical frequency due to the bypass RC circuit. Assume 𝑟́𝑒 = 9.6Ω and β=200.

Solution: The resistance in the emitter bypass circuit is R in(emitter) = ŕ e + R E1 +

R th 68kΩ ∥ 22kΩ ∥ 600Ω = 9.6Ω + 33Ω + = 45.5Ω βac 200

The lower critical frequency is 63


𝑓cl(bypass) =

1 2π(R in(emitter) ∥ R E2 )C2

=

1 = 𝟑𝟔𝐇𝐳 2π(45.5Ω ∥ 1.5kΩ)(100μF)

The Input RC Circuit The input RC circuit for a FET is a basic high-pass filter consisting of the bias resistor (or resistors) and the input coupling capacitor. The FET gate circuit has such high resistance, it can be ignored.

Figure 9: Input RC circuit. High-Frequency Response The high frequency response of inverting amplifiers is primarily determined by the transistor’s internal capacitance and the Miller effect. The equivalent high-frequency ac circuit is shown for a voltage-divider biased CE amplifier with a fully bypassed emitter resistor.

Figure 10: High-frequency equivalent circuit after applying Miller’s theorem. If there is an unbypassed emitter resistor, such as R E1 it is shown in the emitter circuit and acts to increase ŕ e and thus reduce fc. At high frequencies, the input circuit is as shown in Figure 11(a), where βacŕ e is the input resistance at the base of the transistor because the bypass capacitor effectively shorts the emitter to ground. By combining Cbe and Cin(Miller) in parallel and repositioning, you get the simplified circuit shown in Figure 11(b). Next, by thevenizing the circuit to the left of the capacitor, as indicated, the input RC circuit is reduced to the equivalent form shown in Figure 11(c). 64


Figure 11: Development of the equivalent high-frequency input RC circuit. If there is an unbypassed emitter resistor (RE1 in this case), the thevenin resistance is modified to R th = R s ‖R1 ‖R 2 ‖β𝑎𝑐 (ŕ e + R E1 ). The high frequency analysis of FETs is similar to that of BJTs. Like the CE amplifier, the CS amplifier inverts the signal, so the Miller effect must be taken into account. You may see special circuits such as cascode connections in very high frequency applications to minimize the Miller effect. A high frequency ac model of a CS amplifier shown in figure 12.

Figure12; High-frequency equivalent circuit after applying Miller’s theorem. Cgs simply appears as a capacitance to ac ground in parallel with Cin(Miller), as shown in Figure 12. Looking in at the drain, Cgd effectively appears in the Miller output capacitance from drain to ground in parallel with Rd, Cout(Miller) = Cgd

(Av + 1) Av

The Miller input capacitance is given in as follows: 65

Cin(Miller)=Cgd(Av + 1) Assist. Prof. Dr. Hamad Rahman

Example: What is the upper cutoff frequency due to the input circuit? Assume RS=600Ω, ŕ e =3.5Ω, β=200, Cbe=6 pF, Cbc=3.5 pF, and Av= 9.7.

Solution: R th = R s ‖R1 ‖R 2 ‖β(ŕ e + R E1 ) = 600Ω‖10kΩ‖4.7Ω‖200(3.5Ω + 100Ω) = 493Ω Cin(tot) = Cbe +CMiller= Cbe +Cbc(Av(mid) + 1) = 6pF +3.5 pF(9.7 + 1)=43pF 1 1 𝑓c = = = 7.4MHz 2πRC 2π(493Ω)(43pF) Total Amplifier Frequency Response The overall frequency response is the combination of three lower critical frequencies due to coupling and bypass capacitors and two upper critical frequencies due to internal capacitances. Figure 13 shows a generalized ideal response curve (Bode plot) for the BJT amplifier. The three break points at the lower critical frequencies ( fcl1, fcl2, and fcl3) are produced by the three low-frequency RC circuits formed by the coupling and bypass capacitors. The break points at the upper critical frequencies, fcu1 and fcu2, are produced by the two high-frequency RC circuits formed by the transistor’s internal capacitances..

Figure 13: A BJT amplifier and its generalized ideal response curve (Bode plot). 66


For multistage amplifiers, the individual stages have an effect on the overall response. In general, with different cutoff frequencies, the dominant lower cutoff frequency is equal to the highest fcl; the dominant upper critical frequency is equal to lowest fcu. When the critical frequencies for multistage amplifiers are equal, the lower critical frequency is higher than any one as given by

and the upper critical frequency is given by

67


Chapter 9: Thyristors Thyristors Thyristors are a class of semiconductor devices characterized by 4-layers of alternating p- and n-material. Four-layer devices act as either open or closed switches; for this reason, they are most frequently used in control applications such as lamp dimmers, motor speed controls, ignition systems, charging circuits, etc. Thyristors include Shockley diode, silicon-controlled rectifier (SCR), diac and triac. They stay on once they are triggered, and will go off only if current is too low or when triggered off. Some thyristors and their symbols are in figure 1.

(a) 4-layer diode

(b) SCR

(c) Diac

(d) Triac

(e) SCS

Figure 1 Shockley Diode The 4-layer diode (or Shockley diode) is a type of thyristor that acts something like an ordinary diode but conducts in the forward direction only after a certain anode to cathode voltage called the forward-breakover voltage is reached. The basic construction of a 4-layer diode and its schematic symbol are shown in Figure 2.

Figure 2: The 4-layer diode. The 4-layer diode has two leads, labeled the anode (A) and the cathode (K). The symbol reminds you that it acts like a diode. It does not conduct when it is reverse-biased. The concept of 4-layer devices is usually shown as an equivalent circuit of a pnp and an npn transistor. Ideally, these devices would not conduct, but when forward biased, if there is sufficient leakage current in the upper pnp device, it can act as base current to the lower npn device causing it to conduct and bringing both transistors into saturation 68


Figure 3: A 4-layer diode equivalent circuit. Shockley Diode Characteristic Curve The characteristic curve for a 4-layer diode shows the forward blocking region. When the anode-to-cathode voltage exceeds VBR, conduction occurs. The switching current at this point is IS. Once conduction begins, anode current (IA) increases rapidly and will continue until IA is reduced to less than the holding current (IH). This is the only way to stop conduction.

Figure 4: A 4-layer diode characteristic curve. The Silicon-Controlled Rectifier An SCR (silicon-controlled rectifier) is a 4-layer pnpn device similar to the 4-layer diode except with three terminals: anode, cathode, and gate. The basic structure and schematic symbol of SCR are shown in Figure 5.

Figure 5: The silicon-controlled rectifier (SCR). 69


The SCR has two possible states of operation. In the off state, it has a very high resistance. In the on state, the SCR acts ideally as a short from the anode to the cathode; actually, there is a small on (forward) resistance. The SCR operation can best be understood by thinking of its internal pnpn structure as a two-transistor arrangement, as shown in Figure 6. This structure is like that of the 4layer diode except for the gate connection. The upper pnp layers act as a transistor, Q1, and the lower npn layers act as a transistor, Q2. Again, notice that the two middle layers are shared.

Figure 6: SCR equivalent circuit. Turning the SCR On The SCR had its roots in the 4-layer diode. By adding a gate connection, the SCR could be triggered into conduction. This improvement made a much more useful device than the 4-layer diode. The SCR can be turned on by exceeding the forward breakover voltage (VBR(F)) or by gate current, as shown in Figure 7.. Notice that the gate current controls the amount of forward breakover voltage required for turning it on. VBR(F) decreases as IG is increased above 0 V.

Figure 7: SCR characteristic curves. Turning the SCR Off Like the 4-layer diode, the SCR will conduct as long as forward current exceeds IH. There are two ways to drop the SCR out of conduction: 1) anode current interruption and 2) forced commutation. Anode current can be interrupted by breaking the anode 70


current path (shown here), providing a path around the SCR, or dropping the anode voltage to the point that IA < IH.

Figure 8: SCR turn-off by: (a) anode current interruption, and (b) forced commutation. Force commutation uses an external circuit to momentarily force current in the opposite direction to forward conduction. SCRs are commonly used in ac circuits, which forces the SCR out of conduction when the ac reverses. SCR Characteristics and Ratings Several of the most important SCR characteristics and ratings are defined as follows. • Forward-breakover voltage, VBR(F): voltage at which the SCR enters the forward conduction region. • Holding current, IH: This is the value of anode current below which the SCR switches from the forward-conduction region to the forward-blocking region. • Gate trigger current, IGT: This is the value of gate current necessary to switch the SCR from the forward-blocking region to the forward-conduction region under specified conditions. • Average forward current, IF(avg): This is the maximum continuous anode current (dc) that the device can withstand in the conduction state under specified conditions. • Reverse-breakdown voltage, VBR(R): maximum reverse voltage before SCR breaks into avalanche.

71


Figure 9: SCR characteristic curves For IG = 0. SCR Applications A few of the more common areas of application for SCRs include relay controls, timedelay circuits, regulated power suppliers, static switches, motor controls, choppers, inverters, cycloconverters, battery chargers, protective circuits, heater controls, and phase controls. One of the most common applications is to use it in ac circuits to control a dc motor or appliance because the SCR can both rectify and control. The SCR is triggered on the positive cycle and turns off on the negative cycle. A circuit like this is useful for speed control for fans or power tools and other related applications I A

R1 R2 R4

R3 B

M

Figure 10: SCR motor control. Another application for SCRs is an over-voltage protection circuit, which is called a “crowbar” circuits (which get their name from the idea of putting a crowbar across a voltage source and shorting it out). The purpose of a crowbar circuit is to shut down a power supply in case of over-voltage. Once triggered, the SCR latches on. The SCR can handle a large current, which causes the fuse (or circuit breaker) to open.

72


Figure 11: A basic SCR over-voltage protection circuit (shown in blue). The Diac and Triac Both the diac and the triac are types of thyristors that can conduct current in both directions (bilateral). They are four-layer devices. The diac has two terminals, while the triac has a third terminal (gate). The diac is similar to having two parallel Shockley diodes turned in opposite directions. The triac is similar to having two parallel SCRs turned in opposite directions with a common gate. The Diac The diac is a thyristor that acts like two back-to-back 4-layer diodes. It can conduct current in either direction. Because it is bidirectional, the terminals are equivalent and labeled A1 and A2. The diac conducts current after the breakdown voltage is reached. At that point, the diac goes into avalanche conduction, creating a current pulse sufficient to trigger another thyristor (an SCR or triac). The diac remains in conduction as long as the current is above the holding current, IH.

Figure 12: The diac.

Figure 13: Diac characteristic curve.

The Triac The triac is essentially a bidirectional SCR but the anodes are not interchangeable. Triggering is done by applying a current pulse to the gate; breakover triggering is not normally used. When the voltage on the A1 terminal is positive with respect to A2, a gate 73


current pulse will cause the left SCR to conduct. When the anode voltages are reversed, the gate current pulse will cause the right SCR to conduct.

Figure 14: The triac.

Figure 15: Triac characteristic curve.

Triac Applications Triacs are used for control of ac in applications like electric range heating controls, light dimmers, and small motors. Like the SCR, the triac latches after triggering and turns off when the current is below the IH, which happens at the end of each alteration.

Figure 16: Basic triac phase control. The Silicon-Controlled Switch (SCS) The SCS is similar to an SCR but with two gates. It can be triggered on with a positive pulse on the cathode gate, and can be triggered off with a positive pulse on the anode gate. In the Figure 18, the SCS is controlling a dc source. The load is in the cathode circuit, which has the advantage of one side of the load being on circuit ground.

74


Figure 17: The SCS.

Figure 18: SCS characteristic curve.

The Unijunction Transistor (UJT) UJT has only one pn junction. It has an emitter and two bases, B1 and B2. rB1 and rB2 are internal dynamic resistances. The inter-base resistance, rBB=rB1+rB2. rB1 varies inversely with emitter current, IE.

Figure 19: The unijunction transistor. Figure 20: UJT characteristic curve. The UJT consists of a block of lightly-doped (high resistance) n-material with a pmaterial grown into its side. It is often used as a trigger device for SCRs and triacs. The UJT is a switching device; it is not an amplifier. When the emitter voltage reaches VP (the peak point), the UJT “fires”, going through the unstable negative resistance region to produce a fast current pulse. The equivalent circuit for a UJT shows that looks like a diode connected to a voltage divider. The resistance of the lower divider (ŕ B1 ) is inversely proportional to the emitter current. When the pn junction is first forward-biased, the junction resistance of ŕ B1 suddenly appears to drop, and a rush of current occurs. An important parameter is h, which is the intrinsic standoff ratio. It represents the ratio of ŕ B1 to the interbase resistance ŕ BB with no current.

75


Figure 20: UJT equivalent circuit. The Unijunction Transistor (UJT) Application A circuit using a UJT to fire an SCR is shown. When the UJT fires, a pulse of current is delivered to the gate of the SCR. The setting of R1 determines when the UJT fires. The diode isolates the UJT from the negative part of the ac. The UJT produces a fast, reliable current pulse to the SCR, so that it tends to fire in the same place every cycle.

Figure 21 The Programmable Unijunction Transistor (PUT) The PUT is a 4-layer thyristor with a gate. It is primarily used as a sensitive switching device. The gate pulse can trigger a sharp increase in current at the output. The characteristic of a PUT is similar to a UJT, but the PUT intrinsic standoff ratio can be “programmed” with external resistors and the UJT has a fixed ratio.

76


Figure 22: The programmable unijunction transistor (PUT). The principle application for a PUT is for driving SCRs and triacs, but, like the UJT, can be used in relaxation oscillators. +VCC +20 V

R1 220 kW

R2 20 kW A

G

C

0.01 mF

K

R3 10 kW

R4 27 W

Figure 23: PUT relaxation oscillator. For the circuit to oscillate, R1 must be large enough to limit current to less than the valley current (IV). The period of the oscillations is given by: 1 𝑇 = 𝑅1 𝐶 ln 1−𝜂 Where 𝑅3 𝜂= 𝑅2 + 𝑅3 H.W.: What is intrinsic standoff ratio, and the period of the circuit in the figure 23? Answer: 𝜂 =0.33, T=0.89 ms

77


Chapter 10: The Operational Amplifiers Operational Amplifiers (op-amp) Op-amp is an electronic device that amplify the difference of voltage at its two inputs. It has two input terminals, one of the inputs is called the inverting input (-) and the other is called the non-inverting input. Usually there is a single output. Most op-amps operate with two dc supply voltages, one positive and the other negative, as shown in Figure 1, although some have a single dc supply. Usually these dc voltage terminals are left off the schematic symbol for simplicity but are understood to be there.

Figure 1:Op-amp symbols. The Ideal Op-Amp Ideally, op-amps have characteristics (used in circuit analysis):  Infinite voltage gain.  Infinite input impedance (does not load the driving sources).  Zero output impedance (drive any load).  Infinite bandwidth (flat magnitude response, zero phase shift).  Zero input offset voltage. The ideal op-amp has characteristics that simplify analysis of op-amp circuits. The input voltage, Vin, appears between the two input terminals, and the output voltage is A vVin, as indicated by the internal voltage source symbol. The concept of infinite input impedance is particularly a valuable analysis tool for several op-amp configurations.

Figure 2: Basic op-amp representations. 77


The Practical Op-Amp Practical op-amps have characteristics that often can be treated as ideal for certain situations, but can never actually attain ideal characteristics. In addition to finite gain, bandwidth, and input impedance, they have other limitations.  Finite open loop gain.  Finite input impedance.  Non-zero output impedance.  Input current.  Input offset voltage.  Temperature effects. Characteristics of a practical op-amp are very high voltage gain, very high input impedance, and very low output impedance. Another practical consideration is that there is always noise generated within the op-amp. Noise is an undesired signal that affects the quality of a desired signal. Today, circuit designers are using smaller voltages that require high accuracy, so low-noise components are in greater demand. All circuits generate noise; op-amps are no exception, but the amount can be minimized. Block Diagram Internally, the typical op-amp has a differential input, a voltage amplifier, and a pushpull output. The differential amplifier amplifies the difference in the two inputs.

+ Vin –

Differential amplifier input stage

Voltage amplifier(s) gain stage

Push-pull amplifier output stage

Vout

Figure 3: Basic internal arrangement of an op-amp. Input Signal Modes The input signal can be applied to an op-amp in differential-mode or in common-mode. Differential-mode signals are applied either as single-ended (one side on ground) or double-ended (opposite phases on the inputs).

Figure 4: Single-ended differential mode. 78


Figure 5: Double-ended differential mode. Common-mode signals are applied to both sides with the same phase on both. Vin

–

–

Vout +

Vout Vin

+ Vin

Figure 6: Common-mode operation. Usually, common-mode signals are from unwanted sources, and affect both inputs in the same way. The result is that they are essentially cancelled at the output. Common-Mode Rejection Ratio The ability of an amplifier to amplify differential signals and reject common-mode signals is called the common-mode rejection ratio (CMRR), CMRR is defined as Ao𝑙 CCMR = Acm where Aol is the open-loop differential-gain and Acm is the common-mode gain, Acm is zero in ideal op-amp and much less than 1 is practical op-amps. CMRR=100,000 means that desired signal is amplified 100,000 times more than unwanted noise signal. CMRR can also be expressed in decibels as CCMR = 20 log (

Ao𝑙 ) Acm

Example: What is CMRR in decibels for a typical 741C op-amp? Solution: The typical open-loop differential gain for the 741C is 200,000 and the typical common-mode gain is 6.3. CCMR = 20 log (

Ao𝑙 200 = 90dB ) = 20 log Acm 6.3

(The minimum specified CMRR is 70 dB) 79


Voltage, Current, and Impedance Parameters VO(p-p): The maximum output voltage swing is determined by the op-amp and the power supply voltages. VO(p-p): The maximum output voltage swing is determined by the op-amp and the power supply voltages. IBIAS: The input bias current is the average of the two dc currents required to bias the differential amplifier, I1 + I2 IBIAS = 2 IOS: The input offset current is the difference between the two dc bias currents, IOS = |I1 − I2 | ZIN(d): The differential input impedance is the total resistance between the inputs

ZIN(cm): The common-mode input impedance is the resistance between each input and ground

Zout: The output impedance is the resistance viewed from the output of the circuit – Zout

+

Other Parameters Slew rate: The slew rate is the maximum rate of change of the output voltage in response to a step input voltage ∆Vout Slew Rate = ∆t Example: Determine the slew rate for the output response to a step input.

80


𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

Slew Rate =

∆Vout (+12V) − (−12V) = = 6V/μs ∆t 4μ

Negative feedback Negative feedback is the process of returning a portion of the output signal to the input with a phase angle that opposes the input signal. The advantage of negative feedback is that precise values of amplifier gain can be set. In addition, bandwidth and input and output impedances can be controlled.

Figure 7 Noninverting Amplifier A noninverting amplifier is a configuration in which the signal is on the noninverting input and a portion of the output is returned to the inverting input. Feedback forces Vf to be equal to Vin, hence Vin is across Ri. With basic algebra, you can show that the closedloop gain of the noninverting amplifier is

Acl(NI) = 1 +

Rf Ri

Figure 8: Noninverting amplifier. Example: Determine the gain of the noninverting amplifier shown. Solution: Acl(NI) = 1 +

Rf 82kΩ =1+ = 25.8 Ri 3.3kΩ

81


A special case of the noninverting amplifier is when Rf=0 and Ri=∞. This forms a voltage follower or unity gain buffer with a gain of 1. The input impedance of the voltage follower is very high, producing an excellent circuit for isolating one circuit from another, which avoids "loading" effects. Inverting Amplifier An inverting amplifier is a configuration in which the noninverting input is grounded and the signal is applied through a resistor to the inverting input.

Figure 9: Inverting amplifier. Feedback forces the inputs to be nearly identical; hence, the inverting input is very close to 0 V. The closed-loop gain of the inverting amplifier is: Rf Acl(I) = − Ri Example: Determine the gain of the inverting amplifier if Rf=82kΩ and Ri =3.3kΩ . Solution: R f 82kΩ Acl(I) = − = = −24.8 The minus sign indicates inversion R i 3.3kΩ Impedances of Noninverting amplifier: Zin(NI) = (1 + 𝐴𝑜𝑙 𝐵)𝑍𝑖𝑛 Generally, assumed to be ∞ Zout Zout(NI) = Generally, assumed to be 0 (1 + Aol B) Impedances of Inverting amplifier Zin(I) ≅ 𝑅𝑖 Generally, assumed to be R 𝑖 Zout Zout(I) = Generally, assumed to be 0 (1 + Aol B) Bias Current Compensation For op-amps with a BJT input stage, bias current can create a small output error voltage. To compensate for this, a resistor equal to Ri||Rf is added to one of the inputs. 82


Figure 10: Bias current compensation in the noninverting and inverting amplifier configurations.

Bandwidth Limitations Many op-amps have a roll off rate determined by a single low-pass RC circuit, giving a constant -20 dB/decade down to unity gain. Op-amps with this characteristic are called compensated op-amps. The sold line represents the open-loop frequency characteristic (Bode plot) for the op-amp.

Figure 11: Ideal plot of open-loop voltage gain versus frequency for a typical op-amp. The frequency scale is logarithmic. For op-amps with a -20 dB/decade open-loop gain, the closed-loop critical frequency is given by fc(cl)=fc(ol)(1+BAol(mid)).

Figure 12: Closed-loop gain compared to open-loop gain.

83


The closed-loop critical frequency is higher than the open-loop critical frequency by the factor (1+BAol(mid)). This means that you can achieve a higher BW by accepting less gain. For a compensated op-amp, Acl f(cl)=Aol fc(ol). The equation, Acl f(cl)=Aol fc(ol) shows that the product of the gain and bandwidth are constant. The gain-bandwidth product is also equal to the unity gain frequency. That is fT = Acl fc(cl), where fT is the unity-gain bandwidth. Example: The fT for a 741C op-amp is 1 MHz. What is the BWcl for the amplifier? Vin

+ 741C

Vout

–

Rf 82 kW

Ri 3.3 kW

Ac𝑙(NI) = 1 + BWc𝑙 =

Rf 82kΩ =1+ = 25.8 Ri 3.3kΩ

𝑓T 1MHz = = 38.8 𝑘𝐻𝑧 Ac𝑙 25.8

84


Chapter 11: Basic Op-Amp Circuits Comparators A comparator is a specialized nonlinear op-amp circuit that compares two input voltages and produces an output state that indicates which one is greater. Comparators are designed to be fast and frequently have other capabilities to optimize the comparison function. An example of a comparator application is shown in Figure 1. The circuit detects a power failure in order to take an action to save data. As long as the comparator senses Vin, the output will be a dc level.

Figure 1 Comparator with Hysteresis Sometimes the input signal to a comparator may vary due to noise superimposed on the input. The result can be an unstable output. To avoid this, hysteresis can be used. Hysteresis is incorporated by adding regenerative (positive) feedback, which creates two switching points: the upper trigger point (UTP) and the lower trigger point (LTP). After one trigger point is crossed, it becomes inactive and the other one becomes active.

Figure 2: Device triggers only once when UTP or LTP is reached; A comparator with hysteresis is also called a Schmitt trigger. The trigger points are found by applying the voltage-divider rule: R2 R2 VUTP = (+Vout(max) ) and VLTP = (−Vout(max) ) R1 + R 2 R1 + R 2 Example: What are the trigger points for the circuit if the maximum output is ±13 V? 85


𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

VUTP =

R2 10kΩ (+13V) = 2.28V (+Vout(max) ) = R1 + R 2 47kΩ + 10kΩ

By symmetry, the lower trigger point = -2.28 V. Output Bounding Some applications require a limit to the output of the comparator (such as a digital circuit). The output can be limited by using one or two zener diodes in the feedback circuit. The circuit in Figure 3 is bounded as a positive value equal to the zener breakdown voltage.

Figure 3: Operation of a bounded comparator (Bounded at a positive value). Comparator Applications Simultaneous or flash analog-to-digital converters use 2n-1 comparators to convert an analog input to a digital value for processing. Flash ADCs are a series of comparators, each with a slightly different reference voltage. The priority encoder produces an output equal to the highest value input. In IC flash converters, the priority encoder usually includes a latch that holds the converter data constant for a period after the conversion.

Figure 4: A simplified simultaneous (flash) analog-to-digital converter (ADC) using op-amps as comparators. 86


Summing Amplifier A summing amplifier has two or more inputs; normally all inputs have unity gain, and its output voltage is proportional to the negative of the algebraic sum of its input voltages. A two-input summing amplifier is shown in Figure 5, but any number of inputs can be used.

Figure 5: Two-input inverting summing amplifier. Averaging Amplifier A summing amplifier can be made to produce the mathematical average of the input voltages. This is done by setting the ratio Rf/R equal to the reciprocal of the number of inputs (n). 𝑅𝑓 1 = 𝑅 𝑛 Example: What is VOUT and average of the input voltages if the input voltages are +5.0V, -3.5V and +4.2V and all resistors =10 kW?

Solution: VOUT = -(VIN1 + VIN2 + VIN3) = -(+5.0 V - 3.5 V+ 4.2 V) = -5.7V VIN(avg)=-⅓(VIN1 + VIN2 + VIN3) = -⅓(+5.0 V - 3.5 V + 4.2 V)= -1.9V Scaling Adder A scaling adder has two or more inputs with each input having a different gain. The output represents the negative scaled sum of the inputs. Example: Assume you need to sum the inputs from three microphones. The first two microphones require a gain of -2, but the third microphone requires a gain of 3. What are the values of the input R’s if Rf = 10 kW? 87


Solution: Rf 10kΩ =− = 5kΩ Av1 −2 Rf 10kΩ R3 = − =− = 3.3kΩ Av3 −3 R1 = R 2 = −

Application of Scaling Adder An application of a scaling adder is the D/A converter circuit. The resistors are inversely proportional to the binary column weights. A more common method for D/A conversion is known as the R/2R ladder method. Figure 6 shows a four-digit digital-to-analog converter (DAC) of this type (called a binary-weighted resistor DAC). Because of the precision required of resistors, the method is useful only for small DACs.

Figure 6: A scaling adder as a four-digit digital-to-analog converter (DAC) As mentioned before, the R/2R ladder is more commonly used for D/A conversion than the scaling adder and is shown in Figure 7 for four bits. Assume that the D 3 input is HIGH (5V) and the others are LOW (ground, 0V). The gain for D3 is -1. Each successive input has a gain that is half of previous one. The output represents a weighted sum of all of the inputs (similar to the scaling adder). An advantage of the R/2R ladder is that only two values of resistors are required to implement the circuit. 88


Figure 7: An R/2R ladder DAC. The Integrator The ideal integrator is an inverting amplifier that has a capacitor in the feedback path. The output voltage is proportional to the negative integral (running sum) of the input voltage. Op-amp integrating circuits must have extremely low dc offset and bias currents, because small errors are equivalent to a dc input. The ideal integrator tends to accumulate these errors, which moves the output toward saturation. The practical integrator overcomes these errors– the simplest method is to add a relatively large feedback resistor.

Figure 8: Ideal Integrator

practical integrator

If a constant level is the input, the current is constant. The capacitor charges from a constant current and produces a ramp. The slope of the output is given by the equation: ∆Vout Vin =− ∆t RiC Example: Sketch the output wave, to the input wave, as shown in the following Figure:

89


Solution: ∆Vout Vin 2V =− =− = 2V/ms (10kΩ)(0.1μF) ∆t RiC The output is a triangular wave as shown in the following Figure

The Differentiator The ideal differentiator is an inverting amplifier that has a capacitor in the input path. The output voltage is proportional to the negative rate of change of the input voltage. The small reactance of Cat high frequencies means an ideal differentiator circuit has very high gain for high-frequency noise. To compensate for this, a small series resistor is often added to the input. This practical differentiator has reduced high frequency gain and is less prone to noise.

Figure 9: Ideal differentiator

practical differentiator

Since the current at the inverting input is negligible, IR=IC. Both currents are constant because the slope of the capacitor voltage (VC/t) is constant. The output voltage is also constant and equal to the voltage across Rf because one side of the feedback resistor is always 0 V (virtual ground).The output voltage is given by VC Vout = − ( ) R𝑓 C 𝑡 Example: Sketch the output wave, to the input wave, as shown in the following Figure:

90


Solution: Vout = − (

VC −1V ) R𝑓 C = ( ) (10kΩ)(0.1μF) = 2V t 0.5ms

The output is a square wave as shown in the following Figure

Instrumentation Amplifiers An instrumentation amplifier (IA) amplifies the voltage difference between its terminals. It is optimized for small differential signals that may be riding on a large common mode voltages. The gain is set by a single resistor that is supplied by the user. The output voltage is the closed loop gain set by RG multiplied by the voltage difference in the inputs.

Figure 10: The basic instrumentation amplifier with an external gain-setting resistor RG. The external gain-setting resistor can be calculated for a desired voltage gain by applying the following equation: 2R RG = A𝑐𝑙 − 1 H.W.: Determine the value of the external gain-setting resistor RG for a certain IC instrumentation amplifier with R1=R2= 25kΩ. The closed-loop voltage gain is to be 500. Answer: 100Ω Noise Effects in Instrumentation Amplifier Applications Guarding is available in some IAs to reduce noise effects. By driving the shield with the common-mode signal, effects of stray capacitance are effectively cancelled. Guarding is 91


useful in applications such as transducer interfacing, and microphone preamps where very small signals need to be transmitted.

Figure 11: Degradation of common-mode rejection in a shielded cable connection due to unwanted phase shifts. The AD522 is a low-noise IA that has a Data guard output, which is connected to the shield. The AD522 has a programmed gain from 1 to 1000 depending on R G. The frequency response rolls off at -20 dB/decade. Isolation amplifier An isolation amplifier is designed to provide an electrical barrier between the input and output in order to provide protection in applications where hazardous conditions exist. A typical isolation amplifier uses a high frequency modulated carrier frequency to pass a lower frequency signal through the barrier.

Figure 12: Simplified block diagram of a typical isolation amplifier. The 3656KG is a transformer coupled isolation amplifier that uses pulse width modulation to transmit data across the barrier. The 3656KG can have gain for both the input and output stages. The 3656KG is suited for patient monitoring applications, such as an ECG amplifier. The manufacture’s data sheet shows detailed connection diagrams for various applications. 92


Figure 13: The 3656KG isolation amplifier. The operational transconductance amplifier The operational transconductance amplifier (OTA) is a voltage-to-current amplifier. As in the case of FETs, the conductance is output current divided by input voltage. Thus, Iout gm = Vin Like FETs, the gain of an amplifier is written in terms of gm: Av=gmRL Unlike FETs, the OTA has a gm that can be “programmed” by the amount of bias current. Thus, gain can be changed electronically by varying a dc voltage.

Figure 14: An OTA as an inverting amplifier with a variable-voltage gain. The OTA adds a measure of control to circuits commonly implemented with conventional op-amps. Applications for OTAs include voltage-controlled low-pass or high-pass filters, voltage controlled waveform generators and amplifiers, modulators, comparators, and Schmitt triggers. The Logarithmic Amplifier A diode has the characteristic in which voltage across the diode is proportional to the log of the current in the diode. Compare data for an actual diode on linear and logarithmic plots: 93


Figure 15 When a diode is placed in the feedback path of an inverting op-amp, the output voltage is proportional to the log of the input voltage. The gain decreases with increasing input voltage; therefore, the amplifier is said to compress signals. Many sensors, particularly photo-sensors, have a very large dynamic range outputs. Current from photodiodes can range over 5 decades. A log amp will amplify the small current more than larger current to effectively compress the data for further processing.

Figure 16: A basic log amplifier using a diode as the feedback element. For the circuit shown in Figure 16, the equation for Vout is: Vin Vout ≅ −(0.025V) ln IR is a constant for a given diode. IR R 1 Example: What is Vout? (Assume IR = 50 nA) Vin

+11 V

R1 +

1.0 kW

VF

–

– Op-amp

Vout

+

94


Solution: Vout ≅ −(0.025V) ln

Vin 11𝑉 = −(0.025V) ln = −307mV IR R 1 (50nA)(1kΩ)

Log Amplifier with a BJT When a BJT is used in the feedback path, the output is referred to the ground of the base connection rather than the virtual ground. This eliminates offset and bias current errors. For the BJT, IEBO replaces IR in the equation for Vout: Vin Vout ≅ −(0.025V) ln IEBO R1 Log amplifiers are available in IC form with even better performance than the basic log amps shown in Figure 17. For example, the MAX4206 operates over 5 decades and can measure current from 10 nA to 1 mA.

Figure 17: A basic log amplifier using a transistor as the feedback element. The Antilog Amplifier An antilog amplifier produces an output proportional to the input raised to a power. In effect, it is the reverse of the log amp. The equation for Vout for the basic BJT antilog amp is: Vin Vout = −R𝑓 𝐼𝐸𝐵𝑂 antilog ( ) 25mV IC antilog amps are also available. For example, the Datel LA-8048 is a log amp and the Datel LA-8049 is its counterpart antilog amp. These ICs are specified for a 6 decade range.

Figure 18: A basic antilog amplifier.

95


Example: For the antilog amplifier in the following Figure, find the output voltage. Assume IEBO = 40 nA.

Solution: Vout = −R f IEBO antilog (

Vin ) 25mV

= −(68kΩ)(40nA) antilog (

175.1mV ) = −3V 25mV

Other Op-amp Circuits

Constant-current source

Current-to-voltage converter

Voltage-to-current converter

Peak detector Figure 19

96

Electronic Devices

Chapter 12: Active Filters Basic filter Responses A filter is a circuit that passes certain frequencies and rejects all others. The passband is the range of frequencies allowed through the filter. The critical frequency, fc, (also called the cutoff frequency) defines the end (or ends) of the passband and is normally specified at the point where the response drops -3dB (70.7%) from the passband response. Filters are usually categorized by the manner in which the output voltage varies with the frequency of the input voltage. The categories of active filters are low-pass, highpass, band-pass, and band-stop. In the Figure 1, the passband is a region called the transition region that leads into a region called the stopband. There is no precise point between the transition region and the stopband.

Figure 1: Low-pass

High-pass

Band-pass

Band-stop

Low-Pass Filter Response The low-pass filter allows frequencies below the critical frequency to pass and rejects other. The simplest low-pass filter is a passive RC circuit with the output taken across C. The bandwidth of an ideal low-pass filter is equal to fc BW = fc

Figure 2: (a) Comparison of an ideal low-pass filter response (shading area) with actual response. 97

(b) Basic low-pass circuit Assist. Prof. Dr. Hamad Rahman

Figure 3 illustrates three idealized low-pass response curves including the basic one-pole response.  The ideal response is not attainable by any practical filter.  Actual filter responses depend on the number of poles,  Pole, a term used with filters to describe the number of RC circuits contained in the filter.  This basic RC filter has a single pole, and it rolls off at -20db/decade beyond the critical frequency.  20dB/decade means that at a frequency of 10fc the output will be -20dB (10%) of the input.  This roll-off allows too much unwanted frequencies through the filter.  Actual filters do not have a perfectly flat response up to the cutoff frequency.  More steeper response cannot be obtained by simply cascading the basic stages due to loading effect.  With combination of op-amps, the filters can be designed with higher roll-offs.  In general, the more poles the filter uses, the steeper its transition region will be.  The exact response depends on the type of filter and the number of pole.

Figure 3: Idealized low-pass filter responses Active Filters

Figure 4: One-pole low-pass filter.

The number of filter poles can be increased by cascading.

98


High-Pass Filter Response The high-pass filter passes all frequencies above a critical frequency and rejects all others. The simplest high-pass filter is a passive RC circuit with the output taken across R.

(a) Comparison of an ideal high-pass filter response (shading area) with actual response.

(b) Basic high-pass circuit

Figure 5 The Band-Pass Filter Response A band-pass filter passes all frequencies between two critical frequencies. The simplest band-pass filter is an RLC circuit. The bandwidth (BW) is defined as the difference between the upper critical frequency (fc2) and the lower critical frequency (fc1). BW= fc2 – fc1 The frequency about which the passband is centered is called the center frequency, f0, defined as the geometric mean of the critical frequencies. 𝒇𝟎 = √𝒇𝒄𝟏 𝒇𝒄𝟐

(a) RLC circuit

(b) General band-pass response curve. Figure 6 99


The quality factor (Q) of a band-pass filter is the ratio of the center frequency to the bandwidth 𝒇𝟎 𝑸= 𝐁𝐖 Band-Stop Filter Response A band-stop filter rejects frequencies between two critical frequencies; the bandwidth is measured between the critical frequencies. The simplest band-stop filter is an RLC circuit.

Figure 6: (a) RLC circuit

(b) General band-stop filter response.

Active Filters Active filters include one or more op-amps in the design. One of the three characteristic can be achieved with active filters:  Flat band pass with Butterworth  Sharp roll-off rate with Chebyshev  Linear phase response.

Figure 7: Comparative plots of three types of filter response characteristics.

100


Chapter 13: Oscillators The Oscillator An oscillator is a circuit that produces a periodically oscillating waveform on its output with dc input. The output voltage can be either sinusoidal or nonsinusoidal, depending on the type of oscillator. Two major classifications for oscillators are feedback oscillators and relaxation oscillators. An oscillator converts electrical energy from the dc power supply to periodic waveforms. A basic oscillator is shown in Figure 1.

Figure 1 Feedback Oscillators Feedback oscillator operation is based on the principle of positive feedback. A fraction of output signal is returned to input with no net phase shift resulting in a reinforcement of the output signal. After oscillations are started, the loop gain is maintained at 1.0 to maintain oscillations. A feedback oscillator consists of an amplifier for gain (either a discrete transistor or an op-amp) and a positive feedback circuit that produces phase shift and provides attenuation, as shown in Figure 2.

Figure 2: Basic elements of a feedback oscillator. Positive Feedback Positive feedback is characterized by the condition wherein a portion of the output voltage of an amplifier is fed back to the input with no net phase shift, resulting in a reinforcement of the output signal. The inphase feedback voltage (Vf) is amplified to produce the output voltage, which in turn produces feedback voltage; a loop is created 101


in which the signal sustains itself and a continuous sinusoidal output is produced. This phenomenon is called oscillation. In some types of amplifiers, the feedback circuit shifts the phase 180o and an inverting amplifier is required to provide another 180o phase shift so that there is no net phase shift as shown in Figure 3.

Figure 3: Positive feedback produces oscillation. Conditions of Oscillation Two conditions, illustrated in Figure 4, are required for a sustained state of oscillation: 1. The phase shift around the feedback loop must be 0o. 2. The voltage gain, Acl, around the closed feedback loop (loop gain) must be 1.

Figure 4: General conditions to oscillation. Start-Up Conditions Feedback oscillators require a small disturbance such as that generated by thermal noise to start oscillations. This initial voltage starts the feedback process and oscillations. The feedback circuit permits only a voltage with a frequency equal to selected frequency to appear in phase on the amplifier’s input. The voltage gain conditions for both starting and sustaining oscillation are shown in Figure 5, when oscillation starts at t0, the condition Acl>1 causes the sinusoidal output voltage amplitude to build up to a desired level. Then Acl decreases to 1 and maintains the desired amplitude. 102


Figure 5 The Wien-Bridge Oscillator One type of sinusoidal feedback oscillator is the Wien-bridge oscillator. RC feedback is used in various lower frequency (up to 1 MHz) sine-wave oscillators. The Wien-bridge is the most widely used type of RC feedback oscillator for this range of frequencies.

Figure 6: A lead-lag circuit and its response curve. At resonant frequency (fr) the attenuation (Vout/Vin) of the circuit is 1/3. The lead-lag circuit is used in the feedback of Wien-Bridge oscillator as shown in Figure 6(a). It gives 0o phase shift and 1/3 attenuation at resonant frequency. The basic Wien-bridge uses the lead-lag network to select a specific frequency that is amplified. The voltage-divider sets the gain to make up for the attenuation of the feedback network.

Figure 7 103


The non-inverting amplifier must have a gain of exactly 3.0 as set by R1 and R2 to make up for the attenuation. If it is too little, oscillations will not occur; if it is too much the sine wave will be clipped. Wien-Bridge Oscillation Conditions The phase shift around the positive feedback loop must be 0° and the gain around the loop must equal unity (1). The 0° phase-shift condition is met when the frequency is fr because the phase shift through the lead-lag circuit is 0° and there is no inversion from the noninverting (+) input of the op-amp to the output.

Figure 8 Wien-Bridge Oscillator Startup The loop gain should be greater than 1 at startup to build up output.

Figure 9 Relaxation Oscillator A simple relaxation oscillator that uses a Schmitt trigger is the basic square-wave oscillator. The two trigger points, UTP and LTP are set by R2 and R3. The capacitor charges and discharges between these levels: R3 R3 VUTP = +Vmax ( VLTP = −Vmax ( ) ) R2 + R3 R2 + R3 104


The period of the waveform is given by: 2R 3 T = 2R1 C ln (1 + ) R2

Figure 10: A square-wave relaxation oscillator.

Noise Noise is a random fluctuation in an electrical signal. Noise in electronic devices varies greatly, as it can be produced by several different effects. Noise is a fundamental parameter to be considered in an electronic design as it typically limits the overall performance of the system. Noise is a purely random signal, the instantaneous value and/or phase of the waveform cannot be predicted at any time.

Figure 11: Sine wave with superimposed noise. Noise can either be generated internally in the op-amp, from its associated passive components, or superimposed on the circuit by external sources. External refers to noise present in the signal being applied to the circuit or to noise introduced into the circuit by another means, such as conducted on a system ground or received on one of the many antennas formed by the traces and components in the system. Types of internal Noise  Thermal Noise  Shot Noise  Flicker Noise  Burst Noise  Avalanche Noise Some or all of these noises may be present in a design, presenting a noise spectrum unique to the system. It is not possible in most cases to separate the effects, but knowing general causes may help the designer optimize the design, minimizing noise in a particular bandwidth of interest. 105


Thermal Noise Generated by the random thermal motion of charge carriers (usually electrons), inside an electrical conductor. It happens regardless of any applied voltage. Power spectral density is nearly equal throughout the frequency spectrum, approximately white noise.

Figure 12 The root mean square voltage (VRMS) due to thermal noise, generated in a resistance (R) over bandwidth (BW), is given by: VRMS = √4𝑘B TRBW The noise from a resistor is proportional to its resistance and temperature. Lowering resistance values also reduces thermal noise. Shot Noise The name Shot Noise is short of Schottky noise, also called quantum noise. It is caused by random fluctuations in the motion of charge carriers in a conductor.

Figure 13 Some characteristics of shot noise:  Shot noise is associated with current flow. It stops when the current flow stops.  Shot noise is independent of temperature.  Shot noise is spectrally flat or has a uniform power density, meaning that when plotted versus frequency it has a constant value.  Shot noise is present in any conductor. Flicker noise Flicker noise is also called 1/f noise. Its origin is one of the oldest unsolved problems in physics. It is present in all active and many passive devices. It is related to imperfections in crystalline structure of semiconductors, as better processing can reduce it. 106


Some characteristics of flicker noise:  It increases as the frequency decreases, hence the name 1/f.  It is associated with a dc current in electronic devices.  It has the same power content in each octave (or decade). Burst noise  Burst noise consists of sudden step-like transitions between two or more levels.  It is related to imperfections in semiconductor material and heavy ion implants.  As high as several hundred microvolts.  Lasts for several milliseconds.  Burst noise makes a popping sound at rates below 100 Hz when played through a speaker - it sounds like popcorn popping, hence also called popcorn noise.  Low burst noise is achieved by using clean device processing, and therefore is beyond the control of the designer. Avalanche noise Avalanche noise is created when a PN junction is operated in the reverse breakdown mode. Under the influence of a strong reverse electric field within the junction’s depletion region, electrons have enough kinetic energy. They collide with the atoms of the crystal lattice, to form additional electron-hole pair. These collisions are purely random and produce random current pulses similar to shot noise, but much more intense. When electrons and holes in the depletion region of a reversed-biased junction acquire enough energy to cause the avalanche effect, a random series of large noise spikes will be generated. The magnitude of the noise is difficult to predict due to its dependence on the materials.

Figure 14

107


Chapter 14: Voltage Regulation Power Supply Regulation An ideal power supply provides a constant dc voltage despite changes to the input voltage or load conditions. The output voltage of a real power supply changes under load as shown in the second plot. The output is also sensitive to input voltage changes.

Figure 1: (a) Ideal power supply

(b) Real power supply

Line Regulation Line regulation is a measure of how well a power supply is able to maintain the dc output voltage for a change in the ac input line voltage. The formula for line regulation is ∆VOUT Line regulartion = ( ) 100% ∆VIN Line regulation can also be expressed in terms of percent change in VOUT per volt change on the VIN (%/V). (∆VOUT /VOUT )100% Line regulartion = ∆VIN Load regulation Load regulation is a measure of how well a power supply is able to maintain the dc output voltage between no load and full load with the input voltage constant. It can be expressed as a percentage change in load voltage: VNL − VFL ) 100% VFL Load regulation can also be expressed in terms of percent change in the output per mA change in load current (%/mA). Sometimes a maximum error voltage is given in the specification as illustrated in the next slide for a commercial power supply. Commercial power supplies, such as you have in lab, have excellent line and load regulation specifications. Line regulartion = (

108


The BK Precision 1651A is an example of a triple output supply (two 0-24 V outputs and a fixed 5 V output). Voltage regulation specifications for this power supply are: Line regulation: ≤0.01% +3 mV (Main supply) ≤5 mV (Fixed 5 V supply) Load regulation: ≤0.01%+3 mV (Main supply) ≤5 mV (Fixed 5 V supply)

Sometimes the equivalent Thevenin resistance of a supply is specified in place of a load regulation specification. In this case, VOUT can be found by the voltage divider rule: RL VOUT = VNL ( ) R OUT + 𝑅𝐿 In terms of resistances, load regulation can be expressed as: R OUT Load regulartion = ( ) 100% R FL Figure 1 Example: A power supply has an output resistance of 25 mΩ and a full load current of 0.50 A to a 10.0 Ω load. (a) What is the load regulation? (b) What is the no load output voltage? Solution:

Series Regulators The fundamental classes of voltage regulators are linear regulators and switching regulators. Both of these are available in integrated circuit form. Two basic types of linear regulator are the series regulator and the shunt regulator. A simple representation of a series type of linear regulator is shown in Figure 3(a), and the basic components are shown in the block diagram in Figure 3(b). 109


Figure 3 The control element maintains a constant output voltage by varying the collector-emitter voltage across the transistor. A basic op-amp series regulator is shown in Figure 4. The zener diode (D1) holds the other op-amp input at a nearly constant reference voltage VREF

Figure 4 The output voltage for the series regulator circuit is: R2 VOUT = (1 + ) VREF R3 Example: Determine the output voltage for the regulator in the following Figure:

Solution:

110


Short-Circuit Current limiting prevents excessive load current. Q2 will conduct when the current through R4 develops 0.7 V across Q2’s VBE. This reduces base current to Q1, limiting the load current. The current limit is: 0.7V IL(max) = R4 For example, a 1.4 W resistor, limits current to about 0.5 A.

Figure 5: Series regulator with constant-current limiting. Regulator with Fold-Back Current Limiting Fold-back current limiting drops the load current well below the peak during overload conditions. Q2 conducts when VR5+VBE=VR4 and begins current limiting. VR5 is found by applying the voltage-divider rule: R5 VR5 = ( )V R 5 + R 6 OUT An overload causes VR5 to drop because VOUT drops. This means that less current is needed to maintain conduction in Q2 and the load current drops

Figure 6: Series regulator with fold-back current limiting. Basic Linear Shunt Regulators The second basic type of linear voltage regulator is the shunt regulator, as shown in Figure 7. In the shunt regulator, the control element is a transistor in parallel (shunt) with the load, as shown in Figure 8. The control element maintains a constant output voltage by varying the collector current in the transistor. 111


Figure 7 If the output voltage changes, the op-amp senses the change and corrects the bias on Q1 to follow. e.g., a decrease in output voltage causes a decrease in VB and an increase in VC. Although it is less efficient than the series regulator, the shunt regulator has inherent short-circuit protection. The maximum current when the output is shorted is VIN/R1.

Figure 8 Switching Regulators All switching regulators control the output voltage by rapidly switching the input voltage on and off with a duty cycle that depends on the load. Because they use high frequency switching, they tend to be electrically noisy.

Figure 9

112


A step-down switching regulator controls the output voltage by controlling the duty cycle to a series transistor. The duty cycle changes depending on the load requirement. Because the transistor is either ON or OFF on all switching regulators, the power dissipated in the transistor is very small and the regulator is very efficient. The pulses are smoothed by an LC filter.

Figure 10: Basic regulating action of a step down switching regulator. In a step-up switching regulator, the control element operates as a rapidly pulsing switch to ground. The switch on and off times are controlled by the output voltage. Stepup action is due to the fact the inductor changes polarity during switching and adds to VIN. Thus, the output voltage is larger than the input voltage.

Figure 11: Basic step-up switching regulator. 113


Voltage-Inverter Configuration In a voltage-inverter switching regulator, the output is the opposite polarity of the input. It can be used in conjunction with a positive regulator from the same input source. Inversion occurs because the inductor reverses polarity when the diode conducts, charging the capacitor with the opposite polarity of the input.

Figure 11: Basic inverting switching regulator. Integrated circuit voltage regulators Integrated circuit voltage regulators are available as series regulators or as switching regulators. The popular three-terminal regulators are often used on separate pc boards within a system because they are inexpensive and avoid problems associated with large power distribution systems (such as noise pickup).

Figure 12: The 78XX series three-terminal fixed positive voltage regulators. The 78XX series is a fixed positive output regulator available in various packages and with standard voltage outputs. The only external components required with the 78XX series are input and output capacitors and some form of heat sink. These IC’s include thermal shutdown protection and internal current limiting. The 78XX series are primarily used for fixed output voltages, but with additional components, they can be set up for variable voltages or currents. 114


The 79XX series is the negative output counterpart to the 78XX series, however the pin assignments are different on this series. Other specifications are basically the same

Figure 13: The 79XX series three-terminal fixed negative voltage regulators. Adjustable Positive Linear Voltage Regulators The LM317 is an example of a three-terminal positive regulator with an adjustable output IC regulator as shown in figure 14. There is a fixed reference voltage of +1.25 V between the output and adjustment terminals. There is no ground pin. The output voltage is calculated by: R2 VOUT = VREF (1 + ) + IADJ R 2 R1

Figure 14: The LM317 three-terminal adjustable positive voltage regulator. Example: Determine the minimum and maximum output voltages for the voltage regulator in the following Figure. Assume IADJ = 50 µA.

Solution:

115


The External Pass Transistor IC regulators are limited to a maximum allowable current before shutting down. The circuit shown in Figure 15 is uses an external pass transistor to increase the maximum available load current.

Figure 15 Rext sets the point where Qext begins to conduct: 0.7 V R ext = Imax The 78S40 is an IC containing all of the elements needed to configure a switching regulator, using a few external parts. It is a universal switching regulator subsystem because it can be configured as a step-down, step-up, or inverting regulator by the user. The data sheet shows typical circuits for these configurations. In the figure 16 is the step-down configuration.

Figure 16 116

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