A Cascaded Linear High-Voltage Amplifier Circuit for ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 63, NO. 3, MARCH 2016

A Cascaded Linear High-Voltage Amplifier Circuit for Dielectric Measurement Ji Liu, Daning Zhang, Mengqi Wang, Ling Huang, and Dongxu Zhao Abstract—High-voltage amplifiers have the features of high output voltage, wide frequency bandwidth, and desirable linearity. It is widely used for dielectric measurement in industrial and laboratory applications. This paper presents a new type of cascaded high-voltage amplifier with a voltage gain of 40 times for one circuit cell. The unit circuit is given in detail, which is based on an isolation circuit with linear opto-coupler and an amplified circuit with six operational amplifiers. The negative feedback and capacitive loads characteristics are analyzed theoretically. The step response and frequency curves for two units of amplifier circuit have been tested physically in laboratory. The test results show that the expected voltage gain within the frequency range from 10−3 to 104 Hz can be obtained accurately. The new type of linear high-voltage amplifier circuit proposed in this paper is also helpful to insulation diagnosis, electrostatic deflection, and other industrial applications. Index Terms—Cascaded circuit, dielectric response, frequency-domain measurement, high-voltage amplifier, optoelectronic isolation.

I. I NTRODUCTION

H

IGH-VOLTAGE linear amplifiers are mainly used in industrial and research applications, including dielectric studies, electrostatic deflection, and electro-optic modulation. The dielectric frequency response (DFR), also called as frequency-domain spectroscopy (FDS) is a reliable method for evaluating the conditions of electrical insulation systems [1], [2]. High-voltage amplifiers are necessary components used for insulation diagnosis or dielectric spectroscopy measurement, which requires not only a high output voltage but also a high accuracy and slew rate. There are many methods of obtaining the high-voltage amplifiers. A transformer can easily convert low-voltage signals into arbitrary high voltage according to the voltage ratio. Nevertheless, the transformer type of high-voltage amplifier can only generate a sinusoidal voltage waveform,

Manuscript received April 7, 2015; revised July 17, 2015; accepted October 4, 2015. Date of publication November 5, 2015; date of current version February 8, 2016. This work was supported in part by the National Basic Research Program of China under Contract 2012CB723308 and in part by the Natural Science Fund of Heilongjiang, China, under Contract E201450/E070201. J. Liu, D. Zhang, M. Wang, and L. Huang are with the State Key Laboratory Breeding Base of Dielectrics Engineering, Harbin University of Science and Technology, Harbin 150080, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). D. Zhao is with the State Grid Liaoning Electric Power Supply Company Ltd., Shenyang 110004, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2015.2498129

which is not suitable for generating triangle or square voltage waveform [3]. In addition, an ultra-low frequency sinusoidal voltage, which is also necessary for insulation diagnosis [4]– [6], is not easy to be produced by using a transformer. Another type of high-voltage linear amplifier is based on switching circuit [7]. For example, class-D power amplifier is also known as the switching power amplifier, whose working efficiency can be more than 80%. Nevertheless, an obvious fact is that the high loss need to be avoided, and inherent nonlinearity of switched mode led to the distortion of output voltage waveform [8]. The first all-solid-state, high-voltage (±20 kV), high speed, dc-stable amplifier is developed by American Trek Inc. on basis of complementary output of the P-channel MOSFET and Nchannel MOSFET, which is also prone to crossover distortion at the zero point of signal. A new hybrid amplifier combining switching amplifiers with linear amplifiers is presented in [9] and [10]. The total harmonic distortion (THD) of composite amplifiers is less than switching amplifier, but switch-linear hybrid (SLH) power amplifier significantly degrades performance of the linear amplifier. When high-voltage amplifier is used for insulation detection, it can provide extremely low current, which means less power consumption. Therefore, it requires a low THD rather than high efficiency. In addition, a linear amplifier circuit with isolation amplifier is presented in [11]. However, isolation amplifier is the single polarity output and has lower linearity than high-linearity opto-couplers. This paper presents a new type of cascaded high-voltage linear amplifier circuit, which can reach up to desirable linearity and an ac output voltage of 400 Vpp (peak to peak voltage) in each circuit unit. The voltage range can be further extended by cascading a number of high-voltage amplifiers (the power supply of each high-voltage amplifier unit must be electrical isolation). II. A PPLICATION Take power transformer for example, modern power systems face severe challenges such as transformer failures, life assessment, and growing maintenance cost. Extending several operating years to the expected service life of power transformers by optimizing the insulation conditions is based on lots of reliable diagnostic data, which will reduce substantial cost savings for the owners [12]. A frequency of 50/60 Hz often appears in the traditional power-frequency test, which cannot provide power transformer with conclusive information regarding potential problems. The cascaded amplifier circuit applies various frequencies of sinusoidal voltage across the test object, therefore, the relationship between dissipation factor as well as

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LIU et al.: CASCADED LINEAR HIGH-VOLTAGE AMPLIFIER CIRCUIT

Fig. 1. Schematic diagram of an amplifier circuit unit.

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Fig. 2. Output voltage of 200 Vpp to ground with 3.75-kΩ load, 100-V supplies.

TABLE I E LECTRICAL C HARACTERISTICS OF O PERATIONAL A MPLIFIER

the complex permittivity and a wide range of frequencies can be obtained by accurately measuring amplitude of applied voltage and resulting current and their phase difference. It is possible to assess the insulating conditions by comparing with different historical curves. The wide frequencies of dielectric parameter tests are helpful to insulation diagnosis of power transformer, cable, and resin-rich generator. In this paper, a cascaded highvoltage linear amplifier circuit is proposed and used as wide frequencies of high-voltage generator for insulation diagnosis, electrostatic deflection, and other industrial applications.

III. C ASCADED S CHEME OF H IGH -VOLTAGE A MPLIFIER A. Unit Circuit Fig. 1 is the basic diagram of an amplifier circuit unit, which is effective to both ac and dc input signals. The circuit cell comprises six operational amplifiers which is a high-voltage amplifier with high current drive, stable unity gain, and high slew rate. Main electrical characteristics are listed in Table I. It is fully specified to perform over a wide power supply, range of ±5 to ±50 V or on a single supply of 10 to 100 V. It is unity-gain stable and has a gain-bandwidth product of 2.5 MHz. As shown in Fig. 1, a basic voltage-series negative feedback circuit with 20 times of voltage gain is made up of operational amplifiers A1, A2, and A3. Operational amplifiers A1 and A3 constitute a voltage follower and act as the power supply of A2. The maximum withstand voltage of the amplifiers A1-A3 is 100 V. As the changes of the input voltage, the positive voltage V01 and negative voltage V02 of amplifier A2 will be fluctuated subsequently, as shown in Fig. 2. Nevertheless, the absolute value of the supply voltage, that is the difference between V01 and

Fig. 3. Schematic diagram of an opto-isolated circuit.

V02 , will always keep 100 V. The output maximum voltage will reach 400 Vpp. Similarly, amplifiers A4, A5, and A6 are made up of a basic voltage-parallel negative feedback circuit with a gain of 20 times. The overall gain of unit circuit will eventually reach up to 40 times. In practice, considering the supply voltage restriction of maximum 100 V, maximum swing of the input voltage should be limited to a smaller value to ensure that the amplifier is in a linear operating range.

B. Isolation Circuit Considering the independence of each circuit module, it is necessary to design an isolation circuit for the same input signals, avoiding the output electrical interference and the electric shock back to the low voltage input parts. Fig. 3 shows the optoisolated circuit based on high precision opto-coupler HCNR 201. The circuit is designed to operate with input voltage range from 1 mV to 10 V. The gain of isolating circuit can be adjusted to a stable value by changing R2 without the need for an offset adjusting circuit. In order to improve accuracy of the circuit, the input terminals of amplifier and the diodes should be connected with

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The lower limit frequency is 2 + f2 + · · · + f2 . fL = fL1 L2 Ln The upper limit frequency is 1 1 1 1 ≈ 1.1 2 + f2 + · · · + f2 . fH fH1 H2 Hn According to Table I, the slew rate in multiamplifier is SR = 13(V/μs). 2) Cascaded Amplifier: As shown in Fig. 4, magnitudefrequency characteristic in cascaded amplifier is the same as (1). Because of the cascading connections of circuit units, the phase-frequency characteristic is Fig. 4. Cascaded topology of linear high-voltage amplifier.

Kelvin connections in the circuit. The advantages of the isolation circuit are that the amplitude and phase of the output signal are exactly the same as the input signal, meanwhile, the circuit can effectively establish electrical isolation between the input side and the amplifier circuit unit. The insulation working voltage of opto-coupler used in Fig. 3 is 1414 Vpp and the continuous withstanding voltage is 5000 V for 1 min.

φ ≈ φ1 ≈ φ2 ≈ · · · ≈ φn . Lower frequency is fL ≈ fL1 ≈ fL2 ≈ · · · ≈ fLn . Upper limit frequency is fH ≈ fH1 ≈ fH2 ≈ · · · ≈ fHn . Slew rate is

C. Cascaded Topology The circuit unit in Fig. 1 has an output voltage of 400 Vpp, as shown in Fig. 2. V01 is an output voltage of the left part of the circuit unit, and V02 for the other part of circuit, which are both equal in phase. The output voltage range can be increased by cascading external high-voltage units, which is demonstrated in Fig. 4. By cascading circuit with a series of n units, the complete circuit can obtain a gain of 40n times. The signal source is an arbitrary waveform generator which provides with the input signals covering a range of signal frequency from mHz to kHz by software programming. The cascaded modules are built on the basis of a parallel-input small signal and a seriesoutput high voltage. The voltage source from VS1 to VSn is the power supply of the AMPx. Each voltage source is composed of linear voltage regulator module. The key of cascaded linear high-voltage amplifier is the insulation problem among voltage-source modules. There are many differences in the characteristics of multiamplifier and cascaded amplifier. 1) Multiamplifier: The multiamplifier consists of multiple amplifiers connected in series. In magnitude-frequency characteristics of multiamplifier, the relationship between the total gain and unit gain is given by 20 log |AU |=20 log |AU1 |+20 log |AU2 |+ · · · +20 log |AUn | . (1) For phase-frequency characteristic, the total phase shift is n

φ = φ1 + φ2 + · · · + φn = Σ φi . i=1

SR = 13 × 2n (V/µs),

n = 1, 2, 3, . . . .

The transfer gain and phase errors mainly depend on the difference of the devices cascaded. In contrast to multiamplifier, cascaded circuit can provide better flexibility and wider bandwidth. Relying on the increased quantities of floating circuit unit, the overall gain increases to a great extent, nevertheless, the total bandwidth still unchanged. It is worth mentioning that an individual circuit unit or whole cascaded circuit can provide the same current. IV. C HARACTERISTIC A NALYSIS OF L INEAR A MPLIFIER A. Negative Feedback After introducing the negative feedback, the gain of amplifier will be reduced due to many reasons, just as that caused by signal frequency, which is more obvious in broadening the frequency bandwidth. For simplifying the problem, the network with pure resistive loads is assumed at first, and an equivalent circuit diagram of the voltage parallel negative feedback is shown in Fig. 5. Suppose that the gain of circuit unit is Am in middlefrequency band, meanwhile, the upper frequency limit and the lower frequency limit are fH and fL , respectively. Therefore, the gain Ah in high-frequency band is Ah =

Am . 1 + s(f /fH )

(2)


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Fig. 5. Equivalent circuit diagram of the voltage parallel negative feedback.

After introduction of negative feedback, the expression of gain Ahf in high-frequency band can be rewritten as f A / 1 + j m fH Am Ah = = Ahf = 1 + Ah F 1 + A / 1 + j f F 1 + j ff + Am F m H

Fig. 6. Equivalent amplification circuit.

From Kirchhoff’s current law in Fig. 5, we obtain is = if + ii = F Vof + Vi /ri .

fH

(3) where F is the feedback coefficient. Rearranging (3), we have Ahf

Am /(1 + Am F ) Amf = = f f 1 + j (1+Am F )fH 1 + j fHf

where Amf is the gain of negative feedback amplifier circuit in the middle-frequency band. fHf is the upper limit frequency defined by fHf = (1 + Am F )fH .

(5)

It is shown from (4) that the using of negative feedback results in the upper limit frequency increasing up to (1 + Am F ) times in the basic amplifier circuit, as shown in Fig. 5. In Fig. 5, Vs is the voltage of signal source and Rs is expressed as an internal resistance of Vs . Vi is the voltage across ri , which is the input resistance of basic amplifying circuit. ii is the input current of amplifier. ro is the output resistance of amplifier. The output of the basic amplifying circuit can be equivalent to a voltage source Vo = Ao ii in series with the equivalent output resistance ro . Rf is the feedback resistance. After the introduction of negative feedback, the influence of input resistance is usually expressed as the depth of the feedback (1 + AF ). Considering the internal resistance of signal source and load, it cannot fully convey the relationship between each element of output circuit and input resistance. The general form of voltage parallel negative feedback amplifying circuits of A5 in Fig. 1 can be demonstrated as Fig. 5 according to the Thevenin theorem. When the load resistance RL is connected to the output terminal, the dropping of output voltage Vof will bring about the change of input and output current. We thus obtain the output voltage as ro + Ao ii . (6) Vof = ro (if + io ) + Vo = Vof ro F − RL Furthermore, ii =

Vof (1 − ro F + ro /RL ) . Ao

Considering (7) and Vi = ii · ri , the output voltage Vof =

(4)

(7)

(8)

Vi Ao . ri (1 − ro F + ro /RL )

(9)

Inserting (9) into (8), the equivalent input resistance Rif is solved by Rif =

Vi ri . = is Ao F /(1 − ro F + ro /RL ) + 1

(10)

Due to the introduction of series voltage negative feedback to A2 in Fig. 1, input resistance will increases (1 + AF ) times. It is worth noting that the input resistance of A2 and A5 is different in Fig. 1. When selecting the proper input resistance and feedback resistance in an operational amplifier, influence of input resistance on the accuracy of amplifier is negligible. In order to avoid the distortion of the input signal, adding an emitter follower after optical coupling isolation or optimal selection of resistance is essential. B. Capacitive Loads With regard to high-voltage linear amplifier, most of the loads are capacitive, including dielectric materials, piezoelectric crystals, high-voltage apparatus, etc. To a certain extent, capacitive loads often reduce the bandwidth and slew rate of the linear amplifiers. The phase shift generated within the feedback loop is an important factor. Generally, the use of isolation resistance will reduce this phenomenon, but it is still very difficult to avoid spurious oscillations of the amplifiers. As seen in Fig. 6, an amplifier always has an internal output resistance Ro , which leads to an amplifier that can be regarded as an oscillator. When it is connected to the capacitive load, the transfer function of amplifier circuit will add additional pole. The Bode plots with additional pole are relatively steeper than that of dominant pole, which results in a phase shift of −90◦ . As the open-loop gain and feedback attenuation are greater than 1, the amplifier circuit is operating in an unstable state. If the working frequency is lower than the closed-loop bandwidth, the loop phase shift in circuit will exceed 180◦ . Thus, an operational amplifier will act as an oscillator, as shown in Fig. 7,

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Fig. 7. Bode plots of capacitive loads by Tina analysis software (one unit).

Fig. 8. Low-pass filter circuit and Vo /Vs versus time.

which shows the frequency response relationship by using the Tina analysis software of Texas Instruments Co. Ltd. The phase margin of operational amplifier circuit is defined as phase difference between the phase at gain crossover frequency and the phase of −180◦ . In order to extend extra phase margin, the additional poles come from capacitive loads should be more than 10 times the closed-loop bandwidth in the circuit. The frequency of additional pole is given by fp = 1/2πRo CL . C. Step Response When analyzing the step response of amplifier circuit, the equivalent circuit of small signal can be used. The step voltage can be divided into rising and saturation curves, and the circuit can be thereby simplified according to the exponential characteristics. A part of the step voltage rises faster than the steady state voltage at corresponding high-frequency ranges. Thus, a low-pass filter circuit can be used to describe the phenomenon. As seen in Fig. 8, the output voltage is written as t (11) Vo = Vs 1 − e− RC where Vs is the final steady value of step response voltage. The relationship between Vo /Vs and time is shown in Fig. 8. Because the output voltage Vo increases exponentially, it will take some time to reach the final voltage Vs , which will result in the leading edge distortion. The rise time tr (duration from 10% to 90% of the final voltage) is used for representing the leading edge distortion, which is then given by tr = t2 − t1 = RC(ln 9).

(12)

In Fig. 8, the upper frequency limit is fH =

1 . 2πRC

(13)

Therefore, the rise time is approximately solved by tr ≈

0.35 . fH

Fig. 9. Experimental setup (two units cascaded).

According to (14), the rise time tr is inversely proportional to the upper limit frequency fH . The higher the upper limit frequency, the shorter the rise time and the smaller edge distortion. The upper limit frequency depends on the depth of the negative feedback, but linear amplifier generally requires a higher gain. The proper depth of the negative feedback is necessary to ensure smaller edge distortion and higher gain.

V. E XPERIMENTAL R ESULTS A. Experimental Setup With regard to two units of cascaded amplifier circuit, the amplification characteristics are fully tested in laboratory. Fig. 9 shows a photograph of the experimental setup. A Tektronix AGF3101 arbitrary waveform generator is used to provide various signals required. In addition, a FLUKE 199C oscilloscope is used to record the waveforms of output voltage.

B. Time-Domain Response (14)

A typical step response for various capacitive loads with an input signal voltage of 1.0 V is shown in Fig. 10. The curve


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Fig. 10. Step response curves of capacitive loads (two units cascaded).

marked “open” means that the load CL is neglected. Most amplifier circuit usually appears in oscillation with capacitive loads. When the capacitive loads are less than 0.01µF, the stepresponse characteristics are nearly identical. Due to under the excitation with a vertical rising edge, the curves appear slight overshoot which exceeds the slew rate of the amplifier. With the increase of capacitive loads, more significant oscillations will appear. These peaking show that capacitance of the loads would dominate the circuit response. Fig. 11 shows the input and output voltage waveforms of the two units of cascaded amplifier at the frequency of 0.001 Hz, 1.0 Hz, 1.0 kHz, and 10 kHz. The input voltage is 8.0 Vpp and the output voltage is 640 Vpp. It can be seen that there is an obvious phase delay in Fig. 11(d). Higher frequency of input signal were tested in experiment, the phenomena of phase delay appear more significantly, nevertheless, the gain remains 40n times (n = 2) without changing. Actually, the common phase shift does not affect the normal impedance measurement because the output voltage and current will be detected simultaneously.

C. Frequency-Domain Response The experimental results are carried out at the frequency from 10−3 to 104 Hz, which are able to verify the amplification performance of the cascaded amplifier circuit. Fig. 12 is the frequency response curves of amplifier, which is obtained by measuring two units and one unit circuit individually. The cascaded output voltage with two units is 640 Vpp with the input voltage of 8.0 Vpp. It can be concluded that the circuit system can obtain the gain of 80 times by cascading two circuit units. These curves show that the gain of amplifier will be enlarged with the increase of cascaded units and the bandwidth of amplifier is unchanged. No matter how many circuit units cascaded, the phase shift is almost the same. The reason is that the cascaded mode in this paper has no effect on phase shift of the final high-voltage amplifier. The precondition of above conclusions is that the capacitive loads are consistent with the permitted load range. Without considering other effects, it is believed that the system of cascaded n units can achieve the gain of 40n times. The isolation voltage of the opto-couplers and power supplies are also

Fig. 11. Input and output voltage waveforms. (a) 0.001 Hz. (b) 1 Hz. (c) 1 kHz. (d) 10 kHz.

important factors to limit the maximum output voltage of the cascaded high-voltage linear amplifier. D. Linear Amplifier Performance The distortion performance of the linear amplifier is more excellent than switch-mode amplifier and switch-mode assisted linear amplifier (SMALA). Fig. 13 shows the THD of the linear amplifier. Measurements were carried out with a 2.5-kΩ load

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of opto-coupler and power-supply transformer. The cascaded high-voltage amplifier circuit can also be applicable for input dc and other signal waveforms in industrial applications. R EFERENCES

Fig. 12. Frequency response curves of amplifier (two units cascaded).

Fig. 13. THD + noise versus frequency.

over a 20-Hz to 20-kHz bandwidth. The Fig. 11 in [13] shows the THD of switch-mode amplifier and SMALA. Although the THD of SMALA is reduced in comparison with the common switch-mode amplifier, the performance of SMALA is still not as good as the linear amplifier. Nevertheless, the efficiency and power consumption/dissipation of the SMALA and switch-mode amplifier are generally far better than linear amplifier.

VI. C ONCLUSION The new type of cascaded linear high-voltage amplifier was introduced, which comprises multiple units of amplifier circuits. Each amplifier unit includes isolation circuit and amplifier circuit. Due to the use of a high-linearity opto-coupler and high-insulated power supply, a linear high-voltage amplifier can be achieved in the way of cascaded amplification. The experimental results confirmed that the unit amplifier circuit can obtain voltage amplification signal effectively within the frequency range from 10−3 to 104 Hz. The various frequencies of test results demonstrate that each unit can achieve 40 times of voltage gain. The maximum output voltage is 40n times for cascading n sets of unit circuit. Note that the maximum output voltage must be lower than the isolation voltage

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Ji Liu received the M.S. and Ph.D. degree in high voltage and insulation technology from Harbin University of Science and Technology, Harbin, China, in 2000 and 2014, respectively. Since 2010, he has been a major Researcher with the State Key Laboratory Breeding Base of Dielectrics Engineering, Harbin University of Science and Technology. Since 2012, he has also been a Professor with Harbin University of Science and Technology. His research interests include high-voltage techniques, insulation testing, and power electronics.

Daning Zhang was born in 1989. He received the B.S. degree in electrical engineering from Shandong University, Jinan, China, in 2012. Currently, he is working toward the M.S. degree in electrical engineering at Harbin University of Science and Technology, Harbin, China. His research interests include insulation testing and power electronics.


Mengqi Wang was born in 1990. Currently, she is working toward the M.S. degree in electrical machines at Harbin University of Science and Technology, Harbin, China. Her research interests include electrical machines, drives, and power electronics.

Ling Huang received the M.S. degree in control science and control engineering from Harbin University of Science and Technology, Harbin, China, in 2002, and the Ph.D. degree in control science and control engineering from Harbin Institute of Technology, Harbin, China, in 2007. Since 2013, she has been a Professor with Harbin University of Science and Technology. She was a Visiting Scholar at the University of Adelaide, Adelaide, Australia, from 2014 to 2015. Her research interests include T –S fuzzy systems and digital signal processing.

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Dongxu Zhao received the B.S. degree in electrical engineering from Harbin Institute of Electrical Technology, Harbin, China, in 1994. Currently, he is a Senior Engineer with the State Grid Liaoning Electric Power Supply Company Ltd., Shenyang, China. His research interests include power system production and maintenance. Dr. Zhao was the recipient of the First Prize Award of the State Grid Corporation of China in 2006 for his work on the national key project of the 500-kV thyristor controlled series compensation in Yi-min.