# Design of High-Voltage Switch-Mode Power Amplifier Based on Digital-Controlled Hybrid Multilevel Converter

Authors: Yanbin Hou; Wanrong Sun; Aifeng Ren; Shuming Liu
Journal: Active and Passive Electronic Components
 (2016)

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## Abstract

Compared with conventional Class-A, Class-B, and Class-AB amplifiers, Class-D amplifier, also known as switching amplifier, employs pulse width modulation (PWM) technology and solid-state switching devices, capable of achieving much higher efficiency. However, PWM-based switching amplifier is usually designed for low-voltage application, offering a maximum output voltage of several hundred Volts. Therefore, a step-up transformer is indispensably adopted in PWM-based Class-D amplifier to produce high-voltage output. In this paper, a switching amplifier without step-up transformer is developed based on digital pulse step modulation (PSM) and hybrid multilevel converter. Under the control of input signal, cascaded power converters with separate DC sources operate in PSM switch mode to directly generate high-voltage and high-power output. The relevant topological structure, operating principle, and design scheme are introduced. Finally, a prototype system is built, which can provide power up to 1400 Watts and peak voltage up to ±1700 Volts. And the performance, including efficiency, linearity, and distortion, is evaluated by experimental tests.


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## Body

## 1. Introduction

Class-A, Class-B, and Class-AB amplifiers are usually termed as linear amplifiers for their switching devices operate in linear mode, while Class-D amplifiers are also known as switching amplifiers, in which the switching devices are either fully turned on or completely turned off, operating in switch mode. This means that when the switch is conducting (turned on) there is virtually no voltage across the switch and that when the switch is not conducting (turned off) there is no current flowing through the switch. So the ideal efficiency of Class-D amplifier is 100% in theory [1]. In fact, the commonly used semiconductor switching devices, such as IGBT (Insulated Gate Bipolar Transistor) and MOSFET (Metal Oxide Semiconductor Field Effect Transistor), have saturation voltage drop or on-state resistance when they are turned on. Although part of power has been consumed as heat by switches, efficiencies over 85% can be achieved in most situations for Class-D amplifier. By comparison, linear amplifier has a theoretical efficiency of 78% at the utmost [2].In a typical Class-D amplifier, input signal is converted into a series of pulses through pulse width modulation (PWM), which serve as control signals for driving power switches. The switching devices together with DC sources realize power and voltage amplification. At the output stage of Class-D amplifier, low-frequency amplified signal is retrieved across the load by filtering out high-frequency carrier wave. Due to its single half-bridge or full-bridge topology, PWM-based switching amplifier usually outputs a peak voltage of dozens or hundreds of Volts [3]. Step-up transformer seems to be a ready-made solution to boost up output voltage, since existing PWM-based switching amplifiers can provide enough output power. However, the noisy and heavy midfrequency step-up transformer will make the whole amplifier system bulky and expensive. What is worse, the insertion of step-up transformer between amplifier and load will introduce additional power loss, thus reducing the overall system efficiency. One of our outside partners is confronted with such a dilemma. They built an analog PWM-based switching amplifier and used a bulky step-up transformer to produce the rated voltage of 1000 Volts and rated power of 1000 Watts across a 1000-Ohm resistor over the operating frequency range of 100–1000 Hertz. But the average system efficiency is about 70%, presenting a challenge to cool. What is more, the bulky step-up transformer has a weight of over 50 kilograms, almost two-thirds of the gross weight. Our target is to rebuild a switching amplifier with main requirements as follows:Output voltage up to 1000 Vrms.
Output power up to 1000 W.
Overall efficiency above 85%.
Output distortion below 2.5%.
Gross weight less than 80 Kg.The requirements about high efficiency and light weight exclude the possibility of using step-up transformer to boost up voltage. From the view of power electronics, the desired switching amplifier can be considered as a programmable high-voltage power supply operating in switch mode under the control of input signal. NPC- (neutral point clamped-) based and cascaded H-bridge (full-bridge) multilevel converters are two commonly used topologies to directly produce high-voltage output [4, 5]. The former uses a single high-voltage DC source and multiple cascaded semiconductor switches together with clamping diodes or flying capacitors, usually involving complicated voltage balancing measures [6–8]. The latter adopts modular design, of which each converter consists of a low-voltage DC source and four semiconductor switches. Thus it will demand a great number of semiconductor switches and control signals when employing multiple cascaded full-bridge converters to generate high-voltage output.In order to directly generate high-voltage output and reduce power semiconductor switches as well, a new circuit architecture, called hybrid multilevel converter, is proposed in this paper. The corresponding control scheme is designed on the basis of pulse step modulation (PSM) by adopting digital signal processing technology. Section2 introduces the design scheme, Section 3 gives the performance tests, and Section 4 is the conclusion. Experimental results show that this new system can provide up to 1400 Watts and ±1700 Volts peak voltage with high efficiency and low distortion as expected.


## 2. Design of High-Voltage Switching Amplifier

Figure1 shows the functional block diagram of high-voltage switch-mode power amplifier developed in this paper.Figure 1
Block diagram of high-voltage switching amplifier.As shown in Figure1, this switching amplifier consists of four units, which are control unit, hybrid converter unit, power source unit, and auxiliary unit, respectively. The workflow is as follows.Small analog input signal is firstly preprocessed and then digitalized by a 12-bit analog-to-digital converter (ADC). According to the ADC data and user settings, PSM modulator generates a set of switching signals, which are further isolated and driven before applying to hybrid converter unit. Under the control of corresponding switching signals, multilevel power converter transforms energy from separate low-voltage DC sources to augment modulated switching signals and full bridge takes charge of the switchover between positive and negative phase. At the final output stage, a low-pass filter is used to retrieve the expected amplified output waveform.For the sake of efficiency and reliability, the whole system was developed utilizing digital signal processing technology. PSM modulator was implemented with a high-performance floating-point digital signal processor (DSP) and a high-volume field programmable gate array (FPGA). Auxiliary unit adopted digital technologies at the most extent, like human-machine interface (HMI) for setting gain and other parameters, measuring output voltage and current, monitoring temperatures, and so on.The following sections introduce key points in detail to develop a ±1700 Vp/1400 W switch-mode power amplifier, of which efficiency is expected to be no less than 85% with low distortion in the midfrequency range (100–1000 Hz).


### 2.1. Pulse Step Modulation

Brown Boveri Corporation presented pulse step modulation (PSM) and applied it broadly in short-wave transmitter and high-voltage power supply (HVPS) [9–11]. Figure 2 illustrates the schematic circuit and work principle of PSM-based HVPS to quadruple its output voltage of each converter.Figure 2
PSM-based HVPS. (a) Schematic and (b) principle.
(a)
(b)As shown in Figure2(a), a PSM-based HVPS basically consists of multiple (four in this example) power converters connected in series, which work in switch mode under the control of input reference signal (here taking semi-sine wave as an example). Each power converter has a separate low-voltage DC source U
s, a semiconductor switch S, and a free-wheeling diode D [12]. The diode is to provide a low impedance path when the corresponding converter is switched off, allowing current from other working converters to pass through. Regardless of voltage drops across diodes and switches, total output voltage U
o is simply equal to several times of unit step voltage U
s, depending on the number of switched-on power inverters. Obviously, actual output voltage is just a roughly stepwise approximation to the expected waveform, which is referred to as step modulation (SM). To further refine output, pulse width modulation (PWM) and LC components are adopted to smooth the transition from one step to the other. Taking Figure 2(a) as an example, let switches S1~S3 operate in SM mode and let switch S4 operate in PWM mode; the filtered output voltage U
o across the load is plotted as a blue solid line in Figure 2(b).As stated above, PSM consists of coarse SM and fine PWM. Figure2(b) shows that each SM operates at a rather low frequency the same as input reference signal. It is also noticed that PWM need to switch much faster than SM to achieve an accurate representation of the input signal. Following Nyquist theorem, PWM need to run at least twice the maximum input frequency, but actual design generally adopts a much higher ratio (typically 10 to 50) for reducing distortion [13]. In theory, high-frequency PWM can improve output waveform. However, switch loss increases as switching becomes faster. Generally, PWM will take a compromise between output waveform and switch loss, depending on the practical application.


### 2.2. Hybrid Converter Unit

As illustrated in Figure2, PSM-based HVPS can only produce unipolar voltage. In order to operate as an amplifier, circuit needs to be further modified. Conventional method is that every converter adopts full-bridge architecture, employing four switches and two groups switching signals to produce 0~±U
s. However, it will increase system cost and control complexity if many full-bridge converters are used to produce high voltage.In this paper, a hybrid multilevel converter was designed, in which information on amplitude and phase of input signal is separately modulated. As shown in Figure3, eight cascaded power converters (PC1~PC8) produce desired amplitude while full bridge (composed of Q1~Q4) controls phase. Compared with cascaded full-bridge converters, this hybrid architecture employs much fewer switches and control signals.Figure 3
Schematic of hybrid multilevel converter.Power converters PC1~PC8 are identical, except for corresponding to different switching signals. Each one consists of separated 220 V/3 A DC sourceU
s, semiconductor switch S, and free-wheeling diode D. In consideration of switching speed and power loss, semiconductor switches S1~S8 all use power MOSFETs, which have small on-state resistance. Free-wheeling diodes D1~D8 adopt fast recovery diodes. Intensive simulations and tests confirm that MOSFET and diode suffer the maximum potential difference of U
s in all situations, so many power MOSFETs available can be used, such as IRF840, 2SK1507, and FMV11N60E. 2SK1507 with a typical drain-source on-state resistance of R
D
S
(
o
n
) = 0.85 Ω was adopted. Diodes adopted MUR860 with a maximum instantaneous forward voltage drop V
F = 1.5 V. Switches S1~S7 and S8 are under the control of switching signals SM1~SM7 and PWM, respectively.The full bridge is built with four discrete IGBTs Q1~Q4, under the control of switching signals Phase+/Phase−. When the input signal is nonnegative, Q2 and Q3 are switched off simultaneously; meanwhile Q1 and Q4 are switched on simultaneously and vice versa. Although ZVS (Zero Voltage Switching) is applied, dead time is also inserted between commutations to avoid potential shoot-through risk. IGBTs adopted IXYS IXBH12N300 with a maximum saturation voltage dropV
C
E
(
s
a
t
) = 3.2 V.InductorL, capacitor C, and resistive load R make up a Butterworth low-pass filter (LPF) to recover the amplified output signal from high-voltage modulated waveform. Given load resistance and cut-off frequency, inductance and capacitance can be obtained by(1)
L
=
R
2
π
f
C
,
C
=
1
2
2
π
R
f
C
,where f
C denotes the cut-off frequency, f
C in Hertz, L in Henrys, C in Faradays, and R in Ohms, respectively.The LPF filter has a −3 dB cut-off frequency of 5 kHz, corresponding toR
=
1 kΩ, L
=
44 mH, and C
=
18 nF.


### 2.3. Digital PSM Modulator

Unlike carrier-based PWM that adopts analog modulation [14], we designed digital PSM modulator to generate SM and PWM switching signals by the following formula:(2)
M
n
=
fix
G
U
i
n
U
s
d
n
=
rem
G
U
i
n
U
s
Phase
+
=
ON
,
if
U
i
n
≥
0
OFF
,
if
U
i
n
<
0
Phase
-
=
ON
,
if
U
i
n
<
0
OFF
,
if
U
i
n
≥
0
n
=
t
1
,
t
2
,
…
,
t
n
,where U
i
n is the absolute amplitude of sampled input signal at moment t
n. G is predefined voltage gain; U
s is DC source voltage. Function f
i
x
· rounds the data towards zero, resulting in an integer M
(
n
), which is the number of power converters switched on between t
n and t
n
+
1. Function r
e
m
· retrieves the remainder after division, so d
(
n
) is a decimal, representing the “on” time of a power converter relative to sampling interval; that is, d
(
n
) determines the duty cycle of PWM switching signal (e.g., 0.50 is equal to 50%). P
h
a
s
e
+ and P
h
a
s
e
- record the phase information about sampled input signal, serving as the switching signals for full bridge.In other words, during sampling interval betweent
n and t
n
+
1, M
(
n
) power converters work in SM mode, and one power converter operates in PWM mode with a duty cycle of d
(
n
). Obviously, the switching frequency of PWM is equal to the sampling frequency of ADC. Here we adopted unipolar centre-aligned PWM, whose advantages and implementation could be referred to [15].


### 2.4. Software Simulation

The workflow of the above switching amplifier is demonstrated through simulation. For example, a sine wave of 1 kHz and ±1 Vp needs to be amplified by a voltage gain ofG
=
800. It is assumed that sampling frequency of ADC is 40 kSa/s, so that there will be 40 sampled points in a cycle, as shown in Figure 4(a). According to (2), if U
s
=
220 Vdc, it needs that three converters work in SM mode and one converter operates in PWM mode. Digital PSM modulator generates switching signals, as plotted in Figure 4(b). The unused converters are always switched off, which are not plotted in Figure 4(b). Figure 4(c) gives the modulated amplitude after amplification, measured between points a and b (marked in Figure 3). Figure 4(d) shows the output voltages after adding phase information and filtering, measured between points c and d (marked in Figure 3), in which the blue solid line represents modulated waveform after amplification, and the red dotted line is the final output voltage across load after LPF demodulation.Figure 4
Simulation of switching power amplifier. (a) Sampled input signal, (b) switching signals for power converters and full bridge, and ((c) and (d)) voltage waveforms measured between a-b and c-d points, respectively (points a-d marked in Figure3).
(a)
(b)
(c)
(d)In this simulation, zero-crossing points of input signal are all sampled by ADC. However, this may be not true in most actual situations. So ZVS will be applied to force all SM and PWM signals to be off at the moments of commutation, for example, whent
=
0.5,1.0,1.5, and 2.0 ms in Figure 4(b).It is important to note that IGBTs usually take more time to be switched on or off compared to MOSFETs due to finite switching speed. In order to protect full bridge at the moment of voltage phase alternation, proper dead time is added to ensure that short circuit will not happen between points a and b (marked in Figure3), which means that both phase control signals in Figure 4(b) are switched off during the dead time.


## 2.1. Pulse Step Modulation

Brown Boveri Corporation presented pulse step modulation (PSM) and applied it broadly in short-wave transmitter and high-voltage power supply (HVPS) [9–11]. Figure 2 illustrates the schematic circuit and work principle of PSM-based HVPS to quadruple its output voltage of each converter.Figure 2
PSM-based HVPS. (a) Schematic and (b) principle.
(a)
(b)As shown in Figure2(a), a PSM-based HVPS basically consists of multiple (four in this example) power converters connected in series, which work in switch mode under the control of input reference signal (here taking semi-sine wave as an example). Each power converter has a separate low-voltage DC source U
s, a semiconductor switch S, and a free-wheeling diode D [12]. The diode is to provide a low impedance path when the corresponding converter is switched off, allowing current from other working converters to pass through. Regardless of voltage drops across diodes and switches, total output voltage U
o is simply equal to several times of unit step voltage U
s, depending on the number of switched-on power inverters. Obviously, actual output voltage is just a roughly stepwise approximation to the expected waveform, which is referred to as step modulation (SM). To further refine output, pulse width modulation (PWM) and LC components are adopted to smooth the transition from one step to the other. Taking Figure 2(a) as an example, let switches S1~S3 operate in SM mode and let switch S4 operate in PWM mode; the filtered output voltage U
o across the load is plotted as a blue solid line in Figure 2(b).As stated above, PSM consists of coarse SM and fine PWM. Figure2(b) shows that each SM operates at a rather low frequency the same as input reference signal. It is also noticed that PWM need to switch much faster than SM to achieve an accurate representation of the input signal. Following Nyquist theorem, PWM need to run at least twice the maximum input frequency, but actual design generally adopts a much higher ratio (typically 10 to 50) for reducing distortion [13]. In theory, high-frequency PWM can improve output waveform. However, switch loss increases as switching becomes faster. Generally, PWM will take a compromise between output waveform and switch loss, depending on the practical application.


## 2.2. Hybrid Converter Unit

As illustrated in Figure2, PSM-based HVPS can only produce unipolar voltage. In order to operate as an amplifier, circuit needs to be further modified. Conventional method is that every converter adopts full-bridge architecture, employing four switches and two groups switching signals to produce 0~±U
s. However, it will increase system cost and control complexity if many full-bridge converters are used to produce high voltage.In this paper, a hybrid multilevel converter was designed, in which information on amplitude and phase of input signal is separately modulated. As shown in Figure3, eight cascaded power converters (PC1~PC8) produce desired amplitude while full bridge (composed of Q1~Q4) controls phase. Compared with cascaded full-bridge converters, this hybrid architecture employs much fewer switches and control signals.Figure 3
Schematic of hybrid multilevel converter.Power converters PC1~PC8 are identical, except for corresponding to different switching signals. Each one consists of separated 220 V/3 A DC sourceU
s, semiconductor switch S, and free-wheeling diode D. In consideration of switching speed and power loss, semiconductor switches S1~S8 all use power MOSFETs, which have small on-state resistance. Free-wheeling diodes D1~D8 adopt fast recovery diodes. Intensive simulations and tests confirm that MOSFET and diode suffer the maximum potential difference of U
s in all situations, so many power MOSFETs available can be used, such as IRF840, 2SK1507, and FMV11N60E. 2SK1507 with a typical drain-source on-state resistance of R
D
S
(
o
n
) = 0.85 Ω was adopted. Diodes adopted MUR860 with a maximum instantaneous forward voltage drop V
F = 1.5 V. Switches S1~S7 and S8 are under the control of switching signals SM1~SM7 and PWM, respectively.The full bridge is built with four discrete IGBTs Q1~Q4, under the control of switching signals Phase+/Phase−. When the input signal is nonnegative, Q2 and Q3 are switched off simultaneously; meanwhile Q1 and Q4 are switched on simultaneously and vice versa. Although ZVS (Zero Voltage Switching) is applied, dead time is also inserted between commutations to avoid potential shoot-through risk. IGBTs adopted IXYS IXBH12N300 with a maximum saturation voltage dropV
C
E
(
s
a
t
) = 3.2 V.InductorL, capacitor C, and resistive load R make up a Butterworth low-pass filter (LPF) to recover the amplified output signal from high-voltage modulated waveform. Given load resistance and cut-off frequency, inductance and capacitance can be obtained by(1)
L
=
R
2
π
f
C
,
C
=
1
2
2
π
R
f
C
,where f
C denotes the cut-off frequency, f
C in Hertz, L in Henrys, C in Faradays, and R in Ohms, respectively.The LPF filter has a −3 dB cut-off frequency of 5 kHz, corresponding toR
=
1 kΩ, L
=
44 mH, and C
=
18 nF.


## 2.3. Digital PSM Modulator

Unlike carrier-based PWM that adopts analog modulation [14], we designed digital PSM modulator to generate SM and PWM switching signals by the following formula:(2)
M
n
=
fix
G
U
i
n
U
s
d
n
=
rem
G
U
i
n
U
s
Phase
+
=
ON
,
if
U
i
n
≥
0
OFF
,
if
U
i
n
<
0
Phase
-
=
ON
,
if
U
i
n
<
0
OFF
,
if
U
i
n
≥
0
n
=
t
1
,
t
2
,
…
,
t
n
,where U
i
n is the absolute amplitude of sampled input signal at moment t
n. G is predefined voltage gain; U
s is DC source voltage. Function f
i
x
· rounds the data towards zero, resulting in an integer M
(
n
), which is the number of power converters switched on between t
n and t
n
+
1. Function r
e
m
· retrieves the remainder after division, so d
(
n
) is a decimal, representing the “on” time of a power converter relative to sampling interval; that is, d
(
n
) determines the duty cycle of PWM switching signal (e.g., 0.50 is equal to 50%). P
h
a
s
e
+ and P
h
a
s
e
- record the phase information about sampled input signal, serving as the switching signals for full bridge.In other words, during sampling interval betweent
n and t
n
+
1, M
(
n
) power converters work in SM mode, and one power converter operates in PWM mode with a duty cycle of d
(
n
). Obviously, the switching frequency of PWM is equal to the sampling frequency of ADC. Here we adopted unipolar centre-aligned PWM, whose advantages and implementation could be referred to [15].


## 2.4. Software Simulation

The workflow of the above switching amplifier is demonstrated through simulation. For example, a sine wave of 1 kHz and ±1 Vp needs to be amplified by a voltage gain ofG
=
800. It is assumed that sampling frequency of ADC is 40 kSa/s, so that there will be 40 sampled points in a cycle, as shown in Figure 4(a). According to (2), if U
s
=
220 Vdc, it needs that three converters work in SM mode and one converter operates in PWM mode. Digital PSM modulator generates switching signals, as plotted in Figure 4(b). The unused converters are always switched off, which are not plotted in Figure 4(b). Figure 4(c) gives the modulated amplitude after amplification, measured between points a and b (marked in Figure 3). Figure 4(d) shows the output voltages after adding phase information and filtering, measured between points c and d (marked in Figure 3), in which the blue solid line represents modulated waveform after amplification, and the red dotted line is the final output voltage across load after LPF demodulation.Figure 4
Simulation of switching power amplifier. (a) Sampled input signal, (b) switching signals for power converters and full bridge, and ((c) and (d)) voltage waveforms measured between a-b and c-d points, respectively (points a-d marked in Figure3).
(a)
(b)
(c)
(d)In this simulation, zero-crossing points of input signal are all sampled by ADC. However, this may be not true in most actual situations. So ZVS will be applied to force all SM and PWM signals to be off at the moments of commutation, for example, whent
=
0.5,1.0,1.5, and 2.0 ms in Figure 4(b).It is important to note that IGBTs usually take more time to be switched on or off compared to MOSFETs due to finite switching speed. In order to protect full bridge at the moment of voltage phase alternation, proper dead time is added to ensure that short circuit will not happen between points a and b (marked in Figure3), which means that both phase control signals in Figure 4(b) are switched off during the dead time.


## 3. Experimental Tests and Results

### 3.1. Prototype System

Based on the above introduction, a high-voltage switch-mode power amplifier is developed, as shown in Figure5.Figure 5
Photo of power amplifier system.From top to down, there are main distribution box, electronic case for control unit and auxiliary unit, electric case for hybrid converter unit, and two 4-channel AC-DC 220 V power sources in a 19-inch standard cabinet (600 mm × 600 mm × 1050 mm, W × D × H). A resistor of 1000 Ohms with cooling equipment is used as dummy load, laid outside the cabinet for facilitating heat dissipation.


### 3.2. Total Harmonic Distortion

Many factors in switching amplifier can cause distortion, such as power switches, nonlinearity of output LPF, DC source voltage fluctuations, dead time, and modulation technologies. As one of the most common and important features, total harmonic distortion (THD) is usually used to evaluate system distortion. Given that input signal is a sine wave, THD is most commonly defined as the ratio of the rms amplitude of a set of harmonic frequencies to that of fundamental frequency, which can be formulated as follows [16]:(3)
THD
=
U
2
2
+
U
3
2
+
⋯
+
U
n
2
U
1
,where U
1 denotes the rms voltage of fundamental frequency and U
n is the rms voltage of the nth harmonic frequency.Sine wave of 1 Vrms with frequency sweeping from 100 to 1000 Hz was used as input signal to investigate the prototype system. Figure6 shows the screenshots of output waveforms at frequencies of 100, 500, and 1000 Hz. On the oscilloscope display, the upper channel shows output voltage and the lower one is its corresponding fast Fourier transform (FFT). It is noticed that the FFT spectrum is plotted as magnitude in dB relative to 1 Vrms; the corresponding rms voltage is retrieved by(4)
U
n
=
1
0
d
B
n
/
20
,where d
B
n denotes the voltage gain relative to 1 Vrms at the nth harmonic frequency and U
n is the rms output voltage of the nth harmonic frequency.Figure 6
Oscilloscope screenshots of output voltage at frequencies of (a) 100 Hz (500 V/div, 2 ms/div), (b) 500 Hz (500 V/div, 500 us/div), and (c) 1000 Hz (500 V/div, 200 us/div).
(a)
(b)
(c)Table1 lists THD values measured at four different output power values. Without regard to individual measurement errors, it can be found that THD value increases as signal frequency rises and that THD value decreases as output power increases. It is not difficult to explain this phenomenon. With input signal sweeping from low frequency to high frequency, the sampled points in a single cycle reduce, resulting in output waveform not so smooth as before. When output power increases, signal-to-noise ratio is improved to a certain degree.Table 1
THD values of power amplifier system.
Freq. (Hz)
Output power (W)
300
650
960
1300
100
1.52%
1.47%
1.06%
1.04%
200
1.59%
1.53%
1.12%
1.05%
300
1.65%
1.52%
1.15%
1.04%
400
1.73%
1.58%
1.23%
1.05%
500
1.68%
1.58%
1.26%
1.09%
600
1.69%
1.60%
1.27%
1.19%
800
1.71%
1.66%
1.33%
1.30%
1000
1.77%
1.76%
1.40%
1.34%It is noticed that measured output power in Table1 is an average of output power values measured from 100 to 1000 Hz with a step size of 100 Hz, keeping input signal amplitude constant. Averaging is aimed at diminishing measurement error for high voltage. A typical example is shown in Figure 6. With the same input signal and amplification gain, peak and rms output voltages fluctuated irregularly at different frequencies.


### 3.3. The Maximum Output

To measure the maximum output power, sine wave of 1 kHz is used as input signal and its amplitude increases until output distortion reaches THD = 10%. Figure7 shows output voltage when amplifier outputs the maximum power of about 1500 W.Figure 7
High-voltage output waveform of clipping with THD = 10% (1 kV/div, 200 us/div).As shown in Figure7, waveform appears apparent clipping at the maximum output power value. For the sake of practicability, the maximum output voltage is limited to 3400 Vpp (a critical point of appearing voltage clipping), and the corresponding maximum output power is hence lowered to about 1400 W, estimated by(5)
P
o
=
1
8
R
U
pp
2
=
1
8
×
1000
×
3400
V
2
=
1445
W
a
t
t
s
.


### 3.4. Efficiency and Linearity

The efficiency corresponding to the output power in Table1 is listed in Table 2. P
c represents the whole power consumed by entire amplifier system; P
o is the output power measured on load. It is noticed that P
o is an average of output power values measured from 100 to 1000 Hz with a step size of 100 Hz, as the same reason explained in Section 3.2.Table 2
Efficiency of power amplifier system.
P
c (W)
P
o (W)
Efficiency
350
300
85.7%
712
650
91.3%
1022
960
93.9%
1361
1300
95.5%As for an amplifier, nonlinearity caused by gain variation will affect the waveform shape of analog output with respect to the corresponding analog input. Figure8 plots three groups of output versus input signal amplitude with a constant voltage gain of G
=
1000.Figure 8
Linearity of power amplifier system.As shown in Figure8, the output approximately follows a linear relationship relative to the input. The average voltage gains measured at frequencies of 400, 800, and 1000 Hz are 1027, 1036, and 1021, respectively. That is to say, this new developed high-voltage switch-mode power amplifier has a statistical linearity error less than 4%.


### 3.5. Automatic Protection

The running status of power amplifier system is under real-time surveillance, including output voltage, output current, output power, and system temperature. Once any alarm about overvoltage, overcurrent, or overtemperature is triggered, amplifier system will be shut down within 1 ms, as illustrated in Figure9. In the oscilloscope screenshot, Channel 1 records alarm signal, and Channel 2 is recording switching signal. If a failure occurs, falling edge of alarm signal is first detected and low level of alarm signal is then reconfirmed within about 600 us. If failure does happen, control unit will switch off all power converters one by one within 40 us.Figure 9
Oscilloscope screenshots of automatic protection. (a) CH1: failure alarm signal and CH2: first closed SM1 signal. (b) CH1: failure alarm and CH2: last closed PWM signal (2 V/div, 200 us/div).
(a)
(b)


### 3.6. Overall Comparison

Table3 gives an overall comparison between the new digital PSM-based switching amplifier and the existing analog PWM-based switching amplifier. The specification and performance of the latter are provided by our partner off campus, including modulation technology, circuit topology, output voltage and power, distortion, efficiency, and weight. For convenience, the two switching amplifiers are labelled as PSM-based amplifier and PWM-based amplifier, respectively.Table 3
Comparisons of two power amplifier systems.
Items
PSM-based amplifier
PWM-based amplifier
Modulation
Digital PSM
Analog PWM
Circuit topology
Multilevel
Half bridge
Power supplies
DC 220 V
DC ±80 V
Step-up transformer
No need
Need
Maximum output
±1700 Vp
±1500 Vp
1400 W
1200 W
THD∗
1.38%
0.85%
Efficiency∗
94.2%
82.5%
Gross weight
50 Kg
80 Kg
User interface
Touch LCD
LED indicators
∗The test condition is outputting 1000 Vrms sine at 1 KHz.In PWM-based switching amplifier, a high-speed analog comparator compares a triangular carrier wave of 300 KHz with the input signal to generate PWM switching signals. But, in PSM-based switching amplifier as described in Section2.4, the corresponding PWM switching signal is 40 KHz. High PWM switching frequency means that more sampled points are used to approximate the input signal, thus yielding smooth waveform and low distortion. Furthermore, PWM-based switching amplifier only adopts fast power MOSFETs in the half-bridge stage, while PSM-based switching amplifier adopts IGBTs with much higher blocking voltage in the full-bridge stage. But IGBT switches slower than MOSFET due to tail-current effect at turn-off. Therefore, PWM-based switching amplifier can generate better output waveform. However, the dependence of PWM-based amplifier on step-up transformer lowers overall efficiency and increases gross weight.


## 3.1. Prototype System

Based on the above introduction, a high-voltage switch-mode power amplifier is developed, as shown in Figure5.Figure 5
Photo of power amplifier system.From top to down, there are main distribution box, electronic case for control unit and auxiliary unit, electric case for hybrid converter unit, and two 4-channel AC-DC 220 V power sources in a 19-inch standard cabinet (600 mm × 600 mm × 1050 mm, W × D × H). A resistor of 1000 Ohms with cooling equipment is used as dummy load, laid outside the cabinet for facilitating heat dissipation.


## 3.2. Total Harmonic Distortion

Many factors in switching amplifier can cause distortion, such as power switches, nonlinearity of output LPF, DC source voltage fluctuations, dead time, and modulation technologies. As one of the most common and important features, total harmonic distortion (THD) is usually used to evaluate system distortion. Given that input signal is a sine wave, THD is most commonly defined as the ratio of the rms amplitude of a set of harmonic frequencies to that of fundamental frequency, which can be formulated as follows [16]:(3)
THD
=
U
2
2
+
U
3
2
+
⋯
+
U
n
2
U
1
,where U
1 denotes the rms voltage of fundamental frequency and U
n is the rms voltage of the nth harmonic frequency.Sine wave of 1 Vrms with frequency sweeping from 100 to 1000 Hz was used as input signal to investigate the prototype system. Figure6 shows the screenshots of output waveforms at frequencies of 100, 500, and 1000 Hz. On the oscilloscope display, the upper channel shows output voltage and the lower one is its corresponding fast Fourier transform (FFT). It is noticed that the FFT spectrum is plotted as magnitude in dB relative to 1 Vrms; the corresponding rms voltage is retrieved by(4)
U
n
=
1
0
d
B
n
/
20
,where d
B
n denotes the voltage gain relative to 1 Vrms at the nth harmonic frequency and U
n is the rms output voltage of the nth harmonic frequency.Figure 6
Oscilloscope screenshots of output voltage at frequencies of (a) 100 Hz (500 V/div, 2 ms/div), (b) 500 Hz (500 V/div, 500 us/div), and (c) 1000 Hz (500 V/div, 200 us/div).
(a)
(b)
(c)Table1 lists THD values measured at four different output power values. Without regard to individual measurement errors, it can be found that THD value increases as signal frequency rises and that THD value decreases as output power increases. It is not difficult to explain this phenomenon. With input signal sweeping from low frequency to high frequency, the sampled points in a single cycle reduce, resulting in output waveform not so smooth as before. When output power increases, signal-to-noise ratio is improved to a certain degree.Table 1
THD values of power amplifier system.
Freq. (Hz)
Output power (W)
300
650
960
1300
100
1.52%
1.47%
1.06%
1.04%
200
1.59%
1.53%
1.12%
1.05%
300
1.65%
1.52%
1.15%
1.04%
400
1.73%
1.58%
1.23%
1.05%
500
1.68%
1.58%
1.26%
1.09%
600
1.69%
1.60%
1.27%
1.19%
800
1.71%
1.66%
1.33%
1.30%
1000
1.77%
1.76%
1.40%
1.34%It is noticed that measured output power in Table1 is an average of output power values measured from 100 to 1000 Hz with a step size of 100 Hz, keeping input signal amplitude constant. Averaging is aimed at diminishing measurement error for high voltage. A typical example is shown in Figure 6. With the same input signal and amplification gain, peak and rms output voltages fluctuated irregularly at different frequencies.


## 3.3. The Maximum Output

To measure the maximum output power, sine wave of 1 kHz is used as input signal and its amplitude increases until output distortion reaches THD = 10%. Figure7 shows output voltage when amplifier outputs the maximum power of about 1500 W.Figure 7
High-voltage output waveform of clipping with THD = 10% (1 kV/div, 200 us/div).As shown in Figure7, waveform appears apparent clipping at the maximum output power value. For the sake of practicability, the maximum output voltage is limited to 3400 Vpp (a critical point of appearing voltage clipping), and the corresponding maximum output power is hence lowered to about 1400 W, estimated by(5)
P
o
=
1
8
R
U
pp
2
=
1
8
×
1000
×
3400
V
2
=
1445
W
a
t
t
s
.


## 3.4. Efficiency and Linearity

The efficiency corresponding to the output power in Table1 is listed in Table 2. P
c represents the whole power consumed by entire amplifier system; P
o is the output power measured on load. It is noticed that P
o is an average of output power values measured from 100 to 1000 Hz with a step size of 100 Hz, as the same reason explained in Section 3.2.Table 2
Efficiency of power amplifier system.
P
c (W)
P
o (W)
Efficiency
350
300
85.7%
712
650
91.3%
1022
960
93.9%
1361
1300
95.5%As for an amplifier, nonlinearity caused by gain variation will affect the waveform shape of analog output with respect to the corresponding analog input. Figure8 plots three groups of output versus input signal amplitude with a constant voltage gain of G
=
1000.Figure 8
Linearity of power amplifier system.As shown in Figure8, the output approximately follows a linear relationship relative to the input. The average voltage gains measured at frequencies of 400, 800, and 1000 Hz are 1027, 1036, and 1021, respectively. That is to say, this new developed high-voltage switch-mode power amplifier has a statistical linearity error less than 4%.


## 3.5. Automatic Protection

The running status of power amplifier system is under real-time surveillance, including output voltage, output current, output power, and system temperature. Once any alarm about overvoltage, overcurrent, or overtemperature is triggered, amplifier system will be shut down within 1 ms, as illustrated in Figure9. In the oscilloscope screenshot, Channel 1 records alarm signal, and Channel 2 is recording switching signal. If a failure occurs, falling edge of alarm signal is first detected and low level of alarm signal is then reconfirmed within about 600 us. If failure does happen, control unit will switch off all power converters one by one within 40 us.Figure 9
Oscilloscope screenshots of automatic protection. (a) CH1: failure alarm signal and CH2: first closed SM1 signal. (b) CH1: failure alarm and CH2: last closed PWM signal (2 V/div, 200 us/div).
(a)
(b)


## 3.6. Overall Comparison

Table3 gives an overall comparison between the new digital PSM-based switching amplifier and the existing analog PWM-based switching amplifier. The specification and performance of the latter are provided by our partner off campus, including modulation technology, circuit topology, output voltage and power, distortion, efficiency, and weight. For convenience, the two switching amplifiers are labelled as PSM-based amplifier and PWM-based amplifier, respectively.Table 3
Comparisons of two power amplifier systems.
Items
PSM-based amplifier
PWM-based amplifier
Modulation
Digital PSM
Analog PWM
Circuit topology
Multilevel
Half bridge
Power supplies
DC 220 V
DC ±80 V
Step-up transformer
No need
Need
Maximum output
±1700 Vp
±1500 Vp
1400 W
1200 W
THD∗
1.38%
0.85%
Efficiency∗
94.2%
82.5%
Gross weight
50 Kg
80 Kg
User interface
Touch LCD
LED indicators
∗The test condition is outputting 1000 Vrms sine at 1 KHz.In PWM-based switching amplifier, a high-speed analog comparator compares a triangular carrier wave of 300 KHz with the input signal to generate PWM switching signals. But, in PSM-based switching amplifier as described in Section2.4, the corresponding PWM switching signal is 40 KHz. High PWM switching frequency means that more sampled points are used to approximate the input signal, thus yielding smooth waveform and low distortion. Furthermore, PWM-based switching amplifier only adopts fast power MOSFETs in the half-bridge stage, while PSM-based switching amplifier adopts IGBTs with much higher blocking voltage in the full-bridge stage. But IGBT switches slower than MOSFET due to tail-current effect at turn-off. Therefore, PWM-based switching amplifier can generate better output waveform. However, the dependence of PWM-based amplifier on step-up transformer lowers overall efficiency and increases gross weight.


## 4. Conclusion

In this paper, a switch-mode power amplifier based on digital pulse step modulation and hybrid multilevel converter is designed to directly produce high-voltage output without the aid of step-up transformer.Compared with available PWM-based switching amplifier coupled with a step-up transformer, this new developed system can provide output power up to 1400 Watts and peak voltage up to ±1700 Volts with encouraging efficiency and portability. The major advantages are its hybrid architecture and digital modulation. When directly generating high-voltage output, a lot of control signals and power switches are cut down by modulating the information on amplitude and phase of input signal separately.However, there is further work to improve this design.Firstly, switching frequency needs to be increased for more practical applications. However, MOSFETs in high-voltage converter cannot switch at a frequency as high (300 kHz or above) as they do in PWM-based audio amplifier, because this will lead to serious overshoot and EMI problems. Thus, more elaborate modulation scheme needs to be considered, such as phase-shifting modulation technologies.Secondly, more intelligent strategies should be adopted. For example, redundant power converters can timely replace the failed ones without shutdown. If there is no usable power converter, amplifier will appropriately lower output voltage to prevent serious distortion.



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*Source: 3982594-2016-09-20.xml*