Harmonic modeling method of power amplifier

Abstract

A harmonic modeling method of a power amplifier solves the problem that a traditional modeling method is not suitable for harmonic modeling analysis of a high-switching-frequency topological structure, and comprises the following steps: obtaining baseband harmonic and sideband harmonic caused by modulation nonlinearity according to the number of parallel half bridges, a modulation wave function and a carrier function in the power amplifier; according to the topological structure of the power amplifier, obtaining a circuit equation of the topological structure in the dead-zone time period; calculating the current amplitude envelope of the resonant inductor; and calculating a voltage error caused by the dead-zone time period according to the calculated current amplitude envelope in combination with a circuit equation of the dead-zone time period, performing Fourier decomposition on the voltage error to obtain distortion harmonics caused by the dead-zone time period of the power amplifier, and obtaining total harmonics in combination with the obtained baseband harmonics and sideband harmonics. According to the invention, the switching frequency when the total harmonic distortion is the lowest can be obtained through modeling.

Description

TECHNICAL FIELD

[0001] The application relates to a high-precision harmonic modeling method of a power amplifier, and belongs to the technical field of precise modeling of power amplifiers. BACKGROUND

[0002] Switching power amplifiers (such as class D, class E, etc.) are widely used in the fields of audio, communication, industrial driving, etc. due to their high efficiency. The core principle is that through the conduction and shutdown of the power switch tube, the resonant circuit modulates the input signal into a high-frequency pulse width modulation (PWM) waveform, and then the output LC filter demodulates, restores and amplifies the original signal to output to the load. Ideally, the output after ideal filtering should have a perfect linear relationship with the input signal. However, in actual application, various nonlinear factors will introduce harmonic distortion, causing the total harmonic distortion (THD) of the output signal to increase, which seriously affects the output accuracy and fidelity of the power amplifier.

[0003] In order to improve the output accuracy, in the case of a given output filter design, a common technical means is to increase the switching frequency of the power switch tube. In theory, increasing the switching frequency can make the fundamental component and the high-order harmonic component of the PWM waveform separate further in the frequency domain, so that the LC filter can more effectively filter out the switching harmonics and reduce the THD of the output signal.

[0004] However, as the switching frequency continues to increase, a nonlinear factor that has little impact at lower frequencies, dead time, will have a dramatic negative impact. Dead time is a common shutdown time set to prevent short circuiting of the upper and lower bridge arms of the bridge circuit. During this extremely short time, the output current flows through the body diode or external freewheeling diode of the power tube for freewheeling, causing the actual output PWM voltage pulse width to deviate from the ideal drive signal. This deviation will introduce nonlinear distortion, and the harmonic components generated are closely related to the switching frequency. At low switching frequencies, the harmonic distortion caused by the dead time effect accounts for a small proportion and can usually be ignored or treated as a secondary factor; but at high switching frequencies, due to the significant increase in the relative proportion of the dead time within each switching period, the voltage error accumulation effect caused by the dead time becomes non-negligible, and even becomes the dominant nonlinear factor limiting the improvement of output accuracy.

[0005] Currently, most traditional harmonic modeling methods focus on harmonic distortion caused by the saturation voltage drop of power devices, on-resistance, and the nonlinearity of PWM modulation itself. These methods are usually based on modifications to ideal switching models, but they generally have a limitation: they either completely ignore the effect of dead time or simply treat it as a fixed voltage or time offset, failing to deeply reveal the complex and nonlinear influence mechanism of dead time on the output spectrum under the coupling effect of factors such as switching frequency and load current phase. Therefore, traditional modeling methods are not suitable for harmonic modeling and analysis of high-switching-frequency topologies. Summary of the Invention

[0006] To address the problem that traditional modeling methods are not suitable for harmonic modeling and analysis of high switching frequency topologies, this application provides a high-precision harmonic modeling method for power amplifiers.

[0007] This application provides a harmonic modeling method for a power amplifier, comprising:

[0008] S1. Based on the number of parallel half-bridges, modulation wave function, and carrier function in the power amplifier, obtain the baseband harmonics and sideband harmonics caused by modulation nonlinearity.

[0009] S2. Based on the topology of the power amplifier, obtain the circuit equation of the topology during the dead time period.

[0010] S3. Calculate the current amplitude envelope of the resonant inductor;

[0011] S4. Based on the calculated current amplitude envelope and the circuit equation of the dead time period, calculate the voltage error caused by the dead time period. Perform Fourier decomposition on the voltage error to obtain the distortion harmonics of the power amplifier caused by the dead time period. Combine the obtained baseband harmonics and sideband harmonics to obtain the total harmonics.

[0012] Preferably, the power amplifier is an ACRP power amplifier, and the voltage error caused by the dead time period in S4 is... ,in It represents the product of voltage error caused by a non-ideal falling edge and time during one switching cycle. It represents the product of voltage error caused by a non-ideal rising edge and time during a switching cycle.

[0013] As a preferred option

[0014]

[0015]

[0016] Among them, U dcThis refers to the bus voltage.

[0017] Angular frequency, , Indicates the filter inductance. Indicates resonant inductance. Indicates the resonant capacitance;

[0018] Characteristic impedance, ;

[0019] The upper envelope of the current amplitude flowing through the half-bridge resonant inductor;

[0020] The lower envelope of the current amplitude flowing through the half-bridge resonant inductor.

[0021] As a preferred option, distortion harmonics caused by dead time intervals for:

[0022]

[0023] in, Indicates the switching frequency. Indicates the carrier frequency. Indicates the switching cycle. It is a positive integer. The fundamental angular frequency, For time.

[0024] As a preferred option, the total harmonics are:

[0025]

[0026] in, This represents the modulation ratio, where N is the number of parallel half-bridges, m is the carrier multiple, and n is the modulating wave multiple. Denotes the nth order Bessel function of the first kind. It is the switching angular frequency.

[0027] Preferably, the power amplifier is a half-bridge power amplifier. In S4, the voltage error caused by the dead time period is... ,in It is the product of voltage error caused by a non-ideal rising or falling edge and time during a switching cycle. It represents the product of voltage error caused by dead time and time in a switching cycle.

[0028] As a preferred option

[0029]

[0030] in, Indicates the bus voltage;

[0031] To represent the resonant capacitance;

[0032] Indicates dead time;

[0033] To calculate the upper or lower envelope of the current amplitude of the resonant inductor for a current loop based on a power amplifier.

[0034] As a preferred option, distortion harmonics caused by dead time intervals for

[0035]

[0036] in, Indicates the switching frequency. Indicates the carrier frequency. Indicates the switching cycle. It is a positive integer. The fundamental angular frequency, For time.

[0037] As a preferred option, the total harmonics are:

[0038]

[0039] in, This represents the modulation ratio, where m is the carrier multiple and n is the modulating multiple. Denotes the nth order Bessel function of the first kind. It is the switching angular frequency.

[0040] Preferably, the method further includes:

[0041] S5. Input the obtained baseband harmonics, sideband harmonics, and distortion harmonics caused by the dead time period into the transfer function of the filter under load to obtain the amplitude of each harmonic. Calculate the total harmonic distortion rate based on the amplitude of each harmonic to obtain the harmonic distortion of the output voltage. Further obtain the switching frequency corresponding to the lowest total harmonic distortion rate.

[0042] The beneficial effects of this application are that it considers the effects of dead time and resonance at high switching frequencies, and the modeling is accurate. It is applicable to traditional half-bridge power amplifier topologies and topologies based on auxiliary commutated resonant poles (ACRP). The harmonic expression for the entire frequency band and the switching frequency at which the total harmonic distortion is minimized can be obtained through modeling. Attached Figure Description

[0043] Figure 1 For auxiliary commutator resonant power amplifier;

[0044] Figure 2 It is a traditional half-bridge power amplifier;

[0045] Figure 3 Schematic diagram of ACRP power amplifier switching waveform and dead-time effect

[0046] Figure 4 This is a schematic diagram of the switching waveform and dead-time effect of a conventional topology power amplifier.

[0047] Figure 5 The curve showing the relationship between THD and switching frequency in a traditional half-bridge topology;

[0048] Figure 6 FFT analysis of traditional switching frequency circuits at 5kHz, 90kHz, 700kHz and 1000kHz;

[0049] Figure 7 The curve showing the relationship between THD and switching frequency in ACRP topology is shown, with the horizontal axis representing the switching frequency.

[0050] Figure 8 FFT analysis of ACRP scheme switching frequency circuits at 5kHz, 12kHz, 200kHz and 600kHz. Detailed Implementation

[0051] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0053] The present application will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the application.

[0054] The harmonic modeling method for the power amplifier in this embodiment includes:

[0055] Step 1: Obtain the baseband harmonics and sideband harmonics caused by modulation nonlinearity based on the number of parallel half-bridges, modulation wave function, and carrier function in the power amplifier.

[0056] Specifically, the baseband and sideband harmonics caused by modulation nonlinearity are calculated based on the number of parallel half-bridges in the switching power amplifier, the modulation wave, and the carrier function. When the modulation wave is a sinusoidal wave and the carrier wave is a triangular wave, the baseband harmonic expression obtained by performing a double Fourier decomposition of the output using the modulation wave function and the carrier function is as follows:

[0057] (1)

[0058] Among them, U dc Where N is the bus voltage, m is the number of parallel half-bridges, and n is the carrier multiple and the modulation multiple. It is the fundamental angular frequency. It is the switching angular frequency. Denotes the nth order Bessel function of the first kind. Indicates the modulation ratio;

[0059] The expression for sideband harmonics is:

[0060] (2)

[0061] Step 2: Based on the topology of the power amplifier, obtain the circuit equation of the topology during the dead time period;

[0062] Based on the fact that resonance occurs during the dead time period, the circuit equation for the dead time period is obtained from the resonance equation of the power amplifier topology. This embodiment can accurately describe the dynamically changing dead voltage modulated by the resonance process at high frequencies through the coupled resonance equation and the dead voltage equation. This embodiment specifically describes the ACRP power amplifier and the traditional half-bridge power amplifier respectively.

[0063] For ACRP power amplifiers, combined Figure 3 In the topology circuit of the ACRP power amplifier, resonance will occur during the dead time period. First, based on the resonant inductance and its value, the following calculations are performed: and The characteristic impedance of the circuit during resonance process and angular frequency :

[0064] (3)

[0065] Indicates resonant inductance;

[0066] Indicates the filter inductance;

[0067] Indicates the resonant capacitance;

[0068] Based on the circuit structure and current flow direction exist At time t, the resonance equation of the circuit is:

[0069] (4)

[0070] The upper envelope of the current amplitude flowing through the half-bridge resonant inductor;

[0071] exist At time t, the resonance equation of the circuit is:

[0072] (5)

[0073] Meanwhile, the soft-switching condition that needs to be satisfied to ensure that the equation has a solution is expressed as follows:

[0074] (6)

[0075] This represents the current flowing through the half-bridge resonant inductor.

[0076] The resonance equation of the above circuit is used as the circuit equation of the ACRP power amplifier during the dead time period.

[0077] For traditional half-bridge power amplifiers, combined with Figure 4 Similarly, in the topology circuit, At time t, the resonance equation of the circuit is:

[0078] (7)

[0079] Step 3: Calculate the current amplitude envelope of the resonant inductor;

[0080] Specifically, the peak envelope of the inductor current is calculated based on the current loop of the circuit, which is used in subsequent steps to determine the voltage rise or fall time based on the current, and further used to determine the dead time period.

[0081] For ACRP power amplifiers, The amplitude envelope is calculated using common-mode current and differential-mode current, with no ripple in the common-mode current. The expression is:

[0082] (8)

[0083] This represents the ratio of the modulation amplitude to the carrier amplitude at each moment.

[0084] For load resistance;

[0085] The expression for common-mode current ripple is:

[0086] (9)

[0087] For switching cycles;

[0088] The expression for differential mode current is:

[0089] (10)

[0090] The magnitude of the current flowing through the half-bridge resonant inductor is expressed as:

[0091] (11)

[0092] The lower envelope of the current amplitude flowing through the half-bridge resonant inductor is expressed as:

[0093] (12)

[0094] For a traditional half-bridge power amplifier topology, the equation during the rising phase of the resonant inductor current is as follows:

[0095] (13)

[0096] To represent the resonant inductor current;

[0097] Output voltage to the load

[0098] The amplitude of the resonant inductor current ripple can be obtained as follows:

[0099] (14)

[0100] Indicates the initial current;

[0101] Indicates resonant inductance;

[0102] The upper envelope of the current amplitude of the resonant inductor is:

[0103] (15)

[0104] The lower envelope of the current amplitude of the resonant inductor is:

[0105] (16)

[0106] Step 4: Calculate the voltage error caused by the dead time period based on the calculated current amplitude envelope and the circuit equation of the dead time period. Perform Fourier decomposition on the voltage error to obtain the distortion harmonics of the power amplifier caused by the dead time period. Combine the obtained baseband harmonics and sideband harmonics to obtain the total harmonics.

[0107] Not all dead time intervals allow for an instantaneous voltage change at the output point; sometimes, it requires charging and discharging the resonant capacitor. The specific time required for the voltage to change from one state to another is calculated; this time is the voltage rise time or fall time. In this application, the voltage transition within the dead time interval is a dynamic process, rather than the instantaneous completion or fixed error assumed in traditional models.

[0108] The voltage error caused by the dead time period is determined by multiplying the voltage error caused by the voltage rise time or fall time by the time. Fourier decomposition is performed on the voltage error to obtain the amplitude and phase of each harmonic component contained in the voltage error signal. Furthermore, the harmonic distortion caused by the dead time is obtained, realizing the key transformation from time domain error to frequency domain harmonic components, and obtaining the accurate frequency domain expression of the dead time effect.

[0109] Figure 3 The switching waveforms of the ACRP power amplifier and the voltage error caused by the dead time are given. The voltage error is caused only by the non-ideal turn-on and turn-off of the switching transistor. Approximating the voltage error as a triangle, the voltage error in one switching cycle is A1 + A2. A1 represents the product of the voltage error caused by the non-ideal falling edge and time in one switching cycle; A2 represents the product of the voltage error caused by the non-ideal rising edge and time in one switching cycle.

[0110] For ACRP power amplifiers, based on circuit equations and calculations... upper envelope of amplitude Voltage error Time expression According to equations (4) and (11), we can solve for:

[0111] (17)

[0112] Based on the circuit equations and calculations The lower envelope of the amplitude Voltage error Time expression According to equations (5) and (12), we can solve for:

[0113] (18)

[0114] The area expression is:

[0115] (19)

[0116] The area expression is:

[0117] (20)

[0118] The average voltage error over half a cycle is

[0119] (twenty one)

[0120] right Fourier decomposition yields the distortion harmonics caused by the dead time interval.

[0121] (twenty two)

[0122] in, Indicates the switching frequency; Indicates the carrier frequency; Indicates the switching cycle; It is a positive integer; The fundamental angular frequency; For time.

[0123] The output voltage at point C of the ACRP topology is obtained by combining formulas (1), (2), and (22). That is, the total harmonics, expressed as:

[0124] (twenty three)

[0125] Equation (23) is the total output harmonic obtained by superimposing multiple distortion sources.

[0126] Figure 4 The switching waveforms of the traditional topology and the voltage error caused by the dead time are given, among which... It is the product of voltage error caused by a non-ideal rising or falling edge and time during a switching cycle. It represents the product of voltage error caused by dead time and time in a switching cycle;

[0127] For a traditional half-bridge power amplifier topology, substituting equation (15) into equation (7) during the positive half-cycle of the modulation wave yields the voltage fall time as follows:

[0128] (twenty four)

[0129] Substituting equation (16) into equation (7) during the negative half-cycle of the modulated wave, the voltage fall time is obtained as follows:

[0130] (25)

[0131] The voltage drop time within the positive or negative half-cycle of the modulation wave can be used to calculate... :

[0132] (26)

[0133] :

[0134] (27)

[0135] Since the error caused by the rise time is very small for traditional topologies, the calculation can be simplified, and the error caused by the dead time can be directly calculated. The total average voltage error caused by the dead time at point A within half a modulation wave period is:

[0136] (28)

[0137] right Fourier decomposition yields the total harmonic components caused by the dead time:

[0138] (29)

[0139] Combining formulas (1), (2), and (29), the expression for the output voltage at point A in the traditional topology is:

[0140] (30)

[0141] This application successfully reproduces the curve of THD decreasing and then increasing with switching frequency by accurately quantifying dead zone harmonics and combining it with traditional baseband and sideband harmonic models. It can predict and find the optimal switching frequency that minimizes total harmonic distortion through theoretical modeling.

[0142] Step 5: Input the obtained baseband harmonics, sideband harmonics, and distortion harmonics caused by the dead time period into the transfer function of the filter under load to obtain the amplitude of each harmonic. Calculate the total harmonic distortion rate based on the amplitude of each harmonic to obtain the harmonic distortion of the output voltage. Further obtain the switching frequency corresponding to the lowest total harmonic distortion rate.

[0143] The specific operation is as follows: Calculate the transfer function of the output voltage based on the load and LC filter parameters. The transfer function expression of the LC filter under a purely resistive load is:

[0144] (31)

[0145] in, This represents the Laplace transform of the output voltage;

[0146] Represents the Laplace transform of the input voltage;

[0147] This indicates the capacitance value of the LC filter;

[0148] Represents a complex frequency variable;

[0149] The final output voltage amplitude is obtained by passing each harmonic component through the filter's transfer function, as expressed by the expression.

[0150] (32)

[0151] in, This represents the amplitude of the harmonic input transfer function;

[0152] This indicates the amount of attenuation after passing through the transfer function at that frequency;

[0153] Indicates the harmonic frequency.

[0154] Figure 5 Bus voltage Udc = 150V, modulation ratio M = 0.5, fundamental angular frequency The filter inductor L = 10e-6H, the filter capacitor C = 0.22e-6F, and the load resistance R1 = 9Ω are used to plot the relationship between THD and switching frequency in the range of 5kHz-1000kHz. The orange curve represents the harmonic distortion caused by the switching frequency, the blue curve represents the harmonic distortion caused by the dead zone effect, and the red curve represents the total harmonic distortion. In the curve, the output distortion first rises, then falls, and then rises again. The switching frequency at which THD is lowest is taken at 700kHz.

[0155] Figure 6 A circuit model was built and FFT analysis was performed on key nodes. The results show that (a) the THD is 267.1% when fs = 5kHz, (b) the THD is 315.63% when fs = 90kHz, (c) the THD is 10.2% when fs = 600kHz, and (d) the THD is 10.60% when fs = 1000kHz. Considering the dead zone, the harmonic modeling method is consistent with the simulation results for traditional topologies.

[0156] Figure 7With N=6, resonant inductance Ld = 15e-6H, and resonant capacitance Coss = 200e-12F, under the condition of soft switching and considering dead time, the relationship curves between THD and switching frequency in the range of 5kHz-600kHz were established. The orange curve represents the harmonic distortion caused by the switching frequency, the blue curve represents the harmonic distortion caused by the dead time effect, and the red curve represents the total harmonic distortion. The switching frequency at which THD is lowest is taken at 200kHz.

[0157] Figure 8 The data obtained by FFT analysis of several key nodes through the constructed simulation circuit model are shown in the figure. The results show that (a) the THD is 41.09% when fs = 5kHz, (b) the THD is 43.16% when fs = 12kHz, (c) the THD is 0.32% when fs = 200kHz, and (d) the THD is 2.66% when fs = 600kHz. The harmonic modeling method is consistent with the simulation analysis.

[0158] While this application has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A harmonic modeling method for a power amplifier, characterized in that, include: S1. Based on the number of parallel half-bridges, modulation wave function, and carrier function in the power amplifier, obtain the baseband harmonics and sideband harmonics caused by modulation nonlinearity. S2. Based on the topology of the power amplifier, obtain the circuit equation of the topology during the dead time period. S3. Calculate the current amplitude envelope of the resonant inductor; S4. Based on the calculated current amplitude envelope and the circuit equation of the dead time period, calculate the voltage error caused by the dead time period. Perform Fourier decomposition on the voltage error to obtain the distortion harmonics of the power amplifier caused by the dead time period. Combine the obtained baseband harmonics and sideband harmonics to obtain the total harmonics.

2. The harmonic modeling method for a power amplifier according to claim 1, characterized in that, The power amplifier is an ACRP power amplifier. The voltage error in S4 due to the dead time period is... ,in It represents the product of voltage error caused by a non-ideal falling edge and time during one switching cycle. It represents the product of voltage error caused by a non-ideal rising edge and time during a switching cycle.

3. The harmonic modeling method for a power amplifier according to claim 2, characterized in that, Among them, U dc This refers to the bus voltage. Angular frequency, , Indicates the filter inductance. Indicates resonant inductance. Indicates the resonant capacitance; Characteristic impedance, ; The upper envelope of the current amplitude flowing through the half-bridge resonant inductor; The lower envelope of the current amplitude flowing through the half-bridge resonant inductor.

4. The harmonic modeling method for a power amplifier according to claim 3, characterized in that, Distortion harmonics caused by dead time period for: in, Indicates the switching frequency. Indicates the carrier frequency. Indicates the switching cycle. It is a positive integer. The fundamental angular frequency, For time.

5. The harmonic modeling method for a power amplifier according to claim 4, characterized in that, The total harmonics are: in, This represents the modulation ratio, where N is the number of parallel half-bridges, m is the carrier multiple, and n is the modulating wave multiple. Denotes the nth order Bessel function of the first kind. It is the switching angular frequency.

6. The harmonic modeling method for a power amplifier according to claim 1, characterized in that, The power amplifier is a half-bridge power amplifier. In S4, the voltage error caused by the dead time period is... ,in It is the product of voltage error caused by a non-ideal rising or falling edge and time during a switching cycle. It represents the product of voltage error caused by dead time and time in a switching cycle.

7. The harmonic modeling method for a power amplifier according to claim 6, characterized in that, in, Indicates the bus voltage; To represent the resonant capacitance; Indicates dead time; To calculate the upper or lower envelope of the current amplitude of the resonant inductor for a current loop based on a power amplifier.

8. The harmonic modeling method for a power amplifier according to claim 7, characterized in that, Distortion harmonics caused by dead time period for in, Indicates the switching frequency. Indicates the carrier frequency. Indicates the switching cycle. It is a positive integer. The fundamental angular frequency, For time.

9. The harmonic modeling method for a power amplifier according to claim 8, characterized in that, The total harmonics are: in, This represents the modulation ratio, where m is the carrier multiple and n is the modulating multiple. Denotes the nth order Bessel function of the first kind. It is the switching angular frequency.

10. The harmonic modeling method for a power amplifier according to claim 1, characterized in that, The method further includes: S5. Input the obtained baseband harmonics, sideband harmonics, and distortion harmonics caused by the dead time period into the transfer function of the filter under load to obtain the amplitude of each harmonic. Calculate the total harmonic distortion rate based on the amplitude of each harmonic to obtain the harmonic distortion of the output voltage. Further obtain the switching frequency corresponding to the lowest total harmonic distortion rate.

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