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The Mathematical Model of A Class-D Power Amplifier Based on Analog Second-order Sigma-Delta Modulation
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Xuerui SHENG1, 2, Zhaojun WANG1, 2, Chang ZHANG1, 2
Journal of Power Supply | 2026, 24(5) : 28 - 38
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Journal of Power Supply | 2026, 24(5): 28-38
• Power Converter Modeling and Control •
The Mathematical Model of A Class-D Power Amplifier Based on Analog Second-order Sigma-Delta Modulation
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Xuerui SHENG1, 2, Zhaojun WANG1, 2, Chang ZHANG1, 2
Affiliations
  • 1.Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
  • 2.Science and Technology on Underwater Acoustic Antagonizing Laboratory, Shanghai 201108, China
Published: 2026-05-30 doi: 10.13234/j.issn.2095-2805.2026.5.28
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For an analog second-order Sigma-Delta modulation class-D power amplifier circuit, the continuous domain mathematical model and discrete time domain iterative mathematical model are constructed. For the power amplifier circuit, the continuous domain mathematical model is derived, which shows that the principle of the second order sigma-delta modulation circuit is self-excited oscillation based on positive feedback, so as to realize the output switching signal. Since the continuous domain mathematical model can only obtain the self-excited oscillation frequency, the continuous domain mathematical model is discretized to obtain the discrete time domain iterative mathematical model. This model can calculate the switching frequency value of any input signal and analyze the stability conditions of second-order Sigma-Delta modulation circuit. The experimental results show that the error between the theoretical switching frequency calculated based on the mathematical model and the experimental value is less than 14%, which verifies the correctness of the mathematical model.

Second order Sigma-Delta modulation  /  class-D power amplifier  /  mathematical model  /  switching frequency
盛学锐, 王昭君, 张昌. 基于模拟二阶Sigma-Delta调制D类功放数学模型. 电源学报, 2026 , 24 (5) : 28 -38 . DOI: 10.13234/j.issn.2095-2805.2026.5.28
Xuerui SHENG, Zhaojun WANG, Chang ZHANG. The Mathematical Model of A Class-D Power Amplifier Based on Analog Second-order Sigma-Delta Modulation[J]. Journal of Power Supply, 2026 , 24 (5) : 28 -38 . DOI: 10.13234/j.issn.2095-2805.2026.5.28
Funding
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  • Shanghai Sailing Program(23YF1451500)
Appendix
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Year 2026 volume 24 Issue 5
35
8
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Article Info
doi: 10.13234/j.issn.2095-2805.2026.5.28
  • Receive Date：2024-01-19
  • Online Date：2026-10-29
  • Published：2026-05-30
Article Data
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History
  • Received：2024-01-19
  • Revised：2024-03-08
  • Accepted：2024-04-06
Funding
Shanghai Sailing Program(23YF1451500)
Affiliations
    1.Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
    2.Science and Technology on Underwater Acoustic Antagonizing Laboratory, Shanghai 201108, China
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栓菌属 Trametes 5 2.39
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