Abstract：To keep track of the requirements of driving the high-precision electromechanical system in semiconductor manufacturing, the SNR of the amplifier output current needs to increase by 20 dB every five years. Compared to linear power amplifiers, switching power amplifiers have superior potential in power and efficiency. High-frequency switching power amplifiers can reduce voltage and current distortion. However, the limited digital computation causes a conflict between high switch frequency and high-duty cycle resolution. Therefore, this paper analyzes the noise shaping principles in the pulse-width modulation process and proposes a simple design method for low-order FIR noise shaping filters, which provides sufficient noise attenuation and passband flatness with the least computational cost. Firstly, the signal processing in switch power amplifiers is demonstrated. Quantization noise in digital PWM modulation causes a trade-off between high SNR and high frequency, assumed to be uniformly distributed white noise and independent of the input. The improvement of the SNR via noise shaping is analyzed accordingly. Secondly, an error feedback structure is used to obtain the quantization noise as high-bit digital signals, separating the transmission of target signals and quantization noise shaping processing. Furthermore, the minimum phase and stability constraints of noise-shaping filters are derived. Thirdly, four different types of all-pole IIR filters are derived by the Gegenbauer polynomial. Their inverse forms are FIR filters with the origin cutoff frequency and shaping attenuation as well as the minimum phase and coefficient characteristics. Finally, the noise attenuation requirements are met by selecting the filter order reasonably. The inverse all-pole filter method reduces the complexity of the noise-shaping filter design and enhances the ability to control the ripple in the noise-shaping band. Simulation and experiment have shown that the proposed method achieves a large noise attenuation in the same order as the LMI method and has better ripple control. When PWM modulating at 200 kHz with a resolution lower than 9-bit, a 4th-order FIR noise shaping filter increases the SNR of the reference signal from 62.30 dB to 99.04 dB within a bandwidth of 10 kHz. After the noise shaping, the power level of quantization noise in the target frequency band reduces from -43.12 dB to -81.27 dB, and the quantization noise generated by PWM has been eliminated. In addition to the SNR improvement, the error feedback structure preserves the phase and amplitude characteristics of the target signal. The following conclusions can be drawn: (1) Quantization noise can be modeled as uniform white noise and extracted through an error feedback structure, effectively separating the quantization noise and the control signal in digital signal processing. (2) The inverse all-pole filter makes the FIR noise shaping filter conform to the constraints of the first fixed coefficient and minimum phase, which is an expeditious method for low-cost noise shaping design in high-frequency PWM. (3) Performing noise shaping in PWM modulation can recover SNR loss caused by coarse quantization in modulation, but the best SNR still depends on the analog-to-digital conversion.
陈福祥, 刘凯, 胡傲奇, 张昊, 赵烁, 曾理湛. 基于逆全极点滤波器的高频PWM噪声整形方法[J]. 电工技术学报, 2024, 39(10): 3129-3140.
Chen Fuxiang, Liu Kai, Hu Aoqi, Zhang Hao, Zhao Shuo, Zeng Lizhan. Noise Shaping Method for High Frequency PWM Based on Inverse All Pole Filter. Transactions of China Electrotechnical Society, 2024, 39(10): 3129-3140.
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