基于逆全极点滤波器的高频PWM噪声整形方法

doi:10.19595/j.cnki.1000-6753.tces.230307

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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.

Key words： Switch mode power amplifier high frequency PWM noise shaping all-pole filter signal- to-noise ratio (SNR)

Received: 16 March 2023 Published: 07 June 2024

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	Chen Fuxiang
	Liu Kai
	Hu Aoqi
	Zhang Hao
	Zhao Shuo
	Zeng Lizhan

Cite this article:

Chen Fuxiang,Liu Kai,Hu Aoqi等. Noise Shaping Method for High Frequency PWM Based on Inverse All Pole Filter[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 3129-3140.

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[1] Lemke R, Krcher H J, Noethe L.Telescope posi- tioning and drive system based on magnetic bearings, technical challenges and possible applications in optical stellar interferometry[C]//SPIE Astronomical Telescopes+Instrumentation, Amsterdam, Netherlands, 2012: 844440.
[2] Schellekens J M.A class of robust switched-mode power amplifiers with highly linear transfer characteristics: on the elimination of zero-crossing distortion in switching converters[D]. Eindhoven: Technische Universiteit Eindhoven, 2014.
[3] Berkhout M.An integrated 200-W class-D audio amplifier[J]. IEEE Journal of Solid-State Circuits, 2003, 38(7): 1198-1206.
[4] Nyboe F, Kaya C, Risbo L, et al.A 240 W monolithic class-D audio amplifier output stage[C]//2006 IEEE International Solid State Circuits Conference, San Francisco, CA, USA, 2006: 1346-1355.
[5] Brecher C, Lindemann D, Wenzel C.Influences of closed loop control components on the performance of ultra-precision machines[J]. Key Engineering Materials, 2014, 625: 207-212.
[6] Stubenrauch F, Seliger N, Schmitt-Landsiedel D.Design and performance of a 200 kHz GaN motor inverter with sine wave filter[C]//PCIM Europe 2017; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Nuremberg, Germany, 2017: 1-9.
[7] Tiapkin M, Balkovoi A, Samygina E.Current controller design of precision servo drive[C]//2020 27th International Workshop on Electric Drives: MPEI Department of Electric Drives 90th Anniver- sary (IWED), Moscow, Kussia, 2020: 1-6.
[8] Höllthaler J, Hagl R, Kennel R.Influence of the PWM frequency on dynamic and position stability of servo drives[C]//2020 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Sorrento, Italy, 2020: 23-29.
[9] Höllthaler J, Hagl R, Kennel R.Bandwidth improve- ments of linear direct drives with a 100 kHz PWM- frequency[C]//2019 12th International Symposium on Linear Drives for Industry Applications (LDIA), Neuchatel, Switzerland, 2019: 1-6.
[10] 孙兆君, 董腾辉, 周飞, 等. PWM开关频率对转子损耗和温升影响探究[J]. 微电机, 2020, 53(2): 37-42.
Sun Zhaojun, Dong Tenghui, Zhou Fei, et al.Influence of PWM switching frequency on rotor loss and temperature rise[J]. Micromotors, 2020, 53(2): 37-42.
[11] 胡怡婷, 赵朝会, 吉洪智, 等. PWM频率对高速无刷直流电动机转矩脉动影响分析[J]. 上海电机学院学报, 2019, 22(6): 337-344.
Hu Yiting, Zhao Chaohui, Ji Hongzhi, et al.Analysis of influence of pulse width modulation frequency on torque ripple of high speed brushless DC motor[J]. Journal of Shanghai Dianji University, 2019, 22(6): 337-334.
[12] Mauerer M.Low-noise and low-distortion switch- mode power amplifiers for nano-positioning appli- cations[D]. Zurich: ETH Zurich, 2020.
[13] Texas Instruments Co, TMS320x280x, 2801x, 2804x high resolution pulse width modulator (HRPWM)[EB/OL]. [2011-10]. https://www.ti.com/lit/pdf/spru924.
[14] de Castro A, Sutter G, Huerta S C, et al. High reso- lution pulse width modulators in fpga[C]//2007 3rd Southern Conference on Programmable Logic, Mar del Plata, Argentina, 2007: 137-142.
[15] Froidevaux C.Method and device for generating PWM signals. US08508310B2[P]. 2013.
[16] Enuchenko M S, Korotkov A S.Digital-to-analog converters based on Delta-Sigma modulators[J]. Journal of Communications Technology and Elec- tronics, 2022, 67(1): 1-16.
[17] Tan Zhichao, Chen C-H, Chae Y, et al.Incremental Delta-Sigma ADCs: a tutorial review[J]. IEEE Transactions on Circuits and Systems, 2020, 67(12): 4161-4173.
[18] Pavan S, Schreier R, Temes G C.Understanding Delta-Sigma data converters[M]. New York: Wiley, 2005.
[19] Norris M, Platon L M, Alarcon E, et al.Quantization noise shaping in digital PWM converters[C]//2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 2008: 127-133.
[20] Lukic Z, Rahman N, Prodie A.Multibit Σ-Δ PWM digital controller IC for DC-DC converters operating at switching frequencies beyond 10 MHz[J]. IEEE Transactions on Power Electronics, 2007, 22(5): 1693-1707.
[21] Verhelst W.Noise shaping filter design for minimally audible signal requantization[C]//Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics, New York, 2001: 147-150.
[22] Yagyu M. Design of noise shaping FIR filters by minimizing in-band peak amplitude for stable single- and multi-bit data converters[C]//Proceedings of the2003 International Symposium on Circuits and Systems, Bangkok, Thailand, 2003: I.
[23] Yagyu M, Nishihara A. Fast and efficient algorithm to design noise-shaping FIR filters for high-order overload-free stable sigma-delta modulators[C]//2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), Vancouver, BC, Candan, 2004: I-469.
[24] Nagahara M, Yamamoto Y.Frequency domain min- max optimization of noise-shaping Delta-Sigma modulators[J]. IEEE Transactions on Signal Pro- cessing, 2012, 60(6): 2828-2839.
[25] Tariq M R, Ohno S.An indirect approach to synthesis of noise shaping IIR filters in ΔΣ modulators[C]// 2017 IEEE International Symposium on Circuits and Systems (ISCAS), Baltimore, MD, USA, 2017: 1-4.
[26] Tariq M R, Ohno S.Unified LMI-based design of ΔΣ modulators[J]. Eurasip Journal on Advances in Signal Processing, 2016, 2016(1): 1-14.
[27] Ohno S, Tariq M R.Optimization of noise shaping filter for quantizer with error feedback[J]. IEEE Transactions on Circuits and Systems, 2016, 64(4): 918-930.