鑒於內含有量化訊號之系統於現實生活中的應用廣泛，因此將量化回授系統細分為三種類型，分別為控制力被量化之系統、回授力被量化之系統與兩者皆被量化之系統。而在本文中，最主要是針對控制力被量化之回授系統進行穩定性分析與探討，而其穩定性分析在這裡則是利用順滑模態控制理論，並將此應用於D類音頻放大器與同步降壓式轉換器。
因此首先在第一部分則是利用順滑模態控制理論完一種新型1.5位元調變技術，接著以此調變技術應用於D類音頻放大器，經由模擬與實驗的方式，驗證此D類音頻放大器擁有雜訊低、高效率、高線性度與不需額外的輸出濾波器的優點，並改善了傳統1位元調變技術之 D類音頻放大器在輸入訊號小時，其效率低的問題，而在此設計的D類音頻放大器性能規格為THD+N(%)為0.039%與效率為85.18%。在第二部份則介紹以順滑模態控制理論完成同步降壓式轉換器之控制器，其控制方式使得同步降壓式轉換器能夠自行產生振盪並穩定的操作在順滑模態上，即不需額外的三角波產生器，在此以12V/1.5V之同步降壓式轉換器為例，經由模擬與實驗方式，達到輸出穩態誤差為0.66%，以及當步階電流為15A，且迴轉率為50A/μs時，負載變動誤差為3%。

The systems which contain coarsely quantized signals are commonly found in applications where the actuators and/or sensors can only output a finite number of levels. This thesis focuses on the problem of synthesizing a finite-level control force for a certain control task, first presenting a systematic design method based on the theory of sliding modes and then applying it to the designs of the class-D audio amplifier and synchronous buck converter.
At the first part, a novel three-level modulation technique for a class-D audio amplifier is designed by the sliding mode control theory. The simulated and experimental results conform to the excellent performance of this three-level modulation scheme. In particular, the proposed modulation scheme improves the poor efficiency of a conventional two-level class-D audio amplifier when the audio input signal is small, also excludes the output LC filter. The experiment shows that the designed three-level class-D amplifier achieves a minimum total harmonic distortion plus noise of 0.039% and an efficiency of 85.18%. At the second part, the controller of a synchronous buck converter is designed. The proposed self-oscillating controller stabilizes the buck converter in sliding mode, without the need of a triangular wave generator like the conventional PWM method. A 12V/1.5V synchronous buck converter with proposed control is built in the laboratory. The experiment shows 0.66% of the static output ripple and 3% of the load regulation error in response to the 15A step change of the load current at a slew rate of 50A/μs.

第1章 緒論 1
第2章 順滑模態量化理論 4
2.1 問題描述 4
2.2 順滑模態成立條件 5
2.3 順滑模態量化理論之特性 7
2.4 性能指標 8
第3章 新型1.5位元調變技術與D類音頻放大器 10
3.1 研究背景 10
3.2 新型1.5位元調變技術 11
3.3 設計範例 16
3.3.1 模擬結果 17
3.3.2 實驗結果 24
3.4 各種調變技術之性能比較 34
第4章 同步降壓轉換器的介紹與控制器設計 38
4.1 研究背景 38
4.2 同步降壓轉換器 41
4.3 同步降壓轉換器之控制器設計方向與原理 46
4.3.1 切換控制設計 47
4.3.2 同步降壓轉換器使用切換控制與線性控制 52
4.4 元件不理想效應 54
4.5 模擬結果 58
4.6 實驗結果 68
第5章 結論 74
附錄 A. D類音頻放大器之PCB實現 75
附錄 B. 同步降壓轉換器與控制器之PCB實現 82
參考文獻 87

[1] J.C. Kieffer, “Analysis of DC input response for a class of one-bit feedback encoders,” IEEE Trans. on Communication, Vol. 38, pp. 337-340, 1990.
[2] S. C. Li, V. Chia-Chang Lin, K. Nandhasri, and J. Ngarmnil, “New High-Efficiency 2.5 V/0.45 W RWDM Class-D Audio Amplifier for Portable Consumer Electronics,” IEEE Trans. on Circuits and Systems, Vol. 52, pp. 1767-1774, 2005.
[3] Ph. Dondon and J.M. Nicouleau, “An original approach for the design of a class D power switching amplifier-an audio application,” IEEE International Conference on Electronics Circuits and Systems, pp. 161-164, 1999.
[4] D. Dapkus, “Class-D audio amplifiers: An overview,” IEEE Trans. on Consumer Electronics, ICCE, pp. 400-401, 2000.
[5] A. D. Cheok, Y. Fukuda, “A new torque and flux control method for switched reluctance motor drives,” IEEE Trans. on Power Electronics, Vol. 17, pp. 543-557, 2002.
[6] Y. Panov, M. M. Jovanovic, “Design considerations for 12-V/1.5-V, 50-A voltage regulator modules,” IEEE Trans. on Power Electronics, Vol. 16, pp. 776-783, 2001.
[7] Z. Xunwei, X. Peng, F. C. Lee, “A novel current-sharing control technique for low-voltage high-current voltage regulator module applications,” IEEE Trans. on Power Electronics, Vol. 15, pp. 1153-1162, 2000.
[8] N. Mohan, Tore M. Undeland and W. P. Robbins, Power Electronics, Wiley International Edition, 2003.
[9] J. D. Powell, N. P. Fekete, and C. F. Chang, “Observer-based air fuel ratio control,” IEEE Control Systems Magazine, Vol. 18, pp. 72-83, 1998.
[10] R.W. Adams and R. Schreier, Delta- Sigma Data Converter : Theory, Design and Simulation, S.R. Norsworthy, R. Schreier and G.C. Temes, eds. IEEE Press,1997.
[11] V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, Moscow: MIR publishers, 1978.
[12] V. I. Utkin, “Variable structure systems with sliding mode,” IEEE Trans. on Automatic Control, Vol. 22, pp. 212-222, 1997.
[13] V. I. Utkin, “Sliding mode control design principles and applications to electric drives,” IEEE Trans. Ind. Electron., Vol. 40, no. 1,pp 23-36, 1993.
[14] H. Sira-Ramirez, “Analog signal encoding in delta modulation circuits using the theory of variable structure systems,” in Proc. 27th IEEE conference on Decision and Control, vol. 2, pp. 940-945, 1988.
[15] S. H. Yu and M. H. Tseng, "modulation and control of a three-level class-d audio power amplifier," IEEE International Conference on Power Electronics and Drive Systems, pp. 1447-1450, 2005.
[16] F. Medeiro, A. Perez-Verdu and A. Rodeiguez-Vazquez, Top-Down Design of High-Performance Sigma-Delta modulators, Kluwer Academic Publishers, 1999.
[17] Y. Z. Tsypkin, Relay Control Systems, published in English by Cambridge University Press, 1984.
[18] D. V. Anosov, “Stability of the equilibrium positions in relay systems,” Automation and Remote Control, Vol. 20, pp. 130-143, 1959.
[19] S.H. Yu, "Analysis and design of single-bit sigma-delta modulators using the theory of sliding modes," IEEE Trans. on Control Systems Technology, Vol. 14, No. 2, pp. 336-345, 2006.
[20] Bob Metzier, Audio Measurement Handbook, Published by Audio Precision, 1993.
[21] K. Nielsen, “High-fidelity PWM-based amplifier concept for active loudspeaker systmes with very low energy consumption,” Journal of the Audio Engineering Society, Vol. 45, pp. 554-570, 1997.
[22] H.Ballan and M. Declercq, “12V Σ−Δ class-D amplifier in 5V CMOS technology,” IEEE Custom Integrated Circuits Conference, pp. 559-562, 1995.
[23] Kendall Su, Analog Filters, Kluwer Academic Publishers, 2002.
[24] S. C. Choi, J. W. Lee, W. K. Jin, J. H. So, and S. Kim, “A Design of a 10-W Single Chip Class D Audio Amplifier With Very High Efficiency using CMOS Technology,” IEEE Trans. on Consumer Electronic, vol. 45, pp.465-473, 1999.
[25] S. Burrow and D. Grant, “Efficiency of low power audio amplifiers and loudspeakers,” IEEE Trans. on Consumer Electronics, Vol. 47, pp. 622-630, 2001.
[26] S. C. Choi, J. W. Lee, W. K. Jin, J. H. So, and S. Kim, “A 2 W BTL single-chip class-D power amplifier with very high efficiency for audio applications,” IEEE International Symposium on Circuits and Systems, pp. 11-14, 2000.
[27] TPA2005D1 Data sheet, Texas Instruments, File No. SLOS369E, 2004.
[28] DM74LS74A Data sheet, Fairchild semiconductor, 2000.
[29] LM319 Data sheet, Fairchild semiconductor, 2001.
[30] J. Varona, A. A. Hamoui, and K. Martin, “A Low-Voltage Fully-Monolithic AX-Based Class-D Audio Amplifier,” Solid-State Circuits Conference, pp.545-548, 2003.
[31] TPA005D14 Data sheet, Texas Instruments, File No. SLOS240A, 2000.
[32] 涂榮杰,Multi-phase DC/DC Converters, system Development RichTek Technology Corp. 2005.
[33] VRM 9.1 DC-DC Converter Design Guidelines, INTEL Corp. January 2002.
[34] VRM 9.0 DC-DC Converter Design Guidelines, INTEL Corp. April 2002.
[35] S.H. Yu and C.I. Huang, "Voltage regulator modules with double-loop relay feedback control," IEEE International Conference on Power Electronics and Drive Systems, pp. 1563-1565, 2005.
[36] A. Consoli*, A. Testa', G. Giannetto', F. Gennaro, “A New VRM Topology for Next Generation Microprocessors,” IEEE PESC. Vol. 1, pp.339-344, 2001.
[37] T.Senanayake and T.Ninomiya, “Fast-Response Load Regulation of DC-DC Converter By Inductor-Switching High Current Path,” IEEE TENCON, pp.1986-1989, 2002.
[38] ISL6559EVAL2 Data Sheet, Intersil Corporation, File No. FN9084, 2004.