对数域压扩滤波器（电路）的设计及应用研究
摘要
对数域压扩技术利用BJT晶体管等有源器件的指数Ⅰ-Ⅴ特性，对信号作对数压缩处理，大大降低了电路内部节点电压的摆幅，能在低电源电压下保持大信号动态范围和高工作频率，该技术的主要应用是设计具有低电压、宽调谐范围、高工作频率和宽动态范围特性的连续时间全集成滤波器——对数域滤波器(或电路)。
本文首先介绍了对数域压扩技术利用的有源器件的特性，对数域压扩滤波的基本原理及静态和动态跨导线性原理；基于基本对数域积分器的电路拓扑结构，给出了单输入反相对数域积分器、单输入同相对数域积分器，差分双输入对数域积分器及甲乙类对数域积分器等不同结构的对数域积分器的电路实现，考察了对数域积分器和线性Gm-C积分器的功耗特性，通过对比指出对数域滤波器(电路)在低电源电压下更具低功耗优势；并以对数域积分器电路为例，讨论了晶体管非理想因素对对数域滤波电路性能的影响并提出了有效的补偿措施。
接着，本文依次阐述了几种可行的对数域滤波电路综合设计方法，其一是基于LC梯形网络运算模拟的对数域滤波器设计方法，采用该方法设计实现了三阶切比雪夫低通对数域滤波器、五阶切比雪夫低通对数域滤波器和二阶带通对数域滤波器，并通过仿真分析验证了设计的可行性；其二是基于柏努利单元电路的晶体管级对数域滤波器设计方法，给出了采用该方法设计得到的有损对数域积分器和二阶低通对数域滤波器的电路实现，并通过仿真分析考察了其幅频特性；其三是基于状态空间方程的对数域滤波器(电路)设计方法，并基于该方法利用全NPN指数跨导单元电路改进了一二阶对数域振荡器的设计，而后基于该方法设计了三阶通用对数域滤波器。
最后本文考察了对数域滤波器(电路)在音频滤波、硬盘驱动器读取通道、小波变换VLSI硬件实现等方面的应用，并阐述了与对数域压扩滤波类似的基于强反型MOSFET实现的平方根域压扩滤波的基本原理及设计方法，给出了基本的平方根压扩积分器的设计实现并介绍了平方根压扩滤波电路的研究及应用现状，以期完善压扩滤波的概念。
Log-domain companding technique takes advantage of the exponential I/V characteristics of the active devices such as bipolar junction transistors (BJT), compressing the dynamic range of the input sigal and reducing internal voltage amplitudes, it can maintain large dynamic range and high operating frequency under low supply voltage , the main area of application for this technique is the implementation of continuous-time fully integrated filters (or circuits) with low voltage, wide dynamic range, high-frequency, and wide tenability.
First of all, the thesis introduces the the exponential I/V characteristics of the active devices and the principles of both static and dynamic translinear circuits, and based on the basic topology of log-domain integrators, presents the circuits of non-inverting signal-input log-domain integrator, inverting signal-input log-domain integrator, differential dual-input log-domain integrator and class-AB log-domain integrator, investigates and compares the power efficiency of log-domain integrator and the linear Gm-C integrator, it is shown that log-domain filters are better suited for low-power signal processing at low supply voltages, then effects of transistor nonidealities on log-domain filters are investigated and the compensation schemes are also proposed.
Secondly, several sythesis methods of log-domain filters are introduced, the first method is a modular approach, it is based on the operational simulation of the LC ladder networks, the method is used to design a third-order Chebyshev low-pass log-domain filter, a fifth-order Chebyshev low-pass log-domain filter and a second-order band-pass filter, and the behavior of these filters is verified through the PSPICE simulation; the second method is a systematic transistor-level analysis and
sythesis method of log-domain filters--the Bernoulli Cell approach, a lossy
log-domain integrator and a second-order low-pass log-domain filter are designed based on the method and the results of the simulation are also presented; the third method is state space synthesis of log-domain.filters, based on the novel all-NPN positive and negative exponential transconductance cell, an improved second-order log-domain oscillator is designed using the state-space sythesis method, then a third-order universal log-domain filter is designed also using the state-space sythesis method.
Lastly, the thesis investigate the application of log-domain filter in the hard-disk-drive (HDD) read channels, audio-frequency filtering, the design of current-mode phase-locked loop ( PLL) and the VLSI implementation of wavlet transformation etc, then introduces the square-root domain filters using quadratic law of MOSFET in strong inversion region which also belong to the class of companding filters, a square-root domain integrator is also presented.
本文首先介绍了对数域压扩技术利用的有源器件的特性，对数域压扩滤波的基本原理及静态和动态跨导线性原理；基于基本对数域积分器的电路拓扑结构，给出了单输入反相对数域积分器、单输入同相对数域积分器，差分双输入对数域积分器及甲乙类对数域积分器等不同结构的对数域积分器的电路实现，考察了对数域积分器和线性Gm-C积分器的功耗特性，通过对比指出对数域滤波器(电路)在低电源电压下更具低功耗优势；并以对数域积分器电路为例，讨论了晶体管非理想因素对对数域滤波电路性能的影响并提出了有效的补偿措施。
接着，本文依次阐述了几种可行的对数域滤波电路综合设计方法，其一是基于LC梯形网络运算模拟的对数域滤波器设计方法，采用该方法设计实现了三阶切比雪夫低通对数域滤波器、五阶切比雪夫低通对数域滤波器和二阶带通对数域滤波器，并通过仿真分析验证了设计的可行性；其二是基于柏努利单元电路的晶体管级对数域滤波器设计方法，给出了采用该方法设计得到的有损对数域积分器和二阶低通对数域滤波器的电路实现，并通过仿真分析考察了其幅频特性；其三是基于状态空间方程的对数域滤波器(电路)设计方法，并基于该方法利用全NPN指数跨导单元电路改进了一二阶对数域振荡器的设计，而后基于该方法设计了三阶通用对数域滤波器。
最后本文考察了对数域滤波器(电路)在音频滤波、硬盘驱动器读取通道、小波变换VLSI硬件实现等方面的应用，并阐述了与对数域压扩滤波类似的基于强反型MOSFET实现的平方根域压扩滤波的基本原理及设计方法，给出了基本的平方根压扩积分器的设计实现并介绍了平方根压扩滤波电路的研究及应用现状，以期完善压扩滤波的概念。
Log-domain companding technique takes advantage of the exponential I/V characteristics of the active devices such as bipolar junction transistors (BJT), compressing the dynamic range of the input sigal and reducing internal voltage amplitudes, it can maintain large dynamic range and high operating frequency under low supply voltage , the main area of application for this technique is the implementation of continuous-time fully integrated filters (or circuits) with low voltage, wide dynamic range, high-frequency, and wide tenability.
First of all, the thesis introduces the the exponential I/V characteristics of the active devices and the principles of both static and dynamic translinear circuits, and based on the basic topology of log-domain integrators, presents the circuits of non-inverting signal-input log-domain integrator, inverting signal-input log-domain integrator, differential dual-input log-domain integrator and class-AB log-domain integrator, investigates and compares the power efficiency of log-domain integrator and the linear Gm-C integrator, it is shown that log-domain filters are better suited for low-power signal processing at low supply voltages, then effects of transistor nonidealities on log-domain filters are investigated and the compensation schemes are also proposed.
Secondly, several sythesis methods of log-domain filters are introduced, the first method is a modular approach, it is based on the operational simulation of the LC ladder networks, the method is used to design a third-order Chebyshev low-pass log-domain filter, a fifth-order Chebyshev low-pass log-domain filter and a second-order band-pass filter, and the behavior of these filters is verified through the PSPICE simulation; the second method is a systematic transistor-level analysis and
sythesis method of log-domain filters--the Bernoulli Cell approach, a lossy
log-domain integrator and a second-order low-pass log-domain filter are designed based on the method and the results of the simulation are also presented; the third method is state space synthesis of log-domain.filters, based on the novel all-NPN positive and negative exponential transconductance cell, an improved second-order log-domain oscillator is designed using the state-space sythesis method, then a third-order universal log-domain filter is designed also using the state-space sythesis method.
Lastly, the thesis investigate the application of log-domain filter in the hard-disk-drive (HDD) read channels, audio-frequency filtering, the design of current-mode phase-locked loop ( PLL) and the VLSI implementation of wavlet transformation etc, then introduces the square-root domain filters using quadratic law of MOSFET in strong inversion region which also belong to the class of companding filters, a square-root domain integrator is also presented.
引文
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[3] M.N.El-Gamal, G.W.Roberts. A 1.2V NPN-only integrator for log-domain filtering. IEEE trans on CAS(Ⅱ), 2002, 49 (4)., 257—265
[4] 邱关源．现代电路理论，北京：高等教育出版社，2001，81—88
[5] 蔡理，马西奎．低电压对数域滤波器的低功率性能分析．空军工程大学学报(自然科学版)，2001，2(4)：33—36
[6] E.M.Drakakis, A.J.Payne, C.Toumazou. Log-domain filtering and the Bernoulli Cell. IEEE trans on CAS(Ⅰ), 1999, 46 (5): 599—571
[7] 李树涛，何怡刚，吴杰．一种新的对数域电流模式振荡器．湖南大学学报，1998，25(5)：100—102
[8] R.A.Baki, M.N.El-Gamal.A low-power 5-70-MHZ seventh-order log-domain filter with Programmable boost, group delay, and gain for hard disk drive applieations. IEEE J. Solid-State Circuits, 2003, 38 (2): 205—215
[9] D.Python, C.C.Enz. A mieropower class-AB CMOS log-domain filter for DECT applications. IEEE J. Solid-State Circuits, 2001, 36 (7): 1067—1075
[10] C.Toumazou, J.Ngarmnil, T.S.Lande. Micropower log-domain filter for electronic cochlea. Electron Lett, 1994, 30 (22): 1839—1841
[11] 赵录怀，邱关源．用对数域电流模式积分器实现的高频集成滤波器．电路与系统学报，1996，1(3)：32—37
[12] D.Perry, G.W.Roberts.The design of log-domain filters based on the operational simulation of LC ladders.IEEE Trans CAS-Ⅱ, 1996, 43 (11):：763—774
[13] D.Frey. Log-domain filtering: an approach to current-mode filtering.IEE Proe-G, 1993, 140 (6): 406—416
[14] E.Seevinek. Companding current-mode integrator: a new circuit principle for continuous-time monolithic filters. Electron Lett, 1990, 26 (24): 2046—2047
[15] C.C.Enz, Punzenberger M. Low-power log-domain signal processing in CMOS and BiCMOS.IEEE Trans[J].Cireuits Syst Ⅱ, 1999, 46 (3): 279—289
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