傳統的gm-c濾波器在低電壓時的輸入電壓擺幅較小，可能會限制濾波器訊號的操作，因此本論提出一個新的CMOS companding濾波器取代gm-c濾波器，使得在低電壓的環境下提供較大的動態範圍，而在companding濾波器上，平方根領域濾波器與log領域濾波器同屬於companding濾波。
Abstract (Chinese)
本論文提出一個以up-down TL(translinear loop)電路結構設計而成的一個二階低通平方根領域濾波器，此平方根領域濾波器的基本架構是使用四個geometric-mean cell與三個squarer/divider Cell組合而成。而本論所提出的電路相較其他電路，具有較低的供應電壓、較小的消耗功率、較大的頻寬與較小的總諧波失真之優點。

本研究使用0.35μm CMOS製程製作晶片，其供應電壓為1.5V，調整電流為5μA-30μA。在電容5pF時的截止頻率為3.12MHz-8.11MHz、總諧波失真約0.28%、功率損耗1.09mW。

Conventional gm-c filters have limited voltage swings in low voltage operation. CMOS companding filters replace gm-c filters in low voltage environment for high dynamic range. The square-root domain filter and log-domain filter belongs to this companding filter category.

In this thesis, a second order low pass square root domain filter (SRD filter) based on the up-down TL (translinear loop) circuit structure is presented. The SRD filter consists of four geometric-mean cells and three squarer/divider cells. The advantages of the proposed circuits are low supply voltage, low power consumption, high bandwidth, and low total harmonic distortion (THD).

The circuit has been fabricated with 0.35μm CMOS technology. It operates with a supply voltage of 1.5V, and the bias current varies from 0.5μA to 30μA. Measurement results show that the cutoff frequency can be tuned from 3.12MHz to 8.11MHz when the Capacitance (C) is 5pF.The total harmonic distortion is 0.28%, and the power consumption is 1.09mW.

Abstract (Chinese) I
Abstract (English) II
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 4
1.3 Thesis Organization 5
Chapter 2 Previous SRD Low Pass Filter 6
2.1 Previous SRD Filter Proposals 6
2.2 The Principle of SRD Low Pass Filter 10
2.2.1 Translinear Filter 10
2.2.2 The LPF Transfer Function 11
Chapter 3 The Proposed SRD Filter 13
3.1 The Second Order SRD Low Pass Filter 13
3.2 Squarer and G-mean 16
3.3 The Voltage-Translinear Principle 18
Chapter 4 Simulation and Measurement Results of the Proposed Second Order SRD Filter 28
4.1 Hardware implementation 28
4.2 Simulation and Measurement Result 32
4.2.1 Time Response 33
4.2.2 Frequency Response 36
4.2.3 Total Harmonic Distortion 37
4.2.4 Comparison 38
Chapter 5 Conclusion 39
Reference 40

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