本論文提出一個以運算轉導放大器(OTA)設計的二階低通平方根濾波器。
此平方根濾波器的基本架構使用兩個translinear濾波器和四個運算轉導放大器。
由於運算轉導放大器有較小的電壓擺幅，可能會限制濾波器大訊號的操作。
因此我們探討濾波器的動態範圍，以及品質因素(Q)對動態範圍的影響。
它使用了較少的電晶體數目以及較低的電壓操作，所以有較少的功率損耗和晶片面積。
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10μA~80μA。外接電容3.5pF、7pF時的訊號與偏壓的比值大於40%，截止頻率為1.24MHz~5.53MHz，外接電容3pF、8.5pF時的訊號與偏壓的比值大於53%，截止頻率為900KHz~4.46MHz。總諧波失真約0.908%。功率損耗506μW。

In this thesis, a second-order low pass square root domain filter (SRD filter) based on operational transconductors amplifiers (OTAs) is presented.
The SRD filter consists of two translinear filters and four OTAs.
Because the OTA has small voltage swings, which may violate the large signal natural of the SRD filter. We investigate the dynamic range of this compact SRD filter with different quality factor(Q).
The circuit has fewer numbers of transistors and operate in low voltage, therefore, it has less power consumption and less chip area.
The circuit has been fabricated with 0.35μm CMOS technology. It operates with a supply voltage 1.5V and the biasing current varies from 10uA to 80uA.
Measurement results lts show that Im/I0≥40% when the external capacitance C is 3.5pF、7pF and Im/I0≥53% when the external capacitance C is 3pF、8.5pF. The cutoff frequency of the filter can be tuned from 1.24MHz to 5.53MHz when the external capacitance C is 3.5pF、7pF and the cutoff frequency can be tuned from 900KHz to 4.46MHz when the external capacitance C is 3pF、8.5pF. The total harmonic distortion is 0.908% and the power consumption is 506μW.

Contents
Abstract
Chapter 1 Introduction 1
Chapter 2 Previous SRD filter 6
2.1 The principle of SRD LPF 6
2.1.1 Translinear filter 6
2.1.2 The LPF transfer function 7
2.2 Previous SRD filters 11
2.3 Cruz’s SRD filter 15
2.3.1 Class-AB linear transconductor 15
Chapter 3 The Dynamic Range analysis of the first order compact SRD filter 21
3.1 The linear range of a MOSFET 21
3.2 The dynamic range analysis of the first order SRD filter 24
3.2.1 Operational transconductor amplifier 24
3.2.2 First order SRD filter 26
3.2.3 The large signal linear range analysis of the first order SRD filter 28
Chapter 4 Proposed second order SRD filter and its dynamic range analysis 37
4.1 Proposed second order SRD filter 37
4.1.1 Circuit depiction 37
4.1.2 The large signal linear range analysis of the second order SRD filter 40
Chapter 5 Simulation and Measure Results of the proposed second-order SRD filter 52
5.1 Hardware implementation 52
5.2 Simulation and Measurement results 55
Chapter 6 Conclusion 61
Reference 62

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