- 學位論文
以運算轉阻放大器設計無電容之二階低通及帶通巴特沃茲濾波器
OTRA-based Second-order Lowpass and Bandpass Butterworth Filter without Capacitors
摘要
運算轉導放大器(Operational Trans-Conductance Amplifier；OTA)是目前類比電路設計中公認為最佳主動元件，OTA有著 (V+表示正端輸入電壓、V-表示負端輸入電壓、Gm表示轉導增益值)的輸入與輸出關係式，而OTA和另一種主動元件：運算轉阻放大器(Operational Trans-Resistance Amplifier；OTRA)形成對比，因為OTRA有著 (I+表示正端輸入電流、I-為負端輸入電流、Rm為轉阻增益值)的輸入與輸出關係式。由輸入和輸出關系式，我們可以發現這兩種元件具有對偶關係，這也是OTRA會在近年來成為電路設計學者最佳選擇的原因，本論文也是以OTRA為主動元件來設計電路的。 本論文的OTRA電路設計法不同於過去的OTRA電路設計法，差別在於過去的OTRA電路設計法是採用 ，其中 (與OA設計法一樣( ))，但Vo必須為有限值，所以要讓Vo成為有限值， 一定要等於零。雖然Rm的數值很大，但並非無限大，所以前者採用了 的設計方法，會產生不可避免的輸出誤差。所以本論文是採用 ，當 ，再將 等效成Ceq(Ceq為等效轉移電容)。本論文的電路設計基本特性為1.每個方程式需要包含一個由OTRA實現的等效轉移電容容納。2.方程式中除轉移電容為正的一項外，將其它各項移往方程式的另一邊，而正項表示信號由OTRA正端輸入。3.負項表示信號由OTRA負端輸入。4.在寫出的方程式中不會包含(Vi - Vj)G；i≠j。利用這四個特性和YV=I(導納矩陣設計分析法)將轉移矩陣分解成兩個方程式，而每個方程式都能以OTRA及電阻器來實現，之後把小電路重疊起來所形成的大電路，即為本論文用兩個OTRA、五個電阻所設計出來的無電容之二階巴特沃茲濾波器。 以電腦軟體H-Spice搭配使用TSMC 035um為製程參數進行電路模擬時，轉阻增益 與頻帶寬 將隨開迴路、閉迴路以及輸入信號、頻率的不同而改變，所以如何找到適當的 與 之乘積將成為電路模擬過程中重要的挑戰。
並列摘要
Operational Trans-Conductance Amplifier (OTA) is analog design accepted best active component count at present. It has the relation of the input and output of the Io = (V+ - V-)Gm, and OTA contradistinction of another active component count Operational Trans-Resistance Amplifier (OTRA), it has the relation of the input and output of the Vo = (I+ - I-)Rm, these two component counts has relation of antithesis, so OTRA is best choice by the circuit design scholars recent years, and this thesis also using OTRA design circuit. The output signal of OTRA is Vo = (I+ - I-)Rm, and previous OTRA circuits are used gain of the OTRA infinite, but the output voltage are finite, so both input current are equal. But this thesis use gain of the OTRA finite, we take the maximum gain and bandwidth equal a capacitor. When design circuits, have three emphases: 1.Each equation has to include equal transfer capacitor. 2. In the equation, the other moved to the other side of the equation, except equal transfer capacitor, positive terminal inputs of Circuit are positive. 3. Negative terminal inputs of Circuit are negative. 4. Equation not include (Vi - Vj)G；i≠j. Using this four emphases and admittance matrix analytical synthesis, we make the transfer function into a matrix and decomposed into two equations, each equation can be achieved by an OTRA and several resistances. Then we complete the circuit in this thesis. The simulation of this thesis is use H-Spice and TSMC 035um. The product of maximum gain and bandwidth will be affected by open loop, close loop, circuit structure, and input frequency. So how to find the appropriate product of maximum gain and bandwidth are very important in this simulation.