以運算轉阻放大器設計無電容之三階橢圓濾波電路

OTRA-based 3rd-order elliptic lowpass filter without capacitors

楊君博(Jun-Bo Yang)

指導教授 ： 張俊明

中原大學/工學院/電機工程研究所/碩士(2011年)

https://doi.org/10.6840/CYCU.2011.00218

摘要

摘要
運算轉導放大器(Operational Transconductance Amplifier)簡稱OTA，是目前用於類比電路設計中公認最佳的主動元件。其輸出與輸入關係方程式Iout=(Vin+－Vin-)Gm，其中Vin+及Vin-分別表示正端電壓輸入及負端電壓輸入，Gm表示轉導增益值；另一種元件：運算轉阻放大器(Operational Trans-Resistance Amplifier)簡稱OTRA，其輸出與輸入關係方程式Vout=(Iin+－Iin-)Rm；其中Iin+及Iin-分別表示正端電流輸入及負端電流輸入，Rm表示轉阻增益值。由兩者輸出與輸入關係方程式吾人可以發現OTRA與OTA具有對偶的關係，這也是近年來電路設計學者逐漸對OTRA這個主動元件感到有興趣的原因；本論文就是以運算轉阻放大器(OTRA)當作主動元件來進行電路設計。
過去，設計以OTRA為主動元件的電路時，因Vout=(Iin+－Iin-)Rm，常會假設Rm趨近於無限大，因輸出Vout必須保持有限大小，故Iin+－Iin-一定要等於零，因為實際的Rm雖然數值很大，但並非無限大，所以前面假設 的假設結果產生了不可避免的輸出誤差。實際的轉阻函數Rm(s)為 ，當 時， ，此時OTRA可當做等效轉移電容器的特性。本論文的電路設計法採用上述的等效觀念進行電路設計；首先對一個包含幾個電阻器及一個OTRA的子電路進行研究，吾人得到對以OTRA為主動元件之電路的導納矩陣方程式必須符合下列三個原則：
1. 每個方程式構成之電路一定要包含一個由OTRA實現的轉移電容容納。
2. 方程式中除了電容容納為正的一項外，將其他各項移往方程式的另一邊，則正項表示從OTRA的正端輸入。
3. 方程式中除了電容容納為正的一項外，將其他各項移往方程式的另一邊，則負項表示從OTRA的負端輸入。
利用此三原則，吾人將一個三階橢圓濾波轉移函數分解為三個簡單的方程式，再將各別簡單方程式以OTRA及電阻器實現後，重疊組合此三個簡單的電路即完成本論文電路的設計。
本論文電路驗證使用H-SPICE軟體中TSMC035 m製程參數進行模擬，由於OTRA的等效轉移電容值會隨開迴路、閉迴路以及外接線路結構及輸入信號頻率改變而改變，模擬時如何克服這一個問題也在本論文中被討論。

關鍵字

濾波器

並列摘要

Abstract
Operational Transconductance Amplifier (OTA) is considered the best component that is used in analog circuit design. It’s output equation Iout=(Vin+－Vin-)Gm, which Vin+ and Vin- mean positive input signal and negative input signal respectively. Gm means transconductance gain, Another component：Operational Trans-Resistance Amplifier (OTRA) It’s output equation Vout=(Iin+－Iin-)Rm, which Iin+ and Iin- mean positive input signal and negative input signal respectively. Rm means trans-resistance gain. We can discover that OTA is dual to OTRA by compare OTA’s output equation with OTRA’s. That is the reason why scholars are getting interested in OTRA. In this thesis, OTRA is used an active component to design circuits.
In the past, designer used to let Rm approach to infinite. The output signal Vout is a finite value, so Iin+－Iin- must be equal to zero . Actually, Rm is a very large value, but infinite. Assuming that Rm approach to infinite cause an inevitable output inaccuracy. Actually， , when , . Now, OTRA may equal to a transfer capacitor. In this thesis we design the circuit with the idea that is mentioned fore. First, we researched a sub-circuit that includes several resistants and an OTRA, than we got three rules for Transconductance metrix
(1) Each equation of sub-circuit has to include an elastance constructed from OTRA.
(2) Let the elastance be positive, besides we move other items to another side of equation. Positive items mean input signals from OTRA’s positive side.
(3) Let the elastance be positive, besides we move other items to another side of equation. Negative items mean input signals from OTRA’s negative side.
By these three rules, we decompose the transfer function of several simple equations. We realize these simple equations with resistances and OTRA, than we compose these three sub-circuit to success our circuit design of this thesis.
This circuit simulated with TSMC035 m process by H-SPICE. The equal transfer capacitance of OTRA will be affected by open loop, close loop, circuit structure, and input frequency. It will be mentioned in this thesis to overcome this problem.

並列關鍵字

filter

參考文獻

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