以運算轉導放大器及電容器所設計之具有任意相位差的正弦振盪電路

OTA-C Arbitrary-Phase-Shift Sinusoidal Oscillators

涂淑惠(Shu-Hui Tu)

指導教授 ： 黃育賢

國立臺北科技大學/電資學院/電腦與通訊研究所/博士(2012年)

摘要

西元二零零八年，應用分數微積分的觀念，將普通電容器的容抗1/sC擴大為分數電容器的容抗1/sαC，其中0＜α＜1，因而提出具有任意相位差的輸出信號的二階或三階正弦振盪電路。這個方法，除了電路的實現過程複雜難懂外，在目前現實世界中沒有一個實際存在的元件能夠直接代表這麼一個分數電容器，更遑論在積體電路中被實現。所以，找到一個簡單的實現方法，並且使用在積體電路中能夠容易被實現的普通元件來做設計成為一個在本論文中有價值的研究方向及討論的主題。
在本論文中，首先以N階正弦振盪電路的特徵方程式及代表一個九十度相位差的子轉移函數為實現電路的核心，並以一系列代數分解法合成一個具有九十度相位差的N階正弦振盪電路。然後，再以代表正電導或負電導的運算轉導放大器與需要的接地電容器(屬於具有九十度相位差的N階正弦振盪電路的一部分)並聯，吾人即可獲得具有任意相位差的輸出信號的N階正弦振盪電路。這個轉換無須在回授迴路中增加任何電路元件。
既然這是一個具有任意相位差的輸出信號的N階正弦振盪電路，這個相位差的精準度就很重要。由於本文所提出的這一個具有任意相位差的輸出信號的N階正弦振盪電路的每一個相位差都是對應正弦振盪電路的每一個特別的小部分電路，這一個設計上的優點使得吾人能經由這一個特別小部分的電路中使用的運算轉導放大器的轉導值的非理想頻率響應函數，及運算轉導放大器的輸出及輸入寄生電容及寄生電導的實際相位圖找出其補償的方法。在本論文中，對應六種不同情況的六種補償技術被提出來以增加每一個相位差的精準度。
西元二零零九年，一個不須要外加任何電路，只由振盪電路本身內部參數的改變即可放大或縮小輸出信號振幅大小的技術被提出來。為了降低這個技術產生較高的相對於振幅放大所得輸出信號總諧波扭曲的增大值，新的由振盪電路本身內部參數的改變即可調整輸出信號振幅大小的技術成為本論文進行研究工作的另一個主題。本研究主要採用「能量守恆」定律。當我們提供較大的偏壓電流給當作主動元件的運算轉導放大器時，如果同時增長運算轉導放大器裡面電晶體閘極的長度，就能固定設計電路時所須要的轉導值。所以，在主動元件的偏壓電流變大及電晶體閘極的長度增長下，運算轉導放大器輸出電流與輸入電壓關係圖中的飽和輸出電流值也增大了，這個增大的飽和輸出電流就使得輸出信號的振幅得以增加。這一個振盪電路自身調整振幅大小的新方法證實：當振幅放大時，的確具有較低的總諧波扭曲的增大值。
最後，H-Spice的模擬結果及離散式元件的實驗均證實本論文研究成果的正確性。

關鍵字

類比電路設計 ； 振盪電路 ； 正交振盪電路 ； 具有任意相位差的振盪電路 ； 相位差的補償技術 ； 電路自身的振幅控制技術 ； 運算轉播放大器

並列摘要

In 2008, a fractional calculus approach (due to the phase of sα, απ/2, where 1＞α＞0) was applied to generate a second-/third-order arbitrary-phase-shift sinusoidal oscillator (APSO), whereas the approach is rather complicated. In addition, with a fractional order α of Z =1/Csα, where α = 0.5 or α < 1, the fractional capacitance imitated by a semi-infinite series of RC trees suffers from limited investigations because of the nonexistence of a real fractance device. How to generate an APSO using a simple methodology and practical elements (easy to be fabricated on an IC chip) is worthy of continued investigation.
In the thesis, both the characteristic equation of an nth-order sinusoidal oscillator and the sub-transfer function of a quadrature as a core are simultaneously used to synthesize an nth-order OTA-C quadrature sinusoidal oscillator (QO). Furthermore, the QO is advanced to an nth-order APSO by phase transformation from a quadrature to an arbitrary phase shift via selectively superposing a required number of single-ended-input (SEI) operational transconductance amplifiers (OTAs) with +/− transconductances in parallel with assigned grounded capacitors on the QO. Such advancement acquires no extra circuitries in the feedback loops.
The phase shift accuracy is essential for the output parameter of an nth-order arbitrary-phase-shift sinusoidal oscillator. Since some particular and small part in the APSO may individually and arbitrarily determine the phase shift between two relevant nodal voltages, the synthesis presented in this thesis contributes the advantage which is capable of applying compensation to the sub-circuitry relative to each phase shift. Six compensation schemes for reducing the phase shift deviation are proposed with carefully considering the non-ideal frequency dependent transconduc- tance of an OTA and its input and output parasitics.
In 2009, a native amplitude limiting control for an oscillator was reported without extra sub-circuitries. However, how to reduce rather high variation of THD with respect to amplitude change of the scheme is a piece of valuable work. A transconductance of an OTA employed may be assigned and fixed by magnifying the length of MOS gate and the bias current properly. In addition, when the length of MOS gate is magnified, the output current with respect to input voltage difference is with a broader level between the maximum and minimum output currents. The broader the level between the maximum and minimum output currents is the higher the amplitude of output oscillation signals. Based on energy conservative theorem, the larger input bias current produces the higher output oscillation signal. A new native amplitude limiting scheme without using extra sub-circuitries is then presented which enjoys lower variation of THD with respect to amplitude change.
Finally, H-Spice simulations and one discrete component experiment are used to validate theoretical predictions.

並列關鍵字

analog circuit design ； oscillators ； quadrature oscillators ； arbitrary-phase-shift oscillators ； phase-shift compensation ； native amplitude control ； operational transconductance amplifiers

參考文獻

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