以OTA設計電壓式二階濾波電路於高頻操作時之非理想效應研究與改進

Non-ideal Effect and Improvement of The Voltage-Mode Second-Order High-fequency OTA-C Filter Structure

張惟淳(Wei-Chun Chang)

指導教授 ： 張俊明

中原大學/工學院/電機工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500172

摘要

在OTA-C的電路中，由於寄生電容的種類繁多(包括輸入端寄生電容，輸出端的寄生電容，以及節點上的寄生電容)，使得當電路設計時，如果使用雙輸入端的OTA及浮接電容，便無法讓外加電容的位置與所有寄生電容的位置相同；使得在過去的文獻中，無法找到以吸收寄生電容值的大小，來給予恰當的外加電容值，而得到具有精準輸出訊號的高頻電路的構想。

最近，由於分析合成法(Analytical Synthesis)的提出，所設計的電路同時符合三項OTA-C電路設計的準則：(1)使用單端輸入的OTA(以免除寄生電容的Feedthrough效應)，(2)使用接地電容(可直接吸收寄生電容)，(3)使用較過去為少的主被動元件(使得具有總體較低的寄生電容效應)符合這三項準則的電路，所有外加電容的位置剛恰與所有寄生電容的位置相同；導致吾人提出以吸收寄生電容來調整外加電容值而得到更精準的高頻電路的改進法。

CMOS OTA內部的非理想效應來自其內部諸電晶體的寄生電容及寄生電導。由OTA輸出電流與輸入電壓的相量比值，吾人可求得OTA與頻率變化有關的轉導函數。至於OTA外部的非理想效應則由OTA的輸入端、輸出端及內部節點的寄生電容與輸出端的寄生電導主導。本論文以電壓式二階OTA-C萬用濾波電路為例，説明如何以吸收寄生效應，調整外加電容值或OTA的轉導值以得到精準高頻電路的方法。當模擬的諧振頻率比理想值高時，顯示所給的OTA的轉導值略大吾人可適當減少OTA電導值，使模擬結果更接近理想值。當模擬的諧振頻率較理想值為低時，顯示寄生電容的存在使電路的諧振頻率降低了。這時，吾人可吸收寄生電容，以較小的外加電容來提高諧振頻率。由於OTA的轉導值及寄生電容值與頻率變化有關，經過幾次轉導值的調整或寄生電容的吸收，吾人可獲得精準到誤差僅1%的模擬結果。另外，OTA極點與零點的數目，會隨著頻率的提高而增加，故非理想轉導的數學表示式比須給予適當的修正，以符合實際模擬的情況。

本論文所提出之以吸收寄生電容或減少轉導值來修正外加元件大小的改進法，經H-SPICE 0.5 m製程的模擬結果，證實可將OTA-C濾波電路在高頻操作時的大幅誤差縮減至1%以內，為一具有極大實用價值之電路改進法。

關鍵字

運算轉導放大器 ； 寄生電導 ； 寄生電容

並列摘要

There are several kinds of parasitic capacitances, including input and output parasitic capacitances of an OTA and the nodal parasitic capacitance at the internal node in an OTA-C (Operational Transconductance Amplifier and Capacitor) circuit. This leads to the difficulty to have the same places for both given capacitors and all the parasitic capacitances. When the differential-input OTA and floating capacitances are employed in the circuit structure, and the impossibility to obtain a high–frequency circuit with precise output responses by giving a proper capacitor value after absorbing the parasitic capacitance.

Recently, the “Analytical Synthesis Method” has been proposed to realize the high-order OTA-C circuits which achieving the following three important criteria simultaneously for the design of OTA-C filters: (i) using single-ended-input OTAs (overcoming the feedthrough effect due to the use of differential-input OTAs), (ii) using grounded capacitors (absorbing the shunt parasitic capacitance), and (iii) using the least number of component counts (reducing the total parasitic effects). Note that all the parasitic capacitances have the same places as those of all the given capacitors in the realized circuits achieving the above three important criteria. An improvement approach is then proposed by the absorption of parasitic capacitances from the given capacitors to obtain a precise high-frequency circuit.

The non-ideal effect in an OTA is resulted from the parasitic capacitances spreaded among the MOS transistors which is called the frequency dependent transconduce, namely, the ratio between the output current phasor and the input voltage phasor, of an OTA. The non-ideal effect out of the OTA includes the input and output parasitic capacitance and the output parasitic conductance of an OTA and the nodal parasitic capacitance at each internal node. In this thesis, a voltage-mode second-order OTA-C universal filter structure is used for example to demonstrate this new improvement for a high-frequency circuit. When the simulation resonance frequency is higher than the theoretical value, this implies that the given transconductance is also higher than the exact value. The reduction of the given transconductance leads to approach the theoretical prediction. On the contrary, if the simulation resonance frequency is lower than the theoretical value, it means that the additional parasitic capacitance makes a total capacitance larger than the exact value. The absorption of parasitic capacitance from the given capacitor leads to close the ideal requirement. After several reductions of transconductances or absorptions of capacitances can enter the very precise range with the error lower than 1% for the simulation resonance frequency. Furthermore, as the operational frequency increases, the numbers of pole and zero of the frequency dependent transconductance of an OTA three-OTA circuit increases, too Based upon different simulation results, different frequency dependent transconductance are given to consist with the practical variation.

Finally, The above proposed improvement was verified by UMC05 H-spice simulation with supply voltages ±2.5V.

並列關鍵字

parasitic conductance ； OTA ； parasitic capacitance

參考文獻

[1] C.M. Chang, “6.61 M to 317 MHz Nth-Order Current-Mode Low- Pass and High-Pass OTA-Only-Without-C Filter”, Circuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on Volume 1, 23-26 May 2004.

[2] C. M. Chang , “Voltage-Mode High-Order OTA-Only-Without-C Low-Pass (from 215M to 705M Hz) and Band-Pass (from 214M to 724M Hz) Filter Structure”, accepted for presentation at the Proceedings of IEEE: International Symposium on Circuits and Systems (ISCAS) , Kobe, Japan.

[5] Chun-Ming Chang and Bashir M. Al-Hashimi, “Analytical Synthesis of Current-Mode High-Order OTA-C Filters”, IEEE transactions on circuit and systems-I, Vol.50, No. 9, September 2003.

[6] Michal Bialko and Robert W. newcomb, “Generation of All Finite Linear Circuits Using Integrate DVCC” IEEE Trans. on Circuit Theory, Nov. 1971.

[8] Hspice user’s manual