臺灣博碩士論文加值系統

運算轉阻放大器(Operational Trans-Resistance Amplifier；OTRA)，其關係式為 ，特性與運算轉導放大器(Operational Trans-Conductance Amplifier；OTA)對偶，OTA為廣泛使用之元件，因此OTRA在電路設計有著先天上的優勢。
許多以OTRA為主動元件之電路設計，假設Rm值趨近無限大，然而Rm並非無限大，所以造成較大之誤差。而本文假設Rm為有限值，當操作頻率遠大於主極點時，可得轉移等效電容 。此方法Rm較接近實際情形並以等效轉移電容取代實際電容，達成無電容之振盪器。
本文使用導納矩陣分析設計法，完成矩陣後，將矩陣分解成三個方程式，再以基本架構組成完整電路，基本架構為OTRA的正負輸入端和輸入電壓間連接電阻，且有以下三種特性，1.每個方程式需包含一個由OTRA實現的轉移等效電容2.方程式中除轉移電容為正的一項外，將其他各項移往方程式的另一邊，正項表示信號從OTRA的正端輸入3.方程式中除轉移電容為正的一項外，將其他各項移往方程式的另一邊，負項表示信號從OTRA的負端輸入，
完成後的電路為三階振盪器，由三顆OTRA以及五顆電阻所組成。模擬使用HSPICE 軟體，及TSMC035μm 製程參數進行模擬。電路模擬結果與原先設計接近。最後，調降OTRA的偏壓Vbias，及變動OTRA中的電晶體長度L，來控制振盪器之振幅。

Operational Trans-Resistance Amplifier(OTRA) can be described by the equation . OTRA is dual to Operational Trans-Conductance Amplifier (OTA) which is extensively used in analog circuit design . For this reason , OTRA has great potential in the future.
In the past, designer used to let the (transresistance gain) of OTRA approach to infinity ,but in real circuit it's not accurate , is finite.
Actually,OTRA can be approximated as a transfer capacitor. By this method, it's not need any capacitors in circuit. According to admittance matrix analytical synthesis method, we completed matrix and decomposed it into three equations. Each equation can be achieved by basic circuit structure and has four features:
1. Each equation must include a transfer equivalent capacitance of OTRA.
2.Items are in another side of equation except the positive equivalent capacitance of OTRA .Positive items mean input signals from OTRA‘s positive side.
3.Negative items mean input signals from OTRA‘s negative side.

This thesis proposed a third-order oscillator using OTRAs and resistors without capacitors. The circuit simulated with TSMC035μm process by HSPICE. The simulation result is closed to our design. Finally, we controlled the amplitude of oscillator by changing length(L) of MOS and V¬bias of OTRA.

目錄
摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 V
表目錄 VII
第一章 緒論 1
第二章 主動元件介紹 4
2-1 主動元件簡介 5
2-1-1 電流傳輸器(Current conveyor) 5
2-1-2 第二代電流傳輸器(Second-generation Current Conveyor；CCII) 6
2-1-3 第三代電流傳輸器(Third-generation Current Conveyor；CCIII) 9
2-1-4 運算轉導放大器(Operational Trans-Conductance Amplifier；OTA) 11
2-2運算轉阻放大器(Operational Trans-Resistance Amplifier；OTRA) 13
2-3結論 18
第三章 以OTRA 為主動元件發表之電路 19
3-1 以OTRA為主動元件發表之濾波電路 19
3-2以OTRA為主動元件發表之振盪器 24
3-3 結論 25
第四章 以OTRA 為主動元件設計三階振盪器 26
4-1 振盪器簡介 26
4-2電路設計 27
4-3電路模擬結果 39
4-4 振幅調整 47
4-5 近似與非近似分析 58
4-6 結論 62
第五章 總結及未來研究方向 63
5-1 總結 63
5-2未來研究方向 66
參考文獻 67




圖目錄
圖 2- 1電流傳輸器(Current conveyor) 5
圖 2- 2以第一階電路實現的基本current conveyor 5
圖 2- 3 CCII+之方塊圖 7
圖 2- 4 CCII+之內部電路 8
圖 2- 5 CCII-之方塊圖 8
圖 2- 6 CCII+之內部電路 8
圖 2- 7 以CCII+來實現CCIII 9
圖 2- 8 以COMS實現CCIII 10
圖 2- 9 以COMS實現CCIII之改良 10
圖 2- 10 OTA之方塊圖 11
圖 2- 11 Cascode OTA 12
圖 2- 12 OTRA方塊圖 13
圖 2- 13 OTRA之實現 13
圖 2- 14 OTRA之內部電路(1999年提出) 14
圖 2- 15 OTRA之內部電路(2006年提出) 15
圖 3- 1 Yuh-Shyan Hwang等學者提出MOSFET-C濾波電路 19
圖 3- 2 MOSFET resistor circuit (MRC)，及其方塊圖 19
圖 3- 3 Cem Cakir等學者提出之一階、二階全通濾波電路 20
圖 3- 4 Ugur Cam等學者所提出之一階全通濾波電路 21
圖 3- 5 Selquk Kiling等學者提出之一階全通濾波電路 22
圖 3- 6 由J.-J. Chen,H.-W等學者所提出電流式萬用二階濾波電路 23
圖 3- 7 Chun-Li Hou等學者所提出之OTRA構成的震盪器 24
圖 4- 1迴路分析法示意(1) 27
圖 4- 2 迴路分析法示意(2) 28
圖 4- 3節點分析法示意(1) 29
圖 4- 4節點分析法示意(2) 29
圖 4- 5 本文使用之基本架構 35
圖 4- 6 以OTRA實現(式4-2-24) 37
圖 4- 7以OTRA實現(式4-2-25) 37
圖 4- 8 以OTRA實現(式4-2-26) 38
圖 4- 9 本文之振盪器 38
圖 4- 10 Vbias=-0.75 R= 1050kΩ 之信號 41
圖 4- 11 隨頻率之變化 42
圖 4- 12 隨頻率之變化 42
圖 4- 13 隨頻率之變化 43
圖 4- 14 OTRA輸出端信號比較 44
圖 4- 15 電路之頻譜 46
圖 4- 16 L×1.1時 的信號 48
圖 4- 17 L×1.1之頻譜 48
圖 4- 18 L×1.2時 的信號 50
圖 4- 19 L×1.2之頻譜 50
圖 4- 20 L×1.3時 的信號 52
圖 4- 21 L×1.3之頻譜 52
圖 4- 22 L×1.4時 的信號 54
圖 4- 23 L×1.4之頻譜 54
圖 4- 24 對振幅的變化 56
圖 4- 25 振幅對THD的變化 56
圖 4- 26 對THD的變化 57
圖 4- 27 振盪電路 58























表目錄
表 2- 1 Current Conveyors於主動網路合成之應用 7
表 2- 2 OTRA內部MOS長寬比 16
表 2- 3 OTRA與OTA 比較 17
表 3- 1二階萬用濾波電路輸入與輸出關係 23
表 4- 1 轉移等效電容值 43
表 4- 2 調整後振盪電路之特性 44
表 4- 3 相角差 45
表 4- 4 L調整後數值比較 55
表 4- 5 理想與非理想之比較 62

參考文獻
[1] C. M. Chang and B. M. Al-Hashimi, “Analytical synthesis of voltagemode OTA-C all-pass filters for high frequency operation,” in Proc.IEEE Int. Symp. Circuits Syst. (ISCAS) , vol. I, pp. 461–464, May. 2003.
[2] C. M. Chang and B. M. Al-Hashimi, “Analytical synthesis of currentmode high-order OTA-C filters,” IEEE Trans. Circuits Syst. I, Fundam.Theory Appl, vol. 50, no. 9, pp. 1188–1192, Sep. 2003.
[3] C. M. Chang, B. M. Al-Hashimi, Y. Sun, and J. N. Ross, “New highorder filter structures using single-ended-inp ut OTAs and grounded capacitors,”IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 51, no. 9, pp.458–463, Sep. 2004.
[4] C. M. Chang, C. L. Hou, W. Y. Chung, J. W. Horng, and C. K. Tu, “Analytical
synthesis of high-order single-input OTA-grounded C all-pass and band-reject filter structures,” IEEE Trans. Circuits Syst. I, Fundam.Theory Appl., vol. 53,no. 3, pp. 489–498, Mar. 2006.
[5] C. M. Chang, “Analytical synthesis of the digitally programmable voltage-mode OTA-C universal biquad,” IEEE Trans. Circuits Syst. II,Exp. Briefs, vol. 53, no. 8, pp. 407–411, Aug. 2006.
[6] K. C. Smith and A. Sedra, ―The current conveyor-a new circuit building block‖,
IEEE Proc, vol. 56, pp. 1368-1369, 1968.
[7] A. Sedra and K. C. Smith, “A second-generation current conveyor and its applications”, IEEE Trans on Circuit Theory, CT-17, pp. 132-134,1970.
[8] C. Acar and H. Kuntman ,"Limitations on input signal level in voltage-mode
active-RC filters using current conve" Microelectronics Journal,
vol.30,pp.69–76,1999
[9] A. Fabre, “Third-generation current conveyor：a new helpful active element”,
Electron. Lett., vol. 31, no. 5, 1995.
[10] A. Piovaccari, ―"CMOS integrated third-generation current conveyor"
Electronics Letters, vol. 31, no. 15, pp. 1228-1229, 1995.
[11] M. Bialko and R. W. Newcomb, “Generation of all finite linear circuits using Integrate DVCCS, ” IEEE Trans. on Circuit Theory, vol. 18, No. 6, pp.733–736, Nov. 1971.
[12]U.C.,HAKAN K. and CEVDET A."On the realization of OTA-C oscillator"0020-7217/98 Taylor&;Francis Ltd,1998.
[13] J.-J. Chen, H.-W. Tsao, and C.-C. Chen, “Operational trans-resistance amplifier using CMOS Technology”,Electronic letters22nd,Vol.28 No.22,Oct. 1992.
[14] K. N. Salama and A. M. Soliman, ―CMOS operational trans-resistance
amplifier for analog signal processing‖, Microelectronics J., vol.30, pp. 235-245,
1999.
[15] Mostafa H, Soliman A. ―A modified CMOS realization of the operational
transresistance amplifier ‖, Frequenz,60:70–6, 2006.
[16] Hwang, Y. S., Chen, J. J., and Lee, W. T., “High-order linear transformation MOSFET-C filters using operational transresistance amplifiers”, IEEE Int. Symposium on Circuits and Systems (ISCAS), 2005, 4, pp. 3275-3278.
[17] Cem Cakir, Ugur Cam, and Oguzhan Cicekoglu, “Novel allpass filter configuration employing single OTRA,” IEEE Trans. Circuit Syst. pt-II :express briefs, Vol. 52,no. 3, March 2005, vol. 54, no. 8, pp. 649-652, Nov. 2007.
[18] Ugur Cam, Cem Cakir, and Oguzhan Cicekoglu, “Novel transimpedance type first-order all-pass filter using single OTRA,’’, AEU - International Journal of Electronics and Communications , Vol. 58, Issue 4, Pages 296-298, 2004.
[19] Selquk Kiling and Ugur Cam, “Operational transresistance amplifier based
first-order allpass filter with an application example,’’, The 47th Midwest
Symposium on Circuits and Systems (MWSCAS 2004), vol.1 ,2004.
[20] Chen, J. J., Tsao, H. W., Liu, S. I., and Chiu, W., “Parasitic-capacitance-insensitive current-mode filter using operational transresistance amplifiers”, IEE Proc. Circuits Devices Syst., 1995, 142, (3), pp. 186-192.
[21] Chun-Li Hou, Chin-Wei Chang, Jiun-Wei Horng, “A quadrature oscillator employing the dominant poles of the OTRAs,” Journal of Advanced Engineering Vol. 2, No. 3, pp. 185-187 , July 2007.
[22] A. Fabre, O. Saaid, F. Wiest and C. Boucheron “Current controlled bandpass filter based on translinear conveyors”, Electronics letters, Vol.31, No.20, 1727-1728, 28th Sep. 1995.
[23] Ali TOKER, Ece O. G. and Serder Ö. “New high-Q bandpass filter configuration using current conveyor based all-pass filters,” IEEE Trans. Circuit Theory, 0-7803-7057-0 pp.165-168, 2001.



[24] S. Szczepanski, A. Wyszznski, and R. Schaumann, ‘Highly linearvoltage-
controlled CMOS transconductors’ , IEEE Transactions on Circuits and Systems-Part I, Vol. 40, No. 4 pp. 258-262, 1993.
[25] J. J. Chen, H. W Tsao, and C. C Chen, “Operational transresistance amplifier using CMOS technology,” Electronics Letters, 28, pp. 2087-2088, 1992.
[26] Gokcen, A., Kilinc, S., Cam, U., “Second-order analog filter design using a single OTRA suitable for integration”, IEEE Int. Conf. Signal Processing and Communications Applications, 2007, pp. 1-4.
[27] Soliman, A. M., and Madian, A. H., “MOS-C Tow Thomas filter using voltage op amp, CFOA, and OTRA”, Journal of Circuits, Systems, and Computers, 2009, 18, (1), pp. 151-179.
[28] Soliman, A. M., and Madian, A. H., “MOS-C KHN filter using voltage op amp, CFOA, OTRA, and DVCC”, Journal of Circuits, Systems, and Computers, 2009, 18, (4), pp. 733-769.
[29] Hwang, Y. S., Wu, D. S., Chen, J. J., Shih, C. C., and Chou W. S., “Design of current-mode MOSFET-C filters using OTRAs”, Int. J. Circuit Theory and Applications, 2009, 37, (3), pp. 397-411.
[30] Ravindran, A., Savia, A., Younus, I., Ismail, M., “A 0.8 V CMOS filter based on a novel low voltage operational transresistance amplifier”, The Midwest Symposium on Circuits and Systems (MWCAS), 2002, 3, pp. III-368-371.
[31] K.N. Salama, A.M. Soliman, “Novel oscillators using the operational transresistance amplifier,” Microelectronics Journal 31, 39–47 ,2000.
[32] S. Kılınç, A. U. Keskin, and U. Cam , “Cascadable voltage-mode multifunction biquad employing single OTRA,” Frequenz, 61/3-4, 84-86, Nisan, 2007.
[33] Pandey, R., Bothra, M., “Multiphase sinusoidal oscillators using operational transresistance amplifier”, IEEE Symposium on Industrial Electronics &; Applications, 2009, 1, pp. 371-376.
[34] Kilinc, S., and Cam, U., “Realization of all-pass filters using operational transresistance amplifier (OTRA)”, IEEE Proc. Signal Processing and Communications Applications Conference, 2004, pp. 133-136
[35] Kacar, F., “Operational transresistance amplifier based current-mode all-pass filter topologies”, Applied Electron. (AE), 2009, pp. 149-152.
[36] Salama, K. N., and Soliman, A. M., “CMOS operational trans-resistance amplifier for analog signal processing”, Microelectron. J., 1999, 30, pp. 235-245.
[37] Kafrawy, A. K., and Soliman, A. M., “A modified CMOS differential operational transresistance amplifer (OTRA)”, Int. J. Electron. Commun. (AEU), 2009, 63, pp. 1067-1071.
[38] Chiu, W. W., Jsay, J. H., Liu, S. I., Tsao, H. W., Chen, J. J., “Single-capacitor MOSFET-C integrator using OTRA”, Electron. Lett., 1995, 31, (2), pp. 1796-1797.
[39] Kacar, F., Cam, U., Cicekoglu, O., Kuntman, H., Kuntman, A., “New parallel immittance simulator realizations employing a single OTRA”, The Midwest Symposium on Circuits and Systems (MWCAS), 2002, 1, pp. I-303-306.
[40] Hou, C. L., Chien, H. C., and Lo, Y. K., “Squarewave generators employing OTRAs”, IEE Proc. Circuits Devices Syst., 2005, 152, (6), pp. 718-722.
[41] Lo, Y. K., and Chien, H. C., “Switch-controllable OTRA-based square/triangular waveform generator”, IEEE Trans. Circuits Syst.-II, 2007, 54, (12), pp. 1110-1114.
[42] Lo, Y. K., and Chien, H. C., “Current-mode monostable multivibrators using OTRAs”, IEEE Trans. Circuits Syst.-II, 2006, 53, (11), pp. 1274-1278.
[43] Lo, Y. K., and Chien, H. C., “Single OTRA-based current-mode monostable multivibrator with two triggering modes and a reduced recovery time”, IET Circuits Devices Syst., 2007, 1, (3), pp. 257-261.
[44] Lo, Y. K., Chien, H. C., and Chiu, H. J., “Switch-controllable OTRA-based bistable multivibrators”, IET Circuits Devices Syst., 2008, 2, (4), pp. 373-382.
[45] http://wikipedia.tw/