互補式金氧半場效電晶體指數函數電路及其應用

CMOS Exponential Function Circuits and Their Applications

劉偉行(Weihsing Liu)

指導教授 ： 劉深淵

國立臺灣大學/電機資訊學院/電機工程學研究所/博士(2004年)

https://doi.org/10.6342/NTU.2004.10004

摘要

本論文提出一些可以產生指數函數及其應用之新電路。由於指數函數電路在傳統上是利用雙載子電晶體技術來實現，然而過去十餘年間，互補式金氧半場效 電晶體技術已經成為現代電路設計的主流 ，因此，利用互補式金氧半場效電晶體取代雙載子電晶體來設計指數函數電路將會更有助益。
本文一開始，將會討論在互補式金氧半場效電晶體技術中幾種可能用來產生指數函數電路的方法，如近似之泰勒級數展開式、虛擬指數函數；而金氧半場效電晶體偏壓於弱反轉區時其電壓與電流之特性關係亦將提及。接下來，根據泰勒級數展開式，二種不同的指數函數電路將被提出。然後會介紹一種可以用來實現虛擬指數函數的 “1/x” 電路，利用此一“1/x” 電路，一種電流控制和一種電壓控制的指數函數電路將可實現。 指數函數電路的應用將會在第四章介紹，其中包括有二種可變增益放大器和一種電壓/電流轉換器。論文最後之第五章則是結論部份。本論文中所提出之電路均已利用0.5 mm 2P2M 互補式金氧半場效電晶體製程製作，而實驗結果與理論分析則相吻合。

關鍵字

可變增益放大器 ； 指數函數 ； 電壓/電流轉換器 ； 互補式金氧半場效電晶體取

並列摘要

This dissertation developed some new circuits for generation of exponential function and their applications. Since the exponential function circuits were traditionally implemented by using of the bipolar technology. However, in the past decade, CMOS technology has become the major trend of modern circuit design. Therefore, it would be beneficial to use CMOS technologies rather than bipolar technologies to implement the exponential function circuit.
In the beginning, the possible methods of generating the exponential function in CMOS technology have been discussed, such as the approximated Taylor’s series expansion, pseudo-exponential function and the voltage and current characteristics of the MOSFET in weak inversion are also mentioned. Secondly, based on the Taylor’s series expansion, two different exponential function circuits have been developed. Next, a “1/x” circuit, which can be used to realize the pseudo-exponential function, is proposed. Based on the proposed “1/x” circuit, both the current and voltage-control exponential function circuits can be implemented. The applications of the exponential function circuits are proposed in Chapter 4, which includes two variable-gain amplifiers and a voltage-to-current converter. Finally, the conclusions are given in Chapter 5. All the proposed circuits have been fabricated in the 0.5 mm 2P2M CMOS process. The experimental results are in consistent with the theoretical analysis.

並列關鍵字

CMOS ； exponential function ； variable-gain amplifier ； voltage/current converter

參考文獻

[2] A. Motamed, C. Hwang and M. Ismail, “A low-voltage low-power wide-range CMOS variable gain amplifier”, IEEE Trans. on Circuits and Systems-II： Analog and Digital Signal Processing, pp.800-811, July 1998.

[3] P. C. Huang, L. Y. Chiou and C. K. Wang, “A 3.3-V CMOS wideband exponential control variable-gain-amplifier”, Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, Volume： 1, pp.285-288, 1998.

[4] C. Lin, T. Pimenta, and M. Ismail, “Universal exponential function implementation using highly-linear CMOS V-I converters for dB-linear (AGC) applications”, Proc. of 1998 IEEE Midwest Symposium on Circuits and Systems, pp.360-363, 1998

[5] K. Bult, and H. Wallinga, “A class of analog CMOS circuits based on the square law characteristics of an MOS transistor in saturation”, IEEE J. Solid-state Circuits, 1987, sc-22. pp.357-365

[6] C. C. Chang, and S. I. Liu, “Pseudo-exponential function using MOSFETs in saturation”, IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing, vol. 47, pp. 1318-1321, Nov. 2000.