劉深淵臺灣大學：電機工程學研究所劉偉行Liu, WeihsingWeihsingLiu2007-11-262018-07-062007-11-262018-07-062004http://ntur.lib.ntu.edu.tw//handle/246246/53379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。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.Abstract Chapter 1 Introduction ……………………………………………………….. 1 1.1 Motivation ……………………………………………………..… 1 1.2 Outline of The Dissertation ……………………………………… 2 1.3 Overview of The Techniques ………………………………….… 2 a. Exponential function circuits based on the Taylor’s series expansion…………………………………… 2 b. Exponential function circuits based on the pseudo-exponential function………………………………… 3 c. Voltage-to-current converter………………………………… 3 1.4 Design considerations…………………………………………. 5 Chapter 2 Exponential function circuits using the Taylor’s series expansion……………..………………………… 6 2.0 Overview …………………………………………………….. 6 2.1 CMOS exponential VTC converter using composite NMOS transistors ……………………………………………………… 6 2.1.1 Introduction ………………………………………………… 6 2.1.2 Circuit implementation…………………………………….. 7 2.1.3 Simulation results………………………………………….. 9 2.1.4 Summary………………………………………………….... 10 2.2 CMOS differential-mode exponential VTC converter………… 10 2.2.1 Introduction ……………………………………..…….… 10 2.2.2 Design principle and circuit implementation………….…… 11 2.2.3 Experimental results…….………………………………….. 14 2.2.4 Summary………………………………………………….... 18 2.3 Conclusion…………………………………………………….. 18 Chapter 3 Exponential function circuits using the pseudo-exponential function……………………………………. 20 3.0 Overview………………….…………………………………… 20 3.1 CMOS 1/x circuit……………………………………………… 20 3.1.1 Introduction ………………………………………………… 20 3.1.2 Circuit implementation…………………………………..… 21 3.1.3 Applications……………………………………………...… 23 3.1.4 Experimental results…………………….…………..……… 25 3.1.5 Summary………………………………………….………… 28 3.2 CMOS current-controlled exponential function generator…….. 28 3.2.1 Introduction………………………………………………… 28 3.2.2 Design principle and the implementation of the current-mode divider ………………………………..……… 29 3.2.3 Transistor mismatch analysis………………………..……… 31 3.2.4 Implementation of current-controlled exponential function generator …………………………….………..……..……… 32 3.2.5 Experimental results……………………………………...… 33 3.2.6 Summary…………………………………….……………… 36 3.3 CMOS voltage-control exponential function generator……….. 37 3.3.1 Introduction………………………………………………… 37 3.3.2 Circuit implementation of the voltage-mode divider….… 37 3.3.3 Transistor mismatch analysis……………………….……… 40 3.3.4 Implementation of the voltage-controlled exponential function generator…………………………………………… 42 3.3.5 Experimental results………………………………………… 43 3.3.6 Summary…………………………………….……………… 48 3.4 Conclusion……………………………………………….…….. 49 Chapter 4 Applications of the CMOS exponential function circuits……… 50 4.0 Overview……………………………………………….……… 50 4.1 Low-voltage CMOS variable-gain amplifiers………….……… 50 4.1.1 Introduction……….………………………………………… 50 4.1.2 Circuit implementation…………………………………….. 51 4.1.3 Transistor mismatch analysis………………………………. 55 4.1.4 Experimental results……………………………………..…. 56 4.1.5 Summary……………………………………..…………….. 62 4.2 Low-voltage and low-power variable-gain amplifier……….… 62 4.2.1 Introduction…………..…………………………………….. 62 4.2.2 Circuit implementation…………………………………….. 62 4.2.3 Experimental results……………………………………..…. 64 4.2.4 Summary………………………………..………………….. 68 4.3 Low-voltage and low-power CMOS VTC converter and its application………………………………………..……………. 68 4.3.1 Introduction………………………………………………… 68 4.3.2 Circuit implementation…………………………………..… 69 4.3.3 Mismatch analysis……………………………..…………… 72 4.3.4 Application-A voltage-mode four-quadrant multiplier……… 73 4.3.5 Experimental results ……………………..………………… 74 4.3.6 Summary………………..…………………….……..……… 79 4.4 Conclusion…………………………………………………….. 80 Chapter 5 Conclusions ………………………………………………………… 81 Bibliography …………………………………………..………………………... 83 Publication List ………………………………………………………………… 872087272 bytesapplication/pdfen-US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CMOSexponential functionvariable-gain amplifiervoltage/current converterthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53379/1/ntu-93-D87921004-1.pdf