Translinear Loop Principle and Identification of the Translinear Loops Cheng Yuhua, Wu Xiaobo, Yan Xiaolang Institute of VLSI Design, Zhejiang University Hangzhou 310027, China Email: {chengyh, wuxb, yan}j vlsi.zju.edu.cn Abstract The principle of hybrid translinear (HTL) loop was presented, which made the principle of translinear (TL) loop be more complete. By proposing a method of decomposing an MOS transistor operated in triode region into two MOS transistors operated in saturation region, the principle of TL loop was simplified and the graphical equivalent topology was extended. In addition, the topological method to identify TL loops involved in translinear cell was successfully extended to all types of TL loops especially to HTL loop. Keywords translinear loop principle, hybrid integrated circuit, transistor model, topological method I. INTRODUCTION The translinear (TL) principle proposed by Gilbert in 1975 is one of the important contributions to circuit theory in the electronics era, which provides a way to analyze and synthesize circuits in BJTs that exploit the exponential current-voltage characteristic [1]. With the development of CMOS technology, the translinear principle of MOS transistors in weak inversion exploiting exponential current-voltage characteristic and in strong inversion exploiting square current-voltage are also presented [2]-[4]. The characteristic of MOS transistors in weak inversion is similar to BJTs for they all obey exponential law. Usually MOS transistors are seldom designed to work in weak inversion since the limited dynamic range and quite low speed. But in low voltage low power applications it has bright prospect. The dynamic translinear circuits were presented in some papers like [5], but they are beyond this paper. Now, due to the rapid development of the Integrated Circuit technology including BiCMOS technology, hybrid translinear (HTL) circuits [9] which comprise both BJTs and MOS transistors are becoming more and more important for their high performance of combining the merits of BJTs and MOS transistors. So it is necessary to analyze the principle of HTL circuits. In this paper, the principles of three types of TL circuit: BJTs translinear (BTL) circuits, MOS transistors translinear (MTL) circuits and HTL circuits, are all given out in section II which are simplified by the modes of transistors in section III. This work is sponsored by the National Natural Science Foundation of China under grant No.50237030 and 90207001. It also gains support from the National Semiconductor Corp. (NSC). A graphical representation and topological method to identify the multiple static translinear is presented in [6] in which the MOS transistors are in weak inversion. In section III the graphical representation is extended to MOS transistors in strong inversion and the topological method is extended to all the TL circuits especially to HTL circuits in section IV. II. TANSLINEAR LooP PRINCIPLE As well known, there are two topologies of TL circuits, up- down and stacked topology [7]. They obey the same principle according to KVL. For simplicity the body effect of MOS transistors is not considered because it can be canceled by connecting the source to substrate. A. BTL Circuit Principle The BTL circuit principle has been derived by Gilbert [1]. In a BTL loop with equal numbers of transistors arranged clockwise and counterclockwise. This is an essential requirement. From KVL, the BTL loop follows ZVbe ZVbe (1) cw ccw Where, cw and ccw refer to the connected directions of the devices, clockwise and counterclockwise respectively. Substitute the expression of Vb, to (1), ZVT ln(Ic /I) JVT ln(Ic /I). (2) cw ccw Where IC and IS are collector current and saturation current, respectively. VT is the thermal voltage approximately 26mV at room temperature. For simplicity, all the Is are equal, so HI~ HIc = tI I(3) cw ccw B. MTL Circuit Principle MOS transistor can work in weak inversion or in strong inversion and can work in saturated region or triode region. So there are many types of MTL circuit in theoretically. Usually, the MOS transistors are in saturated region and strong inversion, but as the requirement of low voltage the MOS transistors in triode region or weak inversion are used. The weak inversion transistors and strong inversion transistors have 1667 1-4244-0387-1/06/$20.00 (@2006 IEEE