EE105 Fall 2005 Microelectronic Devices and Circuits Lecture 10 MOS Transistor Small Signal Model Announcements Homework 5 due next Tuesday Lab 3 this week Lab 4 next week Reading Chapter 4 4 5 4 6 8 3 Midterm 1 in two weeks October 13 6 30 8pm Sibley 2 1 Lecture Material Last lecture Sample and hold MOS amplifier example This lecture MOSFET small signal model 3 Large Signal Analysis vO vDS t VDD 0 vIN vGS t 4 2 There is a Better Way What s missing didn t include device output impedance or charge storage effects must solve nonlinear differential equations Approach 2 Do problem in two steps DC voltages and currents ignore small signals sources set bias point of the MOSFET we had to do this to pick VGS already Substitute the small signal model of the MOSFET and the smallsignal models of the other circuit elements This constitutes small signal analysis 5 An MOS Amplifier Input signal RD VDD Supply Rail vo vs vGS VGS vs VGS I DS Output signal 6 3 Small Signal Analysis Step 1 Find DC Bias ignore small signal source IDS Q VGS was found in Lecture 9 7 8 4 Step 2 Small Signal Modeling What are the small signal models of the DC supplies 9 Small Signal Models of Ideal Supplies Small signal model i gsupply supply vsupply rsupply 0 short gsupply isupply vsupply 0 rsupply open 10 5 The Transconductance gm Defined as the change in drain current due to a change in the gatesource voltage with everything else constant I DS sat i gm D vGS W Cox VGS VT 2 1 VDS L 2 VGS VDS i D vGS VGS VDS g m Cox g m Cox W L 0 W Cox VGS VT 1 VDS L W VGS VT L Gate Bias 2 I DS W 2 Cox I DS W L Cox L gm 2 I DS VGS VT Drain Current Bias Drain Current Bias and Gate Bias 11 Output Resistance ro Defined as the inverse of the change in drain current due to a change in the drain source voltage with everything else constant Non Zero Slope I DS VDS 12 6 Evaluating ro iD W Cox VGS VT 2 1 VDS L 2 i ro D vDS r0 VGS VDS 1 1 W Cox VGS VT 2 L 2 r0 1 I DS 13 Total Small Signal Current iDS t I DS ids ids iDS i vgs DS vds vgs vds ids g m vgs Transconductance 1 vds ro Conductance 14 7 Putting Together a Circuit Model ids g m vgs 1 vds ro 15 MOS Amplifier RD vo vs I DS VDD 1 DC solution ID 0 1mA VGS 1 32V VDS 2 5V 2 Small signal gm VGS ro 2IDS 0 625mA V VGS VTn 1 IDS 16 8 17 MOS Amplifier Small Signal vgs vs id gmvgs vo idRd ro gmvsRd v AV o g m Rd vs Av 15 6 18 9 MOS Amplifier Output resistance typical value 0 05 V 1 ro Voltage gain 1 200k IDS 2 0 1 Av 25 200 14 3 0 32 Output resistance lowers voltage gain 19 Input and Output Waveforms Output small signal voltage amplitude 14 x 25 mV 350 Input small signal voltage amplitude 25 mV 20 10 What Limits the Output Amplitude 1 vOUT t reaches VDD or 0 or 2 MOSFET leaves constant current region and enters triode region vo max VDD VDD vo min VDS SAT VGS VTn 0 32V Vo max VDD VGS VTn 2 18V 0 Optimum bias point Vo vIN 21 11
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