Common Source Amplifer Ai j EE105 Fall 2005 Microelectronic Devices and Circuits Lecture 20 Common Source Amplifier Frequency Response DC Bias is problematic what sets VGS 5 CS Short Circuit Current Gain Announcements Homework 9 due next Tuesday Lab 7 this week Lab 8 next week please read Chapter 9 Reading Chapter 10 10 2 10 3 2 10 4 3 5 Transfer function Ai j g m 1 j Cgd g m j Cgs Cgd 2 Lecture Material 6 Magnitude Bode Plot Last lecture Second order circuits Started frequency response of amplifiers Transition frequency Current gain 1 This lecture Common source amplifier frequency response Miller effect Zero order time constants T 3 7 1 Frequency Response MOS Unity Gain Frequency Since the zero occurs at a higher frequency than pole assume it has negligible effect Ai gm 1 j C gs Cgd T KCL at input and output nodes analysis is made complicated due to Zgd branch see H S pp 639 640 for common emitter gm Cgs Cgd Vout g m ro roc RL 1 j z Vin 1 j p1 1 j p 2 W VGS VT g 3 VGS VT L T m 2 2 C gs L2 WLCox 3 Performance improves with L2 for long channel devices For short channel devices the dependence is L1 V V GS T E Time to 3 VGS VT v eff L cross L T 2 channel 2 L L L L 8 Cox Small signal model omit Ccs due to avoid complicated analysis ICS Low frequency gain Zero z T gm Cgs C gd 11 p1 1 Cgd Rout Cgd RS Cgs 1 g m Rout p 2 RS Rout Cgd Rout Cgd RS Cgs 1 g m Rout vOUT Rs vs Poles Common Source Voltage Amplifier VDD RL VGS VSS 9 Miller Impedance CS Voltage Amp Small Signal Model Cgd Rs 12 Consider the current flowing through an impedance Z hooked up to a black box where the voltage gain from one terminal to the other is fixed vout vs Cgs vgs gmvgs ro roc Av RL v2 v1 I Z v1 10 I 1 Av v1 v2 v1 Av v1 v1 Z Z Z v2 13 2 Comparison with Exact Analysis Miller Impedance Notice that the current flowing into Z from terminal 1 looks like an equivalent current to ground where Z is transformed down by the Miller factor Miller result p1 1 1 Av Z I v1 Z M 1 1 Av Z From terminal 2 the situation is reciprocal Exact result 1 Av 1 v v v Av 1v2 I 2 1 2 v2 Z Z Z Z M 2 C Rout C p1 1 RS r C 1 g m Rout Z 1 Av 1 14 17 Some Examples Miller Equivalent Circuit Note Z M 1 Z M 2 Z Common source amplifier AvCgd negative large number 100 Z Z M 1 1 Av Z Z M 1 1 Av 1 Miller multiplied cap has detrimental Impact on bandwidth We can decouple these terminals if we can calculate the gain Av across the impedance Z Often the gain Av is weakly depedendent on Z The approximation is to ignore Z calculate Av and then use the decoupled Miller impedances Common drain amplifier AvCgd slightly less than 1 15 CE Amplifier using Miller Approx This is a technique to find the dominant pole of a circuit only valid if there really is a dominant pole Cgd vout For each capacitor in the circuit you calculate an equivalent resistor seen by capacitor and form the time constant i RiCi vs Cgs vgs 18 Method of Open Circuit Time Constants Use Miller to transform Cgd Rs Bootstrapped cap has negligible impact on bandwidth gmvgs ro roc RL The dominant pole then is the sum of these time constants in the circuit p dom 16 1 1 2 L 19 3 Equivalent Resistance Seen by Capacitor For each small capacitor in the circuit Open circuit all other small capacitors Short circuit all big capacitors Turn off all independent sources Replace cap under question with current or voltage source Find equivalent input impedance seen by cap Form RC time constant This procedure is best illustrated with an example 20 Example Calculation Cgd Rs vout vs Cgs vgs gmvgs ro roc RL 21 4
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