EE105 Fall 2005 Microelectronic Devices and Circuits Lecture 20 Common Source Amplifier Frequency Response 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 2 1 Lecture Material Last lecture Second order circuits Started frequency response of amplifiers This lecture Common source amplifier frequency response Miller effect Zero order time constants 3 Common Source Amplifer Ai j DC Bias is problematic what sets VGS 5 2 CS Short Circuit Current Gain Transfer function Ai j g m 1 j Cgd g m j Cgs Cgd 6 Magnitude Bode Plot Transition frequency Current gain 1 T 7 3 MOS Unity Gain Frequency Since the zero occurs at a higher frequency than pole assume it has negligible effect Ai gm 1 j Cgs Cgd T gm Cgs Cgd W VGS VT 3 VGS VT L 2 L2 2 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 T L channel L2 L L L 2 8 g T m Cgs Cox Common Source Voltage Amplifier Small signal model omit Ccs due to avoid complicated analysis 9 4 CS Voltage Amp Small Signal Model Cgd Rs vout vs Cgs gmvgs vgs ro roc RL 10 Frequency Response KCL at input and output nodes analysis is made complicated due to Zgd branch see H S pp 639 640 for common emitter Vout g m ro roc RL 1 j z Vin 1 j p1 1 j p 2 Low frequency gain Zero z T gm Cgs C gd 11 5 Poles p1 1 Cgd Rout Cgd RS Cgs 1 g m Rout p 2 RS Rout Cgd Rout Cgd RS Cgs 1 g m Rout 12 Miller Impedance 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 Av v2 v1 I Z v1 I 1 Av v1 v2 v1 Av v1 v1 Z Z Z v2 13 6 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 I v1 1 Av Z Z M 1 1 Av Z From terminal 2 the situation is reciprocal I 1 Av 1 v2 v1 v2 Av 1v2 v2 Z Z Z Z M 2 Z 1 Av 1 14 Miller Equivalent Circuit Note Z M 1 Z M 2 Z Z M 1 Z 1 Av Z M 1 Z 1 Av 1 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 15 7 CE Amplifier using Miller Approx Use Miller to transform Cgd Cgd Rs vout vs Cgs vgs gmvgs ro roc RL 16 Comparison with Exact Analysis Miller result p1 1 Exact result C Rout C p1 1 RS r C 1 g m Rout 17 8 Some Examples Common source amplifier AvCgd negative large number 100 Miller multiplied cap has detrimental Impact on bandwidth Common drain amplifier AvCgd slightly less than 1 Bootstrapped cap has negligible impact on bandwidth 18 Method of Open Circuit Time Constants This is a technique to find the dominant pole of a circuit only valid if there really is a dominant pole For each capacitor in the circuit you calculate an equivalent resistor seen by capacitor and form the time constant i RiCi The dominant pole then is the sum of these time constants in the circuit p dom 1 1 2 L 19 9 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 10
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