Miller Effect Examples EE105 Fall 2005 Common source amplifier AvCgd negative large number 100 Microelectronic Devices and Circuits Lecture 21 Miller multiplied cap has detrimental Impact on bandwidth Time Constants Frequency Response of Common Drain Common Source Amplifiers Common drain amplifier AvCgd slightly less than 1 Bootstrapped cap has negligible impact on bandwidth Announcements 4 Method of Open Circuit Time Constants Homework 9 due today Homework 10 due next Tuesday Lab 8 this week please read Chapter 9 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 Friday is a University holiday no lab discussion Friday lab 8 on November 18 No new lab next week The dominant pole then is the sum of these time constants in the circuit Midterm 2 next Thursday Nov 17 Review session on Tuesday Nov 15 6 30 8pm p dom Reading Chapter 10 10 2 10 3 2 10 4 3 5 10 5 10 6 1 1 2 L 2 Lecture Material 5 Equivalent Resistance Seen by Capacitor For each small capacitor in the circuit Last lecture Open circuit all other small capacitors Common source amplifier frequency response Miller effect Short circuit all big capacitors Turn off all independent sources This lecture Replace cap under question with current or voltage source Zero order time constants Common drain common gate frequency response Find equivalent input impedance seen by cap Form RC time constant This procedure is best illustrated with an example 3 6 1 Example Calculation Example Calculation Cgd Rs Cgd Rs vout vs Cgs vout gmvgs vgs ro roc vs RL Cgs gmvgs vgs ro roc RL 7 Gain Bandwidth Product Higher Order Time Constants Result from Miller General two pole transfer function 1 j z 1 z 2 A j A0 1 j 1 j p1 p1 Cgd p1 1 RS Cgs 1 g m Rout 1 j A j A0 a1 N j a2 Low frequency gain v Avo out g m Rout v s R R S L 1 a1 j a2 j 2 1 1 p1 p 2 10 1 p1 p 2 8 Higher Order Time Constants 11 Gain Bandwidth Product Considering only the first pole assuming zero and 2nd pole are at much higher frequencies Coefficient a1 a1 R011C1 R022C2 Avo Av j dB Coefficient a2 a1 R211C1R022C2 R011C1R122C2 Av j Avo p1 Avo A vo 1 j p1 p1 This is exact If p1 p2 1 a1 p1 a a2 1 p 2 Av j 1 Avo p1 9 12 2 Voltage Gain AvC Across C Gain Bandwidth Product For common source amplifier Avo p1 AvCgs g m Rout Cgd RSCgs RS 1 g m Rout Rout 1 RL Rout Note this voltage gain is neither the two port gain nor the loaded voltage gain C in Cgd CM Cgd 1 AvCgs Cgs Special case RS RL ro roc g m RL Avo p1 T RS Cgs g m RLCgd not that great C in Cgd 1 Cgs 1 g m RL C in Cgd 13 Common Drain Amplifier Bandwidth of CC Amplifier VDD Input low pass filter s 3 dB frequency Cgs p 1 RS Cgd 1 g m RL vOUT Rs Substitute favorable values of RS RL vs VGS 16 ICS RS 1 g m RL RL 1 g m Cgd Cgd g m p 1 1 g m Cgd 1 BIG VSS 14 Model not valid at these high frequencies p g m Cgd T 17 Bandwidth of the Common Gate Amplifier Two Port CD Model with Capacitors Ignore gmb Find Miller capacitor for Cgs note that the gate source capacitor is between the input and output 15 18 3 Two Port CB Model with Capacitors Cgd vout Cgs vgs gmvgs ro RL roc Rs vs No Miller transformed capacitor Unity gain frequency is on the order of T for small RL 19 Summary of Single Stage Amplifiers CS suffers from Miller magnified capacitor for highgain case CD Miller transformation nulled capacitor wideband stage CG no Millerized capacitor wideband stage for low load resistance 20 4
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