EECS 105 Spring 2005 Lecture 19 R T Howe Lecture 19 Last time Phasor analysis techniques Rapid sketching techniques for Bode Plots Today 2nd order circuits in the frequency domain MOSFET models Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe thin Film Bulk Acoustic Resonator FBAR RF MEMS Agilent Technologies IEEE ISSCC 2001 Drive Electrode 2 GHz resonator N 1000 Thin Piezoelectric Film Brian Otis Jan Rabaey BWRC low noise oscillator Equivalent Circuit C1 Dept of EECS C0 Cx Sense Electrode R0 Rx C2 Lx University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Phasor Analysis of 2nd Order Circuit Vs j L Vl R Vc Il Ir Ic 1 j C Impedance divider 1 j C Vc Vs 1 j C R j L Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Transfer Function Simplifying 1 H j 2 1 j RC LC Define parameters o 1 LC RC 1 H j 2 1 o j Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Limiting Cases Magnitude and Phase Low frequency o High frequency o Resonant frequency o Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Inductor Capacitor Tuning At resonance the impedance of the capacitor cancels the impedance of the inductor phasor current is maximum and capacitor voltage peaks How sharp or narrow is the resonance o Define the quality factor Q Dept of EECS Q 1 o University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Magnitude Bode Plot 60 H dB 40 20 o 0 o o 20 Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Phase Bode Plot o 0 Phase H o o 45 90 135 180 Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Common Source Amplifer Ai j DC Bias is problematic what sets VGS Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe CS Short Circuit Current Gain Transfer function Ai j Dept of EECS g m 1 j C gd g m j C gs C gd University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe Magnitude Bode Plot Transition frequency Current gain 1 T Dept of EECS University of California Berkeley EECS 105 Spring 2005 Lecture 19 R T Howe MOS Unity Gain Frequency Since the zero occurs at a higher frequency than pole assume it has negligible effect gm Ai 1 j Cgs Cgd T gm Cgs Cgd W Cox VGS VT 3 V V gm GS T L T 2 2 2 Cgs L WLCox 3 Performance improves like L 2 for long channel devices For short channel devices the dependence is like L 1 Dept of EECS VGS VT Time to E v 3 VGS VT eff L cross T L 2 channel L L L University L of California Berkeley 2
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