R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyLecture 19• Last time:– Phasor analysis techniques– Rapid sketching techniques for Bode Plots• Today :–2ndorder circuits in the frequency domain– MOSFET modelsR. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, Berkeleythin-Film Bulk Acoustic Resonator (FBAR)RF MEMS• Agilent Technologies IEEE ISSCC 2001• 2 GHz resonator• N > 1000•Brian Otis, Jan Rabaey(BWRC): low-noise oscillator•Equivalent Circuit:Drive ElectrodeSense ElectrodeThin Piezoelectric FilmC0CxRxLxC1C2R0R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyPhasor Analysis of 2ndOrder Circuit Vs jωL Vc + - R1/( jωC)IlIrIc Vl+ -()++=)(/1/1LjRCjCjVVscωωωImpedance divider:R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyTransfer FunctionSimplifying:()−+=)112LCRCjjHωωωDefine parameters:LCo/1=ωRC=τ()()+−=)/112ωτωωωjjHoR. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyLimiting Cases: Magnitude and PhaseLow frequency:oωω<<High frequency:oωω>>Resonant frequency:oωω=R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyInductor-Capacitor “Tuning”At resonance, the impedance of the capacitor cancelsthe impedance of the inductor Æ phasor current is maximum and capacitor voltage peaksHow “sharp” or “narrow” is the resonance?Define the quality factorωω∆=oQτωoQ1=R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyMagnitude Bode Plot ωoω| H |dB 020 40 60 ωo + ∆ω ωo - ∆ω -20R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyPhase Bode Plot Phase(H) -90 -45 ωoω0ωo + ∆ω ωo - ∆ω -135 -180R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyCommon Source Amplifer: Ai(jω)DC Bias is problematic: what sets VGS?R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyCS Short-Circuit Current GainTransfer function:())(/1)(gdgsmgdmiCCjgCjgjA+−=ωωωR. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyMagnitude Bode Plot ωT Transition frequency:Current gain Æ 1R. T. HoweEECS 105 Spring 2005 Lecture 19Dept. of EECSUniversity of California, BerkeleyMOS Unity Gain Frequency• Since the zero occurs at a higher frequency than pole, assume it has negligible effect:1()migs gdgAjC Cω≈=+()mTgs gdgCCω=+2()()3223ox GS TmGSTTgsoxWCVVgVVLCLWLCµµω−−≈= =Performance improves like L^2 for long channel devices!For short channel devices the dependence is like ~ L^12()3~2GS TeffGS TTLVVEVVvLLLLLµµµωτ−−≈===Time to cross
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