1Department of EECS University of California, BerkeleyEECS 105 Fall 2004, Lecture 41Lecture 41: Review Frequency Response, FET physicsProf. J. S. SmithDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithFinal ExamzCovers the course from the beginningzDate/Time: SATURDAY, MAY 15, 2004 8-11A zLocation: BECHTEL auditorium zOne page (Two sides) of notes2Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithQ&A about the finalQ: Are differential amplifiers going to be on the exam?A: No, there will not be a differential amplifier question.Q: Do we need to know a lot of device physics for BJTs? A: No, there won’t be any BJT physicsQ: Will there be any BJT circuits questions on the exam?A: No, the exam will not have any BJT transistor problems.Q: How much of the material from before Midterm 1 willbe tested in detail? A: Material before midterm 1 is fair game.Q: Also, are we responsible for Chapter 5 i.e.- digital circuits?A: No, nothing specifically on digital circuits or from chapter 5.Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithLast Week of LecturezMonday:–Review of Frequency domain analysis of linear circuits, Bode plots.zWednesday:–Frequency Response–Semiconductor materials, FET physics and modelszFriday:–Review of active linear circuits, amplifiers wrapup3Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithFrequency response: CSzWhen we take into account a finite source impedance in a common source amplifier, the capacitances will reduce the voltage swing at the gate at high frequencies.Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithParasitic CapacitancesThe transfer function will be a low pass filter, with a pole at the frequency determined by the source resistance and the capacitance.vsrs4Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithHigh frequency zeroAt very high frequencies, the gain flattens out again, because the capacitor couples from the gate to the drain directly, as a passive circuitvsrsDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithMagnitude Bode Plot ωpβo zωTω0 dBpoleUnity current gainzeroLow frequencygain5Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithMiller Capacitance CMEffective input capacitance:()[]gdvCgdgdvCMinCAjCjACjZgd−=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−==111111ωωωAV,Cx+─+─VinVoutCxAV,Cx+─+─Vout(1-Av,Cx)Cx(1-1/Av,Cx)CxDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithFrequency response−+gsv−+outvinmvgorgdCgsCLR~SR−+gsv−+outvinmvgorgsCLR~SRMC6Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithSome ExamplesCommon source (emitter) amplifier:=gdvCANegative, large number (-100)Common drain (collector) amplifier:=gsvCASlightly less than 1→Miller Multiplied Cap has Detrimental Impact on bandwidth“Bootstrapped” cap has negligible impact on bandwidth!()gdgdCVMCCACgd1001,≈−=()gsgsCVMCCACgs01,≈−=Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithOpen Circuit Time Constants zFor a circuit dominated by a single polezFor each capacitor in the circuit you calculate an equivalent resistor “seen” by capacitor and form a time constant τi=RiCizThe dominant pole then is the sum of these time constants in the circuit,121p domωττ=++L7Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithEquivalent Resistance “Seen” by CapacitorzFor 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 constantDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithRemember…For a given capacitor:zIf the frequency is high compared to the 1/RC for the capacitor in that location in the circuit–That Capacitor can be modeled as a shortzIf the frequency is low compared to the 1/RC for the capacitor in that location in the circuit–That Capacitor can be modeled by an open circuit.8Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCommon-Drain Amplifier21()2DS ox GS TWICVVLµ=−2DSGS ToxIVVWCLµ=+Weak IDSdependenceDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCD Voltage Gain1out min mb mvgvgg≈≈+9Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCD Output ResistanceSum currents at output (source) node:|| ||tout o octvRrri=tmtmbtigvgv=+1outmmbRgg≈+Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCD Output Resistance (Cont.)ro|| roc is much larger than the inverses of the transconductances Æ ignore1outmmbRgg≈+Function: a voltage buffer• High Input Impedance• Low Output Impedance10Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithAdd capacitorsProcedure:zStart with small-signal two-port modelzAdd device (and other) capacitorsgdCgsC−+inoutvv≈Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCommon Gate AmplifierDC bias:SUP BIAS DSII I==11Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCG→Current bufferout d tii i==−1iA=−Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCG Input Resistancegstvv=−mbminggR+≈1We found the approximation:12Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCG Output Resistance)]1([||][||SmoocSomoocoutRgrrRrgrrR+=+≈Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 41 Prof. J. S. SmithCG Two-Port ModelThe function of the CG amp was a current buffer:•Low
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