Physics116A,12/4/06Draft Rev. 1, 12/12/06D. PellettAmplifier Frequency Response, Feedback, Oscillations;Op-Amp Block Diagram and Gain-Bandwidth Product2Negative Feedback and Voltage Amplifier• See solution of assigned Prob. 10.35 for proof of relations. (I did AFingeneral before. May do RiFon board if time permits.)• Note RiFis increased (improved) and RoFis decreased (also improved).• Example: If A = 200000, Rin= 2 MΩ, Ro= 75 Ω and B = 1/20,then A = 20, RiF= 20 GΩ and RoF= 7.5 mΩ.7(see solutions to Prob. 10.35 for proofs)AB is called the loop gain.3Voltage Amplifier: AFdependence on AB = 1/20, AF= A/(1 + AB) = [A−1+ B]−1:A AF200000 19.998100000 19.99610000 19.961000 19.6500 19.2200 18.2100 16.750 14.3• AFmax= 20. If A >> AFmax, AFis insensitive to A. AFis down ≈ 3 dB frommaximum when A = 50.• Reduces distortion due to A nonlinearity, allows for variations in amplifiergain from device to device. (What Black wanted back in the 1920’s forhis telephone long-distance line amplifiers)• Suppose A is 200000 at low frequency (say 1 Hz) but falling with fre-quency like 1/f at high frequencies due to a built-in low-pass filter withfc= 5 Hz. With feedback, the -3 dB bandwidth would be improved,since AFremains high until A has fallen many orders of magnitude.8Phase-Shift Oscillator and AB = -1Phase-Shift Oscillator• See solution of assigned Prob. 10.35 for proof of relations. (I did AFingeneral before. May do RiFon board if time permits.)• Note RiFis increased (improved) and RoFis decreased (also improved).• Example: If A = 200000, Rin= 2 MΩ, Ro= 75 Ω and B = 1/20,then A = 20, RiF= 20 GΩ and RoF= 7.5 mΩ.7Sinusoidal oscillation when AB=-14Amplifier Low Frequency Limitations5Amplifier Low Frequency Limitations (continued)677Amplifier High Frequency Limits•Model for parallel (shunt) capacitances to ground in amplifier circuit:87Amplifier High Frequency LimitsWhere are these shunt capacitances?•Model for parallel (shunt) capacitances to ground in amplifier circuit:8Common Emitter Amplifier HF Limits•At high frequencies, must consider BE and BC diode capacitancesCBCCBE9Shunt Capacitances In Small-Signal AC Models•How to deal with Cc (or Cgd) which connects input and output?Base-Emitter Diode Capacitance Base-Collector Diode CapacitanceSimple BJT Model at High Frequencies:Simple HF JFET Model:10Use Miller’s Theorem to Split Cc (or Cgd)Apply to HF BJT model in a common emitter amplifier with gain = -A:•Input circuit (be) and output circuit (ce) are now separated11Miller’s Theorem Proof•QED Given:Node 2 (write in terms of v2):Node 1(write in terms of v1):12Common Emitter Amplifier Input StageCE Amplifier13Common Emitter Amplifier Output Stage14FET HF Model and Analysis15Input Circuit Upper Corner Frequency for 9.5416Output Circuit Upper Corner Frequency for 9.5417MOSFET Amplifier Example18Effect of CS on Low Frequency ResponseSimple HF JFET Model:19Upper Corner Frequency: Input StageSimple HF JFET Model:20Output Stage Upper Corner FrequencySimple HF JFET Model:21Ways to Improve Amplifier HF Response•Reduce Miller effect•Common Base amplifier (see solution to Problem 9.21)•Differential Amp using non-inverting input with inverting input grounded•Cascode circuit – similar to above22Common Base Detector Amplifier•No Miller effect since cc, cc grounded at base; fast if use fast BJT (small cc, cc etc.)*small signal AC model*23Can We Understand Amplifier Operation?•This is an amplifier for short pulses of width ~1 ns.•Pulse response is covered in 116B (i.e., beyond the scope of this course) but we can understand its operation based on what we have learned so far in Physics 116A plus basic physics.•We want the output pulse to have a fast risetime (sharp leading edge).•If Rs ≈ 50 Ω, the input emitter circuit has fc ≈ 2 GHz so the BJT delivers a short current pulse at the collector which follows the input voltage: ic(t)≈ αvin(t)/re.•The collector current is integrated: ∫pulse ic(t) dt = Q = Cv′ to charge the combined capacitance C = 2 Cc of the input BJT and the first BJT in the Darlington pair, producing the rapidly rising leading edge of v′ and the output pulse. •Integration occurs because the time constant of the BJT collector circuit is τ = RC = 20 kΩ x 2 pF = 40 ns, much longer than the input pulse width (assume the base current of the Darlington input transistor is negligible).•The pulse height of the output pulse is proportional to the charge of the input pulse.•The output is thus expected to look like the sketch. The tail can be shortened using a “speedup” RC network following the emitter follower output (not shown).(this page is supplementary material – not on final)24Check Simple Model With SPICE•Uses MPSH10 RF amplifier BJT: cc = 1 pfce = 1.5 pf•SPICE BJT model for MPSH10 is available from Fairchild web site:www.fairchildsemi.com•vin = V(5) (red)vout = V(8) (green)•Good agreement with simple modeltimevoltageXXX0.0 20.0 40.0 60.0 80.0 100.0ns-20.0-0.020.040.060.080.0100.0120.0140.0mV V(5) V(8)Page 1 of 1Fas t _P u ls e _Am p.c irPrinted: Sunday, December 10, 2006 5:06:46 PMFast Pulse Amplifier********************VEE!4! 0! DC! -12VBB!2! 0! DC! -6RC! 0! 1! 20KQ1! 1! 2! 3! QMPSH10RE1!3! 4! 20KC1! 5! 3! .01uVS! 9! 0! PWL ( 0 0V 1ns 0.05V 2ns 0V )RS! 9! 5! 50Q2! 0! 1! 6! QMPSH10Q3! 0! 6! 7! QMPSH10RE2!7! 4! 500C2! 7! 8! .01uRO! 8! 0! 1KRI! 5! 0! 10K********************.model QMPSH10 NPN(Is=69.28E-18 Xti=3 Eg=1.11 Vaf=100 Bf=308.6 Ne=1.197 Ise=69.28E-18 + Ikf=22.83m Xtb=1.5 Br=1.11 Nc=2 Isc=0 Ikr=0 Rc=4 Cjc=1.042p Mjc=.2468 Vjc=.75 Fc=.5 + Cje=1.52p Mje=.3223 Vje=.75 Tr=1.558n Tf=135.8p Itf=.27 Vtf=10 Xtf=30 Rb=10)********************.TRAN! .1ns! 100ns.controlrunplot! V(5) V(8).endcontrol.END(this page is supplementary material – not on final)25Other Possibilities to Avoid Miller Effect•Note the common base circuit lurking in bothHigh Av hereHigh Av here26BiFET Op-Amp Simplified Diagram•The differential amplifier and common emitter amplifier use the large Thévenin equivalent AC resistance of a current source along with the input resistance of the following stage to achieve large gain. See text, Sec. 10.2.•Note C1 makes use of the Miller Effect to achieve a large effective capacitance for a dominant low-pass filter.BJTs have identical characteristicsp-channel JFETsCurrent source and input resistance of next stage play role of RD or RC for