Amplifier Frequency Response, Feedback, Oscillations; Op-Amp Block Diagram and Gain-Bandwidth Product Physics116A,12/4/06 Draft Rev. 1, 12/12/06 D. Pellett
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Negative Feedback and Voltage Amplifier AB is called the loop gain. (see solutions to Prob. 10.35 for proofs) 3
Voltage Amplifier: A F dependence on A B = 1/20, A F = A/(1 + AB) = [A 1 + B] 1 : A A F 200000 19.998 100000 19.996 10000 19.96 1000 19.6 500 19.2 200 18.2 100 16.7 50 14.3 A Fmax = 20. If A >> A Fmax, A F is insensitive to A. A F is down 3 db from maximum when A = 50. Reduces distortion due to A nonlinearity, allows for variations in amplifier gain from device to device. (What Black wanted back in the 1920 s for his telephone long-distance line amplifiers) Suppose A is 200000 at low frequency (say 1 Hz) but falling with frequency like 1/f at high frequencies due to a built-in low-pass filter with f c = 5 Hz. With feedback, the -3 db bandwidth would be improved, since A F remains high until A has fallen many orders of magnitude. 8
Phase-Shift Oscillator and AB = -1 Sinusoidal oscillation when AB=-1 Phase-Shift Oscillator 4
Amplifier Low Frequency Limitations 5
Amplifier Low Frequency Limitations (continued) 6
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Amplifier High Frequency Limits Model for parallel (shunt) capacitances to ground in amplifier circuit: 8
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Amplifier High Frequency Limits Model for parallel (shunt) capacitances to ground in amplifier circuit: Where are these shunt capacitances? 8
Common Emitter Amplifier HF Limits At high frequencies, must consider BE and BC diode capacitances CBC CBE 9
Shunt Capacitances In Small-Signal AC Models Simple BJT Model at High Frequencies: Base-Emitter Diode Capacitance Base-Collector Diode Capacitance Simple HF JFET Model: How to deal with Cc (or Cgd) which connects input and output? 10
Use 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 separated 11
Miller s Theorem Proof Given: Node 1(write in terms of v1): Node 2 (write in terms of v2): QED 12
Common Emitter Amplifier Input Stage CE Amplifier 13
Common Emitter Amplifier Output Stage 14
FET HF Model and Analysis 15
Input Circuit Upper Corner Frequency for 9.54 16
Output Circuit Upper Corner Frequency for 9.54 17
MOSFET Amplifier Example 18
Effect of CS on Low Frequency Response Simple HF JFET Model: 19
Upper Corner Frequency: Input Stage Simple HF JFET Model: 20
Output Stage Upper Corner Frequency Simple HF JFET Model: 21
Ways 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 above 22
Common Base Detector Amplifier * *small signal AC model No Miller effect since cc, cc grounded at base; fast if use fast BJT (small cc, cc etc.) 23
Can We Understand Amplifier Operation? (this page is supplementary material not on final) 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). 24
Check Simple Model With SPICE (this page is supplementary material not on final) Uses MPSH10 RF amplifier BJT: cc = 1 pf ce = 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) Fast Pulse Amplifier ******************** VEE!4! 0! DC! -12 VBB!2! 0! DC! -6 RC! 0! 1! 20K Q1! 1! 2! 3! QMPSH10 RE1!3! 4! 20K C1! 5! 3!.01u VS! 9! 0! PWL ( 0 0V 1ns 0.05V 2ns 0V ) RS! 9! 5! 50 Q2! 0! 1! 6! QMPSH10 Q3! 0! 6! 7! QMPSH10 RE2!7! 4! 500 C2! 7! 8!.01u RO! 8! 0! 1K RI! 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.control run mv V(5) V(8) plot! V(5) V(8) 140.0.endcontrol.END 120.0 100.0 80.0 Good agreement with simple model voltage 60.0 40.0 20.0-0.0-20.0 0.0 20.0 40.0 60.0 80.0 100.0 time ns 25
Other Possibilities to Avoid Miller Effect High Av here High Av here Note the common base circuit lurking in both 26
Three-stage amplifier: BiFET Op-Amp Simplified Diagram +VCC p-channel JFETs S D C1 C E VOUT IREF Current source and input resistance of next stage play role of RD or RC for amplifier -VEE BJTs have identical characteristics 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.
Effect of Dominant Low-Pass Filter Finally, Upper corner frequency is multiplied by (loop gain +1) loop gain The product of gain and bandwidth is constant. The maximum phase shift is 90 (won t oscillate for resistive B). High frequency performance is compromised. 28
Bode Plot: AF and Bandwidth At low frequencies in the example above, AF(dB) A(dB) - (AB)(dB) 29
741 Specifications Input Bias Current 80 na Input Offset Current 20 na Input Offset Voltage 1 mv Max. Slew Rate 0.5 V/µs Open Loop Gain 200000 Gain-BW Product 1 MHz Input Resistance 2 MΩ Output Resistance 75 Ω CMRR typ. 80-100 db Output protected against short-circuits Input offset voltage can be balanced out with external pot See Sec. 10.2 for details 30
Bode Plot for µa702a Op-Amp No dominant pole: has 3 low-pass filters in series. Amplifier phase shift >180 with significant gain and can oscillate with a resistive feedback network. No large C 1 : Could make amplifier with BW of several MHz. Considerable gain left when phase shift equals 180 degrees at 12.5 MHz. Not fool-proof: A unity gain voltage follower would oscillate. 31
BJT CE Large Signal Performance The maximum output voltage swing is set by BJT cutoff and saturation Start with the BJT curves of I C vs. V CE for various values of I B, locate Q point Draw straight line through Q point with slope di C /dv CE for midband AC signals (AC Load Line) to determine useful range For AC, v c = R C i c so AC load line slope = i c /v c = 1/R C in this case. Output voltage swing follows AC load line. 3 32
CE Amplifier: DC and AC Load Lines V CC R C + R E 3.0 IC (ma) 3.5 2.5 2.0 1.5 I C vs V CE for 2N2222A npn BJT (SPICE simulation) AC Load Line DC Load Line Q Point I B = 16 µa I B = 12 µa I B = 8 µa 1.0 0.5 0.0 I B = 4 µa I B = 0 µa V CC -0.5 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 V CE (V) Max. symmetrical voltage swing when Q point centered on AC load line At Q, no input, BJT power dissipation p V CE I C = 4 V 2 ma = 8 mw If the Q point is centered, the average power dissipated by the BJT is max. with no AC input actually less when producing a signal. (See sec. 9.4 in text for details) 4 33
Push-Pull Emitter Follower Base bias chain keeps both BJTs just at cutoff (or slightly on ) at Q point No BJT power dissipated if no input signal. AC input causes one or the other BJT to provide the output. Maximum average BJT power now 0.1V CEQ i C(sat) much more efficient use of BJTs and power useful for driving low impedance loads at high power 5 34