Guest Lectures for Dr. MacFarlane s EE3350

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1 Guest Lectures for Dr. MacFarlane s EE3350 Michael Plante Sat., Write name in corner.. Problem Statement Amplifier Z S Z O V S Z I Z L Transducer, Antenna, etc. Coarse Tuning (optional) Amplifier Mixer IF Local Oscillator Noise Formulas simplified, not applicable at RF Noise Factor given by: F 0 = ( noise output ) ( noise from output ) = ( noise from output ) ( noise from output ) Can be rewritten as: F 0 = (noise out) ( gain ) ( src inp ) = ( ) (noise out) inp ( ) ( ) ( ) = (SNR) in > gain src inp out (SNR) out Will use previous formula here, but latter formula useful for nonlinear systems Measures noisiness of amp, relative to source noise Noise Figure NF = 0 log 0 F 0 > 0 (db)

2 . Superposition Review Short voltage, Open current V? 4V 8V 4Ω Ω 4Ω Ω 4Ω Ω V 8Ω V V 8Ω 8Ω V We ll add RMS output noise voltages 3. PSD Primer S xx ( f ) = Bendat and Piersol p. 3 R xx (τ)e jπ f τ dτ G xx ( f ) = S xx ( f ) FT of autocorrelation; used for random signals, while FT of signal itself used for deterministic signals We will use one-sided PSD here, as that is more common; -sided is half as large talk db /dec V V 0 log 0 V 0 = 0 log 0 V ( 0 area = 4kTR f ) V V RMS = area = ( 4kTR f area = ) 4kT f /R A

3 talk equal power per linear range or per decade/octave Johnson noise (WGN), k J/K, k 4 0 K or 6. F /f and H(ω) (Bode/Controls), origin annoyance, just use it Shot noise from discrete events (photons/electrons), rain on tin roof, white, area = qi f ( A ) Reduced by metal film resistors and some types of feedback, not covered q C, shot: ma DC 7.90 pa / Hz, Johnson: 6.5 K nv / Hz Hit flicker, popcorn, avalanche 4. Nonideal Op Amp Primer Harry Black, 97 negative feedback amp, 934 paper, 937 patent, permitted operational amplifiers, used in analog computers Talk input Z, gain, dominant pole, second pole, output resistance, internal compensation Talk about /f, white, averaging operation to get effective noise Mention stability and second pole Mention ideal op-amp problem (equal V, 0 I), and the fact that another problem will come up Draw (not shown separately here) noisy ideal opamp, talk noise src dominance Figure 4.: Noise in TI/BB OPA350 3

4 Good GP op-amp, chose arbitrary BW of 80 khz to 0 khz, meaning f = Hz e n = 5 nv / Hz or e n = µv RMS Fit from 0k to 0MHz gives i n ( f ) f /500 fa / Hz i n Inverting Operational Amplifier f 500 d f 80 fa / Hz or i n = 6 pa RMS V S Define R =. Choice of as either in parallel with R or as zero. Talk bias I. = 75 k, = 75 k, = 300 k, = 00 k, R = 50 k V S, e RS, and e R all see the same gain; e R3, e n, and i np all see the same gain. e RS e R V S i nn i e np R3 e n e R Figure 5.: Noise Sources in Inverting Operational Amplifier 4

5 Source Node Voltage RMS Noise ( µv ) e rs /R 9 e r /R 9 e r 9 e R r3 3 = v O e r3 ( ) R e r3 /R 576 ( e n e n /) 9 i nn i nn 0 v O = 0 i nn 3.04 ( i np i np /) = inp 3.04 Noise from amp at output: [ e R r R e r R ( e r3 R R ) e ( n R R ) i nn R ] i np R = R [ ( 4kT f R R R R ( R )) e ( n R R ) i nn R ] i np R Noise from src at output: [ 4kT f RS R R ] Johnson noise from amp is 960 µv at output Other noise from amp is µv at output Johnson noise from src is 9 µv at output F 0 = or NF 0 log db 6. Instrumentation Amplifier Talk CMRR ( kHz) and high input Z (0 TΩ) 5

6 V a c a V V S V V 3 b V b d G sig = G CM = G sig = G CM 0 Figure 6.: Noiseless Instrumentation Amplifier v O v 3 = v 3 v and v 3 = v 3 v give v O = v v, so the difference propagates with unity gain through the final stage and the common mode signal is greatly attenuated. In the first stage: v v = v v = v v Solving: v = ( ) v v, v = (R ( ) v v, v v = (v v ) R ) Take = 3 k, = 9 k, = 0 M, = 0 k. 6

7 e n V V i np i nn V e RS i R e Ra e Rb a b a V V i nn b e n V V i np V e n, e n and e RS all see the same gain; e Ra and e Rb see the same gain; i np and i np see the same gain; i nn and i nn see the same gain Source Node Voltage RMS Noise ( µv ) e RS G e n e n G 5 v = i R = v i R = e R (G ) 63 a v e Ra = 0 = v e Ra 58.4 i nn.0 i np = v v i np G i nn i nn v = 0 = v i np a c a c e R3a e R3c i nn3 e n3 V 3 i np3 V 3 e R3b e R3d b d b d b and d see the same gain. 7

8 Source Node Voltage RMS Noise ( µv ) a b c e n3 i nn3 e R3a = v O e R3b/ = v O e R3b/ v O e R3c e R3a 6.4 e R3b 6.4 = 0 e R3c 6.4 e n3 = v O e n3 e n 4 i nn3 v O = 0 i nn i np i np3 i np3 / = v O i np3 / Johnson noise due to source is µv Johnson noise due to first stage of amp is 747 µv Opamp noise in first stage is µv Johnson noise due to second stage of amp is 5.6 µv Opamp noise in second stage is 4.05 µv Noise Factor, with current noise on first stage broken off separately: F = , NF 0 log db At very high source impedances, opamp current noise dominates. 7. Loose Ends Draw a string of single-wire amps with G,F written in. Friis: References: SLOD006B Op Amps for Everyone F, = F F G F,,3 = F F G F 3 G G... SLVA043B Noise Analysis in Operational Amplifier Circuits Bendat and Piersol Random Data: Analysis and Measurement Procedures Davenport and Root An Introduction to the Theory of Random Signals and Noise Horowitz and Hill The Art of Electronics Bob Pease Troubleshooting Analog Circuits 8

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