UCD PHY 116A - Experiment 4 Op-Amp Resonant Bandpass Filter

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Experiment 4Op-Amp Resonant Bandpass FilterPhysics 116A, D. Pellettv. 1.2, Oct. 19, 20031 IntroductionIn this experiment you will become familiar with a bandpass filter made with an op-amp (active filter). Youwill compare experimental results on frequency response and phase shift with analytical and SPICE analysis.An optional extra part is to measure the pulse response of the circuit as a function of time and compare withSPICE time-domain analysis.The experimental measurements will be done in the first week. The second week’s lab will provide an intro-duction to SPICE. The SPICE exercises can then be done in the lab or at home, since freely downloadableversions of SPICE exist for a variety of computers (see the Physics 116 web site). Note that there is anintroduction to the use of SPICE and PSPICE in Ch. 16 of the text (Bobrow).The problem solutions are to be included with your lab report.1.1 LRC Bandpass FilterFig. 1 shows the frequency domain and time domain behavior of an LRC resonant bandpass filter as pre-dicted by SPICE. Component values for this figure are L = 47 mH, C = 10 nF and R = 200 Ω. The figureincludes the circuit diagram with node numbers and the SPICE input files used to make the plots.AC network analysis of the circuit results inH(jω) =jω(ωR/Q)(jω)2+ jω(ωR/Q) + ω2R, (1)where ωR=1√LCand Q =1RqLC. Recall that H(jω) ≡ Vout/Vin. The response is critically dampedwhen Q =12and the denominator factors into (jω + ωR)2.Problem 1: Find ωR, Q and |H(jωR)| for those values. Compare with the Bode plot on the handout.Compare the asymptotic falloff (in dB/decade) at high and low frequencies with the expected values.1.2 Active Bandpass FilterFig. 2 shows a resonant bandpass filter implemented with an op-amp and an RC feedback network insteadof the LRC network.1Problem 2: Assume the op-amp is ideal and use AC network analysis to prove:H(jω) =−R2C2jωR1R2C1C2(jω)2+ R1(C1+ C2)jω + 1. (2)Eqn. 2 is of the same form as Eqn. 1 up to an overall multiplicative constant. This constant arises fromthe closed loop midband voltage gain of the op-amp. This becomes evident if we make the substitutionsωR= 1/√R1R2C1C2, 1/Q = ωRR1(C1+ C2) and K = −ω2RR2C2. Eqn. 2 is then identical to Eqn. 1except that the factor, K, appears in the numerator in place of ωR/Q. K is negative since the op-amp is inan inverting amplifier configuration (180◦phase shift relative to the LRC circuit).For the experiment, we will use the following component values: R1= 100 Ω, R2= 47 KΩ and C1=C2= 0.01 µFProblem 3: Find ωR, Q and K for the R and C values given above. Compare with the results of Prob. 1(including midband gain, |H(jωR)|).2 ExperimentWire up the active bandpass filter of Fig. 2 using the component values given in the last section. Be sure toconnect the ±15 V power connections as well. Refer to the op-amp experiment (Lab 2) for the pinout.Measure the voltage gain, AV= |Vout/Vin|, and output phase as a function of frequency as you did for theRC filter circuits in Lab 3. Then make a Bode plot, plotting voltage gain in dB (20 log10AV) and phase vs.log frequency. Collect enough data at large and small frequencies so you can see the fall off on the Bodeplot and compare with the expected linear asymptotes. Collect enough data near the peak, AV max, so youcan also make a linear plot of gain vs. frequency in the region of the maximum. Use this to estimate Q fromthe peak width, ∆ω, at the half-power point (where AV= 0.707AV max; Q ≈ ωR/∆ω). Compare withyour circuit analysis results in the previous section.Observe the following precautions to get good results.1. Be sure to use capacitors with no worse than ±20% tolerance (marked “.01M,” for example; the “M”indicates the tolerance in this case). Use ±5% capacitors if available (marked “103J,” read as 10×103,with units assumed as pf, and “J” tolerance, or 5%).2. The source impedance of the signal generator must be low (<< R). Otherwise, it contributes signifi-cantly to the resistance of the series LRC circuit.3. When you are near the resonance peak, the input signal, Vin, must be small (≈ 10 mV amplitude) toavoid overloading the op-amp. A larger signal is needed when you are far away from the peak.4. The signal generator output may depend on frequency, so Vinneeds to be measured at each frequency.Many of the above requirements will be met if you drive the circuit with a voltage divider as shown in Fig. 3,so do that. Try RA= 100 Ω and RB= 1 Ω (RA= 1 KΩ and RB= 10 Ω would be maximum values).22.1 Pulse Response (Optional)If time permits, look at the pulse response (time domain) of your circuit (use a narrow pulse with a longrepetition rate). Compare with the time-domain SPICE results for the LRC circuit in Fig. 1.3 SPICE Analysis (may be done outside of lab period)1. Use SPICE to simulate the circuit in Fig. 2 and produce the Bode plot showing the frequency domainresponse. You can start from the SPICE input file for the Bode plot in Fig. 1. Note that the phase wasplotted in degrees. On the department computer, the angle will be in radians. Model the op-amp as asimple voltage-controlled voltage source as follows, using the node numbers of Fig. 2:E 4 0 0 3 1G(see Example 16.6 on p. 1047 of the text). Compare with your experimental result and calculations.2. Modify the SPICE analysis to use a more realistic op-amp simulation, such as the one in Example16.37 on p. 1115 of the text or the one here (including an example of its use):∗ subcircuit definition of a real op-amp, type 741∗ 1 = non-inverting input: +∗ 2 = inverting input: -∗ 3 = output∗ open loop gain = 100000∗ ft = 1 Mhz (freq. at which open loop gain = 1)∗ call: Xyyyyy n1 n2 n3 op741.subckt op741 1 2 3E1 4 1 1 2 1R 4 5 1KC 5 1 15.9U IC=0VE2 3 1 5 1 100K.ends∗ usage:VIN 1 0 AC 1X 1 2 3 op741The point here is that the open-loop response of the 741 op-amp is not flat. Gain falls with fre-quency, reaching unit gain at fT= 1 MHz or so. Does this op-amp model give better ageement withyour experimental results?3. Perform the time-domain SPICE analysis for your circuit (use the time-domain analysis of Fig. 1 foran example of a pulse input and transient analysis).Problem 4 (extra credit): Use SPICE to simulate the critical damping case for the LRC circuit (Q =12) andcompare the time response with Fig. 3.38 in the text. Explain why the behavior of Voutlooks like i(t). Alsomake the Bode plot for this case.33.1 Minimal Notes on SPICE


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UCD PHY 116A - Experiment 4 Op-Amp Resonant Bandpass Filter

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