Op Amps II, Page 1Op Amps IIOp-amp relaxation oscillatorBuild the relaxation oscillator shown in Figure 1 above. The output should be asquare wave with a frequency about 1/(2RC). Resistor R1 can be any value between 1Kand 1 M. Resistor R is one side of a potentiometer. Examine the voltages at (+) and (-)inputs and at the output and follow the action of the switching. It is useful to display v+and v- simultaneously on the same scale to illustrate that the switching occurs at thecrossover of v+ and v-. Note that the small triangular symbols indicate connections toground.Low-pass resonant filterShow that the transfer function for the low pass resonant filter, shown in Figure 2,is given by:† H(w) =11- x + x(1+ jwt)3where t = RC and x is the ratio of R1 to the total pot resistance R1 + R2.R1R1CR-+Figure 1: Relaxation Oscillator.RC-+RC-+RC-+-+Figure 2: Low pass resonant filter.Op Amps II, Page 2[Hint: Begin by naming the output voltages of each op amp, from left to right, as v1through v4. Then use the infinite gain assumption to show that:(v4- vin)R1=(vin- v1)R2Next, use what you know about RC filters to find v4 in terms of v1.]When you understand the equation for the transfer function, build the circuit. It isconvenient to use a TL084 with four op amps in a package.Choose RC so that the resonant frequency is 2 to 5 kHz. Tune the pot until thecircuit nearly oscillates. See how close you can get. Notice how oscillations grow anddie exponentially. Find the resonant frequency by feeding in a sine signal from afunction generator. (You may need to decrease the input voltage considerably to avoidsaturating the filter near resonance.) Check the high frequency roll off. It should beproportional to 1/w3. Estimate the gain at resonance. Observe how the phase shiftchanges at resonance. Observe that the phase shift is not zero at the frequency where thegain is maximum. Make a Bode plot of the transfer function. (Spend your time wiselyhere by starting with a survey to find the frequencies where important features occur.Important features include resonance, high-frequency roll off and low-frequency
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