Design a circuit with an op amp that provides a gain of 7.5 having a Rin resistor of 12k ohm. What value of resistance would you choose for Rf? Please draw the design for your circuit.

- V2 15Vdo 3 U1A R1 2 1k V- LM324 1k V3 15Vde | VOFF = 0 VAMPL = 1 FREQ = 2k AC = 0 0. R2 Figure 4. Operational amplifier circuit. What frequency does the output voltage (across R3) have? What is the amplitude of the output voltage? From the output waveform and the input waveform, determine the gain of the op-amp circuit. Does this match with what you predicted? How could you change this circuit so that the output voltage would be nearly the same as the input voltage? What purpose would that serve? Can you modify the existing circuit and verify this experimentally? What is the phase difference between the output and input voltage? Derive the transfer function for the output-input relationship for the operational amplifier. How would the gain and the output change if a capacitor were in the feedback path instead of a resistor? (Examine the circuit using phasors and impedance and circuit analysis techniques). -w-

Please show all the work.

2. One of the earliest uses of operational amplifiers (OPAMPS) is to perform mathematical operations on analog signals. Of the two OPAMP circuits shown below, one of them is known as an analog differentiator while the other an analog integrator. Analyse these circuits to discover why by finding an equation for their output VOUT in terms of their time-varying input VIN(t). (You may assume the OPAMPS are ideal.) VIN(t) RF Circuit A ☑ RF VOUT VIN(t) Circuit B VOUT