Figure (Q1) shows an ideal voltage amplifier with a gain of +2 V/V implemented with an Op Amp connected in the noninverting configuration and a resistance R connected between the output and the input. a) Using Miller's theorem, show that the input resistance is Rm = -R b) Using Norton's theorem to replace Vig, Rig, and Rin with a signal current source and an equivalent parallel resistance. Show that by selecting Rig = R, the equivalent parallel resistance becomes infinite and the current I, into the load impedance Z, becomes Vig /R +2 R Figure (Q1)

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

= Make a inverting op amp to have a voltage gain of -5 with an R, 2 kn. You must ensure that the output does not exceed +12 V. a. Specify the value of Rf and the supply voltages +Vcc. Vs b. For this circuit, what is the range of the source voltage, vº, to ensure that the op amp remains linear? + Rs Rf +Vcc -Vcc + Vo

(Q1) Design a circuit with Op-Amp when Vi 3v and Vo = 12v (i) Using Inverting Amplifier (ii) Using Non-Inverting Amplifier Assume any value if necessary.