1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics. R2 Vi σ R₁ Vo Figure 1: Differentiator circuit. (a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal op-amp: Vo Gain = Vi -jwC₁R₂ (1 + jwC₁R₁) (b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R2 is 120 kn, design the rest of the component values. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 108 Hz.

Please show all work

Discussion: 1- What kind of restrictions Non- inverting op-amp face compared to inverting op-amp? 2- State 5 different types of op amp. Demonstrate them briefly then draw the circuit diagram for each kind. 3- For an inverting op amp, if the voltage input peak equal to 10.2 V, R=10KQ and RF 2002, find Vo and the voltage gain. Assume the input signal has a sinusoidal behavior. 4- Consider an OP amp connected to the inverting configuration to realize a closed-loop gain of -50 V/V utilizing resistors o f 1 k2 and 50 kQ. A load resistance RL is connected from the output to ground, and a low-frequency sine wave signal of peak amplitude Vp is applied to the input. Let the OP amp be ideal except that its output voltage saturates at +/- 10V and its output current is limited to the range +/-15 mA. For RL = 1 k2, what is the maximum possible value of Vp while an undistorted output sinusoid is obtained?

7. Two important conclusions of an ideal operational amplifier are are ( ). A. Virtual ground and opposite phase B. Virtual short and virtual ground C. Virtual short and virtual open D. Open circuit and short circuit