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

5 please all parts will give like!!!

Figure 6 (a) shows the circuit diagram for a differential amphfier. You may assume that M and M, have identical parameters. Referring to Figure 6 (a): (a) What kind of amplifier is it? What is its role in a three-stage op amp? Draw the small signal equivalent eircuit and derive the differential voltage gain Aag. For the analysis consider RDI RD2 >>Rp State any assumption. (b) RD. gml gm gm, and r re=r What is the new Adr in the circuit of Figure 6 (b), where a PMOS current source has replaced the two drain resistors Ror R Rp and a NMOS current sink has replaced the source resistor Rs? (c) What are the advantages in using the circuit of Figure 6 (b) instead of Figure 6 (a) to realize an op amp? (d) Ven Ms Mg Rp1 Rpa Vo HM, My M Ma M3 Vss 0 V Vss 0 V Figure 6(b) Figure 6 (a)

Assuming an ideal· op-amp's saturation voltage- UsSAT = +15V. For the- circuit in Figure · if u = 3V, the output voltage of op-amp is (404) i 10

+Vcc Vin VI Vo Vref VN -Vcc Ry RxL Figure Q.A2(e). Inverting Schmitt-trigger circuit. (ii) The operational-amplifier (op-amp) of the inverting Schmitt-trigger in Figure Q.A2(e) has saturation voltages of +Vsat = +11 V and -Vsat = -11 V. The voltage divider circuit has the relationship of Rx = 2RY with the value of RY being 100 kn. Using the relationships derived above: (a) Calculate the values of the upper threshold point (UTP or Vi*), lower threshold point (LTP or Vr). (b) Now, sketch the input-output characteristic of the inverting Schmitt- trigger. Clearly label axes, the threshold voltages and the saturation voltages in your sketch.