Note: assume ideal op-amp behaviors for Problems 1-4. Which of the following op-amp circuits can be considered to have negative feedback. For those that have negative feedback, write down Vinvand Vout. You may assume the op-amps are powered by +9V. a) Vin c) +1.2V Vout Vout b) d) Vin Vin +1.2V out Vout

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)

+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.

please do question 2 and 3