3. (40 pts) The circuit below describes an active current-reuse strategy that re

Question

3. (40 pts) The circuit below describes an active current-reuse strategy that replaces the active load in a current-source amplifier with an amplifying device as shown in Fig. below. This topology is similar to a CMOS inverter. The designer using this circuit inadvertently forgot to attach a DC bias to this circuit and finds the circuit malfunctioning when fabricated. a) Can you suggest a way to self-bias the circuit (using passive circuit elements only) (5 pts)? b) Explain qualitatively the small-signal behavior of the circuit how does the output vary with a change in small-signal input voltage (5 pts). c) The circuit designer besides biasing ignored another important detail - the effect of supply variation on the output node. Can you identify the small-signal voltage gain of this circuit from GND to Vout i.e. find AZtGd (10 pts) d) Calculate the small-signal gain of this circuit from Vin to V(5 points). e) Now replace the circuit below with a telescopic cascode as shown in Fig. (b) and Fig. (c). Compare the output resistance and the small-signal gain of these three circuits. (15 points) M4 Qa vin Cage M2 M2 M3 M3 Show DC Biasing Show DC Basing Show DC Riasino

Explanation / Answer

a)The self bias can be implemented by adding the resistor rd between the power supply and the NMOS device at the top for all circuits.

b) The PMOS device serves as an constant current source. And NMOS acts as an amplifying device. suppose both transistors are in saturation and Vin increases to small amout of Vdd. Two changes now occur 1)id1 increases pulling vout lower 2)M1 injects the less current into the output node allowing vout to drop. These two changes will aid together and results in high voltage gain

c) Since Vgs1 +|Vgs2|=Vdd variations in the Vdd or threshold voltage variations directly translate to variations in the drain currents. So the circuit amplifies the supply voltage variations. This can be given by if Vb is enough to make the transistors M1 and M2 in saturation the small signal gain will be given by

                  Vout/Vdd=(gm2+1/r02)(r01||r02)

d) The two transistor operate in parallel and collapse into one then the Vout can be

                    Vout=-(gm1+gm2)(r01||r02)

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