This set of Microelectronics Multiple Choice Questions & Answers (MCQs) focuses on “MOS Cascode – Set 2”.

1. What is the impedance looking into the drain of M_{3} in presence of channel length modulation & body effect?

a) [1+(g_{mb3}+g_{m3})*r_{o4})]*r_{o4}+r_{o3}

b) [1+(g_{mb4}+g_{m4})*r_{o3})]*r_{o4}+r_{o3}

c) [1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}

d) [1+(g_{mb4}*r_{o3})]*r_{o4}+r_{o3}

View Answer

Explanation: M

_{3}is a PMOS and is degenerated by M

_{4}. M

_{4}is also a PMOS and is degenerated by R

_{3}and it offers an output resistance of [1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4}to the source of M

_{3}. Hence, the impedance looking into the drain terminal of M

_{3}will be [1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}. Note that the circuit below the drain terminal will not affect the impedance. This impedance can be verified by the small signal analysis.

2. What is the impedance looking into the drain of M_{2} in presence of channel length modulation & body effect?

a) [1+(g_{mb3}*r_{o4})]*r_{o4}+r_{o3}

b) [1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2}

c) [1+(g_{mb2}*r_{o2})]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2}

d) [1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})]*R+r_{o1})+r_{o2}

View Answer

Explanation: M

_{2}is a NMOS and is degenerated by M

_{1}. M

_{1}is also a NMOS and is degenerated by R and it offers an output resistance of [{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}to the source of M

_{2}. This impedance is in parallel to R

_{4}. The total impedance degenerating M

_{2}is [1+(g

_{m1}*r

_{o1})*R+r

_{o1}]||R

_{4}. Hence, the impedance looking into the drain terminal of M

_{3}will be [1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4})+r

_{o2}. Note that the circuit above the drain terminal will not affect the impedance.

3. What is the output impedance of the following circuit if all the MOSFETs suffer from channel length modulation & body effect?

a) [1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o3}]*([{1+(g_{m2}*r_{o1})}*R+r_{o2}]||R_{3})+r_{o1}

b) [1+(g_{mb1}*r_{o1})]*([1+(g_{m2}*r_{o4})]*R_{2}+r_{o3})+r_{o3}||[1+((g_{mb1}+g_{m2})*r_{o4}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2}

c) [1+(g_{mb2}*r_{o3})]*([1+(g_{m2}*r_{o3})]*R_{4}+r_{o3})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2}

d) [1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2}

View Answer

Explanation: At the output node, we have primarily two branches. One branch is connected to a degenerated PMOS M

_{3}, degenerated by M

_{4}, which offers an output impedance of [1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}. Another branch is connected to a degenerated NMOS M

_{2}, degenerated by a degenerated M

_{1}, which offers an output impedance of [1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]|| R

_{4})+r

_{o2}. These two impedance appear in parallel to each other and the overall output impedance is [1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}||[1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4})+r

_{o2}.

4. What is the transconductance of M_{2} if all the MOSFETs suffers from Channel Length Modulation and body effect?

a) g_{m2}*r_{o2}/[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]+[1+(g_{m2}+g_{mb2})[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]]r_{o2}

b) g_{m1}*r_{o1}/[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]+[1+(g_{m4}+g_{mb4})[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]]r_{o4}

c) g_{m2}*r_{o2}/[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]+[1+(g_{m3}+g_{mb3})[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]]r_{o3}

d) g_{m3}*r_{o3}/[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]+[1+(g_{m1}+g_{mb3})[{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4}]]r_{o3}

View Answer

Explanation: We know that in presence of channel length modulation, body effect and a source resistance – the transconductance of an NMOS or PMOS is g

_{m}*r

_{o}/R

_{S}+[1+(g

_{m}+g

_{mb})R

_{S}]r

_{o}. For M

_{2}, the source resistance is R

_{4}in parallel to the output impedance of a degenerated M

_{1}. This comes out to be ro1 [{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4}. Henceforth, for M

_{2}, the transconductance becomes g

_{m2}*r

_{o2}/[[{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4}]+[1+(g

_{m2}+g

_{mb2})[[{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4}]]r

_{o2}. We can check the unit will come out to be Siemens and this can also be confirmed by a small signal analysis. Note that we are not concerned with the impedance connected to the drain of M

_{2}for now. In absence of body effect, we omit the g

_{mb}terms.

5. What is the voltage gain of the following circuit if each MOSFET suffer from Channel Length Modulation & Body effect?

a) {(g_{mb}+g_{m})*r_{o}+1}[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})] * R_{3}+r_{o4}) + r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}] * ([{1+(g_{m1}*r_{o1})} * R++[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]]+[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2})]

b) {(g_{mb}+g_{m})*r_{o}+1}[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})] * R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R++[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]]+[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+1)]

c) {(g_{mb3}+g_{m1})*r_{o}+1}[[1+(g_{mb2}*r_{o3})]*([1+(g_{m4}*r_{04})] * R_{3}+r_{o4})+r_{o1}]||R_{4})+r_{o2}]/(r_{o}+(g_{mb}+g_{m})*r_{o}[[{1+(g_{m1}*r_{o1})}*R+r_{o3}]]+[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]]+[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o2})}*R+r_{o1}]||R_{4})+r_{o2})]

d) {(g_{mb2}+g_{m2})*r_{o2}+1}[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})] * R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}] * ([{1+(g_{m1}*r_{o1})} * R+r_{o1}]||R_{4})+r_{o2}]/(r_{o2}+(g_{mb2}+g_{m2})*r_{o2}[[{1+(g_{m1}*r_{o1})}*R+r_{o1}]]+[[{1+(g_{m1} * r_{o1})}*R+r_{o1}]]+[[1+(g_{mb3}*r_{o3})]*([1+(g_{m4}*r_{o4})]*R_{3}+r_{o4})+r_{o3}||[1+(g_{mb2}+g_{m2})*r_{o2}]*([{1+(g_{m1}*r_{o1})}*R+r_{o1}]||R_{4})+r_{o2})]

View Answer

Explanation: We analyze this circuit by observing that the output is taken from the drain of M

_{2}which behaves as a CG stage. In presence of Body effect and Channel Length modulation, the voltage gain of a CG stage is {(g

_{mb}+g

_{m})*r

_{o}+1}R

_{D}/(r

_{o}+(g

_{mb}+g

_{m})*r

_{o}R

_{S}+R

_{S}+R

_{D}). Now, R

_{D}is the total impedance connected to the drain of M

_{2}& it is the output impedance at the drain terminal. This resistance comes out to be [1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}||[1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4})+r

_{o2}]. Moreover, the source resistance is [{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]. Now, we simply replace R

_{D}& R

_{S}& the overall voltage gain comes out to be {(g

_{mb2}+g

_{m2})*r

_{o2}+1}[[1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}||[1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4})+r

_{o2}]/(r

_{o2}+(g

_{mb2}+g

_{m2})*r

_{o2}[[{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]]+[[1+(g

_{mb3}*r

_{o3})]*([1+(g

_{m4}*r

_{o4})]*R

_{3}+r

_{o4})+r

_{o3}||[1+(g

_{mb2}+g

_{m2})*r

_{o2}]*([{1+(g

_{m1}*r

_{o1})}*R+r

_{o1}]||R

_{4})+r

_{o2})]. We note that the expression is very long & we can always use some approximations to calculate the voltage gain.

6. What is the voltage gain from node B to node A in presence of Channel Length Modulation & Body Effect?

a) {(g_{m1}+g_{mb1})r_{o1}+1}/r_{o2}+(g_{m2}+g_{mb1})*r_{o2}*([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{3})+([1+(g_{m2}-g_{mb2})r_{o1}]R+r_{o1}||R_{4})+R_{3}

b) {(g_{m2}+g_{mb2})r_{o2}+1}/r_{o2}+(g_{m2}+g_{mb2})*r_{o2}*([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4})+([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4})+R_{3}

c) {(g_{m1}+g_{mb2})r_{o2}+1}/r_{o1}+(g_{m1}+g_{mb2})*r_{o2}*([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{3})+([1+(g_{m2}-g_{mb2})r_{o1}]R+r_{o2}||R_{4})+R_{3}

d) {(g_{m2}+g_{mb1})r_{o1}+1}/r_{o1}+(g_{m2}+g_{mb2})*r_{o2}*([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4})+([1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o2}||R_{4})+R_{3}

View Answer

Explanation: From Node B to Node A, M

_{2}plays the role of a CG stage. The total resistance connected to the source of M

_{2}is a parallel combination of two impedances. The first is looking into the drain of M

_{1}which is degenerated by R and in presence of channel length modulation & body effect, it becomes [1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}. The second impedance is R

_{4}. The overall impedance is [1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}||R

_{4}. The total resistance connected to the drain of M

_{2}is R

_{3}. From the expression of Voltage gain of a CG stage, in presence of channel length modulation & Body effect, the voltage gain is {(g

_{m2}+g

_{mb2})r

_{o2}+1}/r

_{o2}+(g

_{m2}+g

_{mb2})*r

_{o2}*([1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}||R

_{4})+([1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}||R

_{4})+R

_{3}. Note that in absence of body effect, only g

_{mb}will disappear from the expression.

7. Which circuit is more linear?

Circuit: A Ciruit: B

a) Circuit A

b) Circuit B

c) It depends on the biasing

d) It depends on the supply voltage

View Answer

Explanation: Circuit B is more linear than circuit A since both the MOSFETs are degenerated & degeneration leads to linearization of the circuit.

8. What is the role of M_{4} in the following circuit?

a) Degenerating device

b) Input device

c) Amplifier

d) Error in the circuit

View Answer

Explanation: M

_{4}plays the role of a degenerating device. It is connected to the source of M

_{3}& it degenerates M

_{3}which leads to an increase in the impedance of M

_{3}which is seen looking into its drain terminal.

9. What is the voltage gain at Node B in presence of Channel length modulation and body effect in both the MOSFETs?

a) g_{m1}*r_{o}/R+[1+(g_{m1}+g_{mb1})R]r_{o1}*(R_{3}+r_{o2})/(1+(g_{m2}+g_{mb2})*r_{o2})||[1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4}

b) g_{m2}*r_{o}/R+[1+(g_{m2}+g_{mb2})R]r_{o1}*(R_{3}+r_{o2})/(1+(g_{m2}+g_{mb2})*r_{o2})||[1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4}

c) g_{m1}*r_{o}/R+[1+(g_{m2}+g_{mb1})R]r_{o1}*(R_{3}+r_{o2})/(1+(g_{m2}+g_{mb2})*r_{o2})||[1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4}

d) g_{m1}*r_{o}/R+[1+(g_{m1}+g_{mb1})R]r_{o1}*(R_{3}+r_{o2})/(1+(g_{m2}+g_{mb2})*r_{o2})||[1+(g_{m2}+g_{mb2})r_{o1}]R+r_{o1}||R_{4}

View Answer

Explanation: We analyze the circuit by observing that M

_{1}behaves as a CS stage. The transconductance of M

_{1}is g

_{m}*r

_{o}/R+[1+(g

_{m}+g

_{mb})R]r

_{o1}. The output impedance of is the parallel combination of the three impedances. The first impedance is looking into the source of M

_{2}, which is (R

_{3}+r

_{o2})/(1+(g

_{m2}+g

_{mb2})*r

_{o2}). The second is looking into the drain of M

_{1}which is degenerated by R and in presence of channel length modulation & body effect, it becomes [1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}. The final impedance is R

_{4}. The overall output impedance is (R

_{3}+r

_{o2})/(1+(g

_{m2}+g

_{mb2})*r

_{o2})||[1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}||R

_{4}& the voltage gain becomes g

_{m1}*r

_{o}/R+[1+(g

_{m1}+g

_{mb1})R]r

_{o1}*(R

_{3}+r

_{o2})/(1+(g

_{m2}+g

_{mb2})*r

_{o2})||[1+(g

_{m2}+g

_{mb2})r

_{o1}]R+r

_{o1}||R

_{4}.

10. What is the transconductance of M_{1} in presence of Channel Length Modulation & Body effect?

a) g_{m2}*r_{o2}/R+[1+(g_{m2}+g_{mb1})R]r_{o2}

b) g_{m1}*r_{o2}/R+[1+(g_{m2}+g_{mb2})R]r_{o1}

c) g_{m1}*r_{o1}/R+[1+(g_{m1}+g_{mb1})R]r_{o1}

d) g_{m2}*r_{o2}/R+[1+(g_{m1}+g_{mb2})R]r_{o2}

View Answer

Explanation: In order to calculate the transconductance of M

_{1}, we analyze M

_{1}by neglecting M

_{2}since the current leaving the drain of M

_{1}is independent of R

_{D}(the impedance of the branch connected to the drain terminal). Note that the voltage drop across R

_{D}plays a role in establishing the region of operation but the transconductance i.e. ΔI

_{D}/ΔV

_{GS}is independent of R

_{D}. We draw the small signal model of M

_{1}with channel length modulation and Body effect. Henceforth, we write a KCL at the source after noting that I

_{2}=g

_{mb}*V

_{S}=g

_{mb}*(I

_{OUT}*R) & I

_{1}=g

_{m}*V

_{GS}=g

_{m}*(V

_{in}-I

_{OUT}*R) & I

_{ro1}=V

_{S}/r

_{o1}=I

_{OUT}*R/r

_{o1}. The KCL revel as I

_{OUT}=I

_{1}–I

_{2}–I

_{ro1}& we replace the terms and rearrange to find the transconductance as g

_{m}*r

_{o}/R+[1+(g

_{m}+g

_{mb})R]r

_{o1}.

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