# Microelectronics Questions and Answers – MOS Current Mirror – Set 2

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

1. The aspect ratio of M2 is not less than 4 times of M1 & the transconductance of M1 is gm1. In absence of channel length modulation, what is the voltage gain for M2 in the following circuit?

a) -8*gm1*(2KΩ)
b) -8*gm1*(2KΩ)
c) -4*gm1*(1KΩ)
d) 8*gm1*(1KΩ)

Explanation: If the aspect ratio of M2 is 4 times of M1, it’s transconductance is defined at 4gm0. Noting that M2 is behaving as a simple CS stage, its voltage gain becomes -4*gm1*(3KΩ).

2. The aspect ratio of M2 is not less than 4 times of M1 & the transconductance of M1 is gm1 & that of M3 is gm3. In absence of channel length modulation, what is the voltage gain from M2 to M3 in the following circuit?

a) -4*gm1*(1KΩ)*gm3*(1KΩ)
b) 4*gm1*(5KΩ)*gm3*(2KΩ)
c) -4*gm1*(2KΩ)*gm3*(5KΩ)
d) 4*gm1*(1KΩ)*gm3*(1KΩ)

Explanation: The voltage gain from M2 to M3 is the product of two voltage gains of each transistor behaving as a CS stage. This leads us to the overall voltage gain, with the given data, as -4*gm1*(1KΩ)*gm3*(1KΩ).

3. If μnCox=100µA/V2, (W/L)M2=4*(W/L)M1, find the transconductance of M2 in absence of channel length modulation.

a) 8.984mS
b) 8.913mS
c) 17.856mS
d) 17.888mS

Explanation: The transconductance of M2 is given by √(2µnCox(W/L)ID. If (W/L)M2=4*(W/L)M1, the drain current through M2 is 4mA. Now, we can replace the values and get the transconductance as 17.888mS.

4. The aspect ratio of M2 is not less than 4 times of M1 & the transconductance of M1 is gm1 & that of M3. In absence of channel length modulation, what is the voltage gain from gate to drain of M2 in the following circuit?

a) (1kΩ)/(1/4*gm1)+R)
b) –(RkΩ)/(1/2*gm1)+R)
c) –(2kΩ)/(1/4*gm1)+R)
d) –(1kΩ)/(1/4*gm1)+R)

Explanation: M2 behaves as a degenerated CS stage. The expression of voltage gain is -RC/(1/gm2+RE). Since the drain current of M2 is 4 times of M1, the transconductance increases 4 times and the overall voltage gain becomes –(1kΩ)/(1/4*gm1)+R).

5. The drain current of M2 is not less than 8 times of M1 & the transconductance of M1 is gm1. In absence of channel length modulation, if the aspect ratio is scalable, what is the voltage gain from gate to drain of M2 in the following circuit?

a) (RkΩ)/(1/16*gm1)+R)
b) -(1kΩ)/(1/16*gm1)+R)
c) -(1kΩ)/(1/8*gm1)+R)
d) (2kΩ)/(1/8*gm1)+R)

Explanation: M2 behaves as a degenerated CS stage. The expression of voltage gain is -RC/(1/gm2+RE). Since the aspect ratio of M2 is 8 times of M1, which leads to an increase in the drain current by 8 times, the transconductance increases 4 times and the overall voltage gain becomes –(1kΩ)/(1/8*gm1)+R).

6. What is the voltage gain of M2 from the gate to its source, in absence of channel length modulation, if the aspect ratio of M2 is almost 9 times of M1? Note that the transconductance of M1 is kept constant.

a) (1kΩ)/(3/(16*gm1))+R)
b) -(1kΩ)/(1/(16*gm1))+R)
c) (1kΩ)/(16gm1)+R)
d) -(1kΩ)/(1/(16*gm1))+R)

Explanation: The voltage gain of the circuit is similar to that of a degenerated C.E. stage. We note that M2 will have a transconductance gm2 (approximately) and this increases 9 times since it is proportional to the square root of the product of drain current and aspect ratio. The voltage gain becomes -(1kΩ)/(1/(16*gm1))+R). Note that the voltage gain increases after all.

7. What is the transconductance of M2 from the gate to its source, in presence of channel length modulation, if the aspect ratio of M2 is almost 2 times of M1? Note that the transconductance of M1 is proportional to the drain current if the drain current is proportional to the aspect ratio for a constant overdrive voltage.

a) $$\frac {1}{ [ 1+R_S*g_{m2})}$$
b) $$\frac {g_{m2}}{ [ 1+R_S*g_{m2})}$$
c) $$\frac {g_{m2}}{[1+\frac {R_S}{g_{m2}})}$$
d) $$\frac {g_{m2}}{[R_S+g_{m2})}$$

Explanation: For the degenerated MOS transistor M2,we know that the transconductance is $$\frac {g_{m2}}{[ 1+R_S*g_{m2})}$$. If the aspect ratio doubles, the transconductance (in absence of degeneration) doubles and the overall transconductance increases. The voltage gain increases.

8. If the source voltage of M3 & M1 are equal, find the equation relating the aspect ratio of each transistor.

a) AM3/AM0=AM2/AM1
b) AM1/AM2=AM3/AM0
c) AM3/AM1=AM2/AM0
d) AM3/AM2=AM1/AM0

Explanation: If VGS1=VGS1 then, VDS2=VDS0 since VGS1+VDS0=VGS3+VDS2. This will happen if the drain current of M3 is equal to the drain current of M1 and the drain current of M2 is equal to the drain current of M0. Henceforth, we can write that AM3/AM1=AM2/AM0 where AM(i) is the aspect ratio of the ith MOSFET.

9. If the source voltage of M3 & M1 are equal, find the equation relating the transconductance of each transistor.

a) gM0/gM1=gm2
b) gM3/gM1=gM0/gM2
c) gM3/gM0=gM2/gM1
d) gM3/gM1=gM2/gM0

Explanation: We know that the aspect ratio of each MOSFET is related by AM3/AM1=AM2/AM0. For a constant overdrive voltage, the transconductance is related by gM3/gM1=gM2/gM0. We note that this configuration is independent of channel length modulation.

10. The following configuration is not prone to body effect?

a) True
b) False

Explanation: The source voltage of each MOSFET is constant if the aspect ratio of each MOSFET is related by AM3/AM1=AM2/AM0. Hence, the given statement is true.

Sanfoundry Global Education & Learning Series – Microelectronics.

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