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

1. The aspect ratio of M_{2} is not less than 4 times of M_{1} & the transconductance of M_{1} is g_{m1}. In absence of channel length modulation, what is the voltage gain for M_{2} in the following circuit?

a) -8*g_{m1}*(2KΩ)

b) -8*g_{m1}*(2KΩ)

c) -4*g_{m1}*(1KΩ)

d) 8*g_{m1}*(1KΩ)

View Answer

Explanation: If the aspect ratio of M

_{2}is 4 times of M

_{1}, it’s transconductance is defined at 4g

_{m0}. Noting that M

_{2}is behaving as a simple CS stage, its voltage gain becomes -4*g

_{m1}*(3KΩ).

2. The aspect ratio of M_{2} is not less than 4 times of M_{1} & the transconductance of M_{1} is g_{m1} & that of M_{3} is g_{m3}. In absence of channel length modulation, what is the voltage gain from M_{2} to M_{3} in the following circuit?

a) -4*g_{m1}*(1KΩ)*g_{m3}*(1KΩ)

b) 4*g_{m1}*(5KΩ)*g_{m3}*(2KΩ)

c) -4*g_{m1}*(2KΩ)*g_{m3}*(5KΩ)

d) 4*g_{m1}*(1KΩ)*g_{m3}*(1KΩ)

View Answer

Explanation: The voltage gain from M

_{2}to M

_{3}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*g

_{m1}*(1KΩ)*g

_{m3}*(1KΩ).

3. If μ_{n}C_{ox}=100µA/V^{2}, (W/L)_{M2}=4*(W/L)_{M1}, find the transconductance of M_{2} in absence of channel length modulation.

a) 8.984mS

b) 8.913mS

c) 17.856mS

d) 17.888mS

View Answer

Explanation: The transconductance of M

_{2}is given by √(2µ

_{n}C

_{ox}(W/L)I

_{D}. If (W/L)

_{M2}=4*(W/L)

_{M1}, the drain current through M

_{2}is 4mA. Now, we can replace the values and get the transconductance as 17.888mS.

4. The aspect ratio of M_{2} is not less than 4 times of M_{1} & the transconductance of M_{1} is g_{m1} & that of M_{3}. In absence of channel length modulation, what is the voltage gain from gate to drain of M_{2} in the following circuit?

a) (1kΩ)/(1/4*g_{m1})+R)

b) –(RkΩ)/(1/2*g_{m1})+R)

c) –(2kΩ)/(1/4*g_{m1})+R)

d) –(1kΩ)/(1/4*g_{m1})+R)

View Answer

Explanation: M

_{2}behaves as a degenerated CS stage. The expression of voltage gain is -R

_{C}/(1/g

_{m2}+R

_{E}). Since the drain current of M

_{2}is 4 times of M

_{1}, the transconductance increases 4 times and the overall voltage gain becomes –(1kΩ)/(1/4*g

_{m1})+R).

5. The drain current of M_{2} is not less than 8 times of M_{1} & the transconductance of M_{1} is g_{m1}. In absence of channel length modulation, if the aspect ratio is scalable, what is the voltage gain from gate to drain of M_{2} in the following circuit?

a) (RkΩ)/(1/16*g_{m1})+R)

b) -(1kΩ)/(1/16*g_{m1})+R)

c) -(1kΩ)/(1/8*g_{m1})+R)

d) (2kΩ)/(1/8*g_{m1})+R)

View Answer

Explanation: M

_{2}behaves as a degenerated CS stage. The expression of voltage gain is -R

_{C}/(1/g

_{m2}+R

_{E}). Since the aspect ratio of M

_{2}is 8 times of M

_{1}, 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*g

_{m1})+R).

6. What is the voltage gain of M_{2} from the gate to its source, in absence of channel length modulation, if the aspect ratio of M_{2} is almost 9 times of M_{1}? Note that the transconductance of M_{1} is kept constant.

a) (1kΩ)/(3/(16*g_{m1}))+R)

b) -(1kΩ)/(1/(16*g_{m1}))+R)

c) (1kΩ)/(16g_{m1})+R)

d) -(1kΩ)/(1/(16*g_{m1}))+R)

View Answer

Explanation: The voltage gain of the circuit is similar to that of a degenerated C.E. stage. We note that M

_{2}will have a transconductance g

_{m2}(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*g

_{m1}))+R). Note that the voltage gain increases after all.

7. What is the transconductance of M_{2} from the gate to its source, in presence of channel length modulation, if the aspect ratio of M_{2} is almost 2 times of M_{1}? Note that the transconductance of M_{1} 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) \(\frac {g_{m2}}{[R_S+g_{m2})}\)

View Answer

Explanation: For the degenerated MOS transistor M

_{2},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 M_{3} & M_{1} are equal, find the equation relating the aspect ratio of each transistor.

a) A_{M3}/A_{M0}=A_{M2}/A_{M1}

b) A_{M1}/A_{M2}=A_{M3}/A_{M0}

c) A_{M3}/A_{M1}=A_{M2}/A_{M0}

d) A_{M3}/A_{M2}=A_{M1}/A_{M0}

View Answer

Explanation: If V

_{GS1}=V

_{GS1}then, V

_{DS2}=V

_{DS0}since V

_{GS1}+V

_{DS0}=V

_{GS3}+V

_{DS2}. This will happen if the drain current of M

_{3}is equal to the drain current of M

_{1}and the drain current of M

_{2}is equal to the drain current of M

_{0}. Henceforth, we can write that A

_{M3}/A

_{M1}=A

_{M2}/A

_{M0}where A

_{M(i)}is the aspect ratio of the i

^{th}MOSFET.

9. If the source voltage of M_{3} & M_{1} are equal, find the equation relating the transconductance of each transistor.

a) g_{M0}/g_{M1}=g_{m2}

b) g_{M3}/g_{M1}=g_{M0}/g_{M2}

c) g_{M3}/g_{M0}=g_{M2}/g_{M1}

d) g_{M3}/g_{M1}=g_{M2}/g_{M0}

View Answer

Explanation: We know that the aspect ratio of each MOSFET is related by A

_{M3}/A

_{M1}=A

_{M2}/A

_{M0}. For a constant overdrive voltage, the transconductance is related by g

_{M3}/g

_{M1}=g

_{M2}/g

_{M0}. 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

View Answer

Explanation: The source voltage of each MOSFET is constant if the aspect ratio of each MOSFET is related by A

_{M3}/A

_{M1}=A

_{M2}/A

_{M0}. Hence, the given statement is true.

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