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

1. What is the voltage gain of the following circuit if M_{1} suffers from Channel length modulation but M_{2} doesn’t suffer from any second order effect?

a) \(\frac {(r_{o1}+\frac {1}{g_{m2}})}{ (\frac {1}{g_{m}}+(r_{o1}+\frac {1}{g_{m2}}))}\)

b) \(\frac {(r_{o1}+\frac {1}{g_{m2}})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}))}\)

c) \(\frac {(r_{o1}||\frac {1}{g_{m2}})}{ (\frac {1}{g_{m}}+(r_{o1}+\frac {1}{g_{m2}}))}\)

d) \(\frac {(r_{o1}||\frac {1}{g_{m2}})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}))}\)

View Answer

Explanation: M

_{2}is a PMOS and the MOSFET being a unilateral device, the source will be the terminal which is connected to the higher potential. Hence, the source of M

_{2}is connected to the output node which is connected to the source of M

_{1}. The resistance offered by M

_{2}is 1/g

_{m2}, at the source end, and the expression of voltage gain becomes \(\frac {(r_{o1}||\frac {1}{g_{m2}})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}))}\).

2. What is the voltage gain of the following circuit if M_{1} & M_{2} suffers from Channel length modulation?

a) \(\frac {(r_{o1}||\frac {1}{g_{m2}} || r_{o2})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}} + r_{o2}))}\)

b) \(\frac {(r_{o1}+\frac {1}{g_{m2}} || r_{o2})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}} || r_{o2}))}\)

c) \(\frac {(r_{o1}||\frac {1}{g_{m2}} || r_{o2})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}} || r_{o2}))}\)

d) \(\frac {(r_{o1}+\frac {1}{g_{m2}} + r_{o2})}{ (\frac {1}{g_{m}}+(r_{o1}+\frac {1}{g_{m2}} + r_{o2}))}\)

View Answer

Explanation: The source of M

_{2}is connected to the output node which is connected to the source of M

_{1}. The resistance offered by M

_{2}is 1/g

_{m2}||r

_{o2}, due to channel length modulation, at the source end. The expression of voltage gain becomes \(\frac {(r_{o1}||\frac {1}{g_{m2}} || r_{o2})}{ (\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}} || r_{o2}))}\). We can always perform a small signal analysis but it becomes a long process. Remembering the expression of voltage gain and representing the MOSFET by a single resistance allows us to simplify the process.

3. What is the voltage gain of the following circuit if M_{1} & M_{2} suffers from Channel length modulation and M_{1} also suffers from Body Effect?

a) g_{m1}*(r_{o1}+1/g_{m2}+r_{o2})/(1+(g_{m1}||g_{mb})(r_{o1}+1/g_{m2}+r_{o2}))

b) g_{m1}*(r_{o1}||1/g_{m2}||r_{o2})/(1+(g_{m1}||g_{mb})(r_{o1}+1/g_{m2}+r_{o2}))

c) g_{m1}*(r_{o1}+1/g_{m2}+r_{o2})/(1+(g_{m1}+g_{mb})(r_{o1}||1/g_{m2}||r_{o2}))

d) g_{m1}*(r_{o1}||1/g_{m2}||r_{o2})/(1+(g_{m1}||g_{mb})(r_{o1}||1/g_{m2}||r_{o2}))

View Answer

Explanation: The source of M

_{2}is connected to the output node which is connected to the source of M

_{1}. The resistance offered by M

_{2}is 1/g

_{m2}||r

_{o2}, due to channel length modulation, at the source end. The expression of voltage gain of the follower in presence of channel length modulation and body effect becomes g

_{m1}*(r

_{o1}||1/g

_{m2}||r

_{o2})/(1+(g

_{m}||g

_{mb})(r

_{o1}||1/g

_{m2}||r

_{o2})).

4. What is the voltage gain of the following circuit if M_{1} & M_{2} suffers from Channel length modulation and Body Effect?

a) g_{m1}*(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})/(1+(g_{m1}+g_{mb})(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})

b) g_{m1}*(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})/(1+(g_{m1}+g_{mb})(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})

c) g_{m1}*(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})/(1+(g_{m1}+g_{mb})(r_{o1}+1/(g_{m2}+g_{mb})+r_{o2})

d) g_{m1}*(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})/(1+(g_{m1}+g_{mb})(r_{o1}||1/(g_{m2}+g_{mb})||r_{o2})

View Answer

Explanation: The source of M

_{2}is connected to the output node which is connected to the source of M

_{1}. The resistance offered by M

_{2}is 1/(g

_{m2}+g

_{mb})||r

_{o2}, due to channel length modulation and body effect, at the source end. The expression of voltage gain of the follower in presence of channel length modulation and body effect becomes g

_{m1}*(r

_{o1}||1/(g

_{m2}+g

_{mb})||r

_{o2})/(1+(g

_{m1}+g

_{mb})(r

_{o1}||1/(g

_{m2}+g

_{mb})||r

_{o2}). Note that if M

_{2}will suffer from body effect because the source of the MOSFET is connected to the output node and this leads to a change in the Source voltage with respect to the substrate.

5. What is the output impedance of the following circuit if M_{1} & M_{2} doesn’t suffer from any second order effect?

a) 1/g_{m1}

b) 1/g_{m1}||1/g_{m2}

c) 1/g_{m1}+1/g_{m2}

d) Infinite

View Answer

Explanation: The source of M

_{1}& M

_{2}offers an output resistance of 1/g

_{m1}and 1/g

_{m2}. Since the output node is connected to the source of each MOSFET, the output resistance becomes 1/g

_{m1}||1/g

_{m2}.

6. What is the output impedance of the following circuit if M_{1} & M_{2} suffer from channel length modulation?

a) (1/g_{m1}+r_{o1})||(1/g_{m2}+r_{o1})

b) 1/g_{m1}||r_{o1}-1/g_{m2}||r_{o1}

c) 1/g_{m1}||r_{o1}||1/g_{m2}||r_{o1}

d) 1/g_{m1}||r_{o1}+1/g_{m2}||r_{o1}

View Answer

Explanation: The source of M

_{1}& M

_{2}offers an output resistance of 1/g

_{m1}||r

_{o1}and 1/g

_{m2}||r

_{o2}respectively. Since the output node is connected to the source of each MOSFET, the output resistance becomes 1/g

_{m1}||r

_{o1}||1/g

_{m2}||r

_{o1}.

7. What is the output impedance of the following circuit if M_{1} & M_{2} suffer from channel length modulation?

a) 1/(g_{m1}||g_{mb1})||r_{o1}||1/(g_{m2}||g_{mb2})||r_{o2}

b) 1/(g_{m1}+g_{mb2})||r_{o1}||1/(g_{m2}+g_{mb1})||r_{o2}

c) 1/(g_{m2}+g_{mb1})||r_{o1}||1/(g_{m1}+g_{mb2})||r_{o2}

d) 1/(g_{m1}+g_{mb})||r_{o1}||1/(g_{m1}+g_{mb})||r_{o2}

View Answer

Explanation: The source of M

_{1}& M

_{2}offers an output resistance of 1/(g

_{m1}+g

_{mb})||r

_{o1}and 1/(g

_{m1}+g

_{mb})||r

_{o2}respectively. Since the output node is connected to the source of each MOSFET, the output resistance becomes 1/(g

_{m1}+g

_{mb})||r

_{o1}||1/(g

_{m1}+g

_{mb})||r

_{o2}.

8. What is the behavior of M_{1} in the following circuit?

a) CG Amplifier

b) Degenerating MOSFET

c) Cascode MOSFET

d) Follower

View Answer

Explanation: M

_{1}behaves as a follower since the input is taken from the gate while the output is taken from the source. It doesn’t take the form of a Cascode since the Cascode stage behaves like a Common Source Stage. Moreover, it doesn’t behave as a degenerating MOSFET since it is not connected to the Source of any MOSFET.

9. What is the behavior of M_{2} in the following circuit?

a) Amplifier

b) Degenerating MOSFET

c) Cascode MOSFET

d) Follower

View Answer

Explanation: M

_{2}behaves as a degenerating MOSFET since it is connected to the source of M

_{1}. It degenerates M

_{1}and hence, the impedance looking into the drain of M

_{1}has increased substantially. Moreover, it behaves as a CS amplifier since the output node is connected to its drain but noting that it is biased at a fixed operating point, the output is considered to be from M

_{1}. Note that the impact of V

_{B}is present in the output impedance of M

_{2}which does affect the output impedance and in turn the output voltage.

10. What is the voltage gain for the following circuit if channel length modulation is present in both the MOSFETs?

a) \(\frac {(r_{o1}||\frac {1}{g_{m2}}||r_{o2})}{(\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}||r_{o2}))}\)

b) \(\frac {(r_{o1}||\frac {1}{g_{m2}}||r_{o2})}{(\frac {1}{g_{m}}+(r_{o1}+\frac {1}{g_{m2}}+r_{o2}))}\)

c) \(\frac {(r_{o1}||\frac {1}{g_{m2}}+r_{o2})}{(\frac {1}{g_{m}}+(r_{o1}+\frac {1}{g_{m2}}||r_{o2}))}\)

d) \(\frac {(r_{o1}+\frac {1}{g_{m2}}||r_{o2})}{(\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}+r_{o2}))}\)

View Answer

Explanation: M

_{2}behaves as a diode connected device and looking into the source of M

_{2}, the impedance is 1/g

_{m2}||r

_{o2}. The voltage gain is evaluated to be \(\frac {(r_{o1}||\frac {1}{g_{m2}}||r_{o2})}{(\frac {1}{g_{m}}+(r_{o1}||\frac {1}{g_{m2}}||r_{o2}))}\).

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