This set of Analog Circuits Multiple Choice Questions & Answers (MCQs) focuses on “MOSFET Amplifier with CG Configuration – 1”.

1. In the following circuit, what is the voltage at the source of the M_{1}?

a) V_{in} * R_{s} / (R_{s} + 1/g_{m})

b) V_{in} * R_{s} / (R_{s} + g_{m})

c) V_{in} * R_{s} / (R_{s} – 1/g_{m})

d) V_{in} * R_{s} / (R_{s} + 2/g_{m})

View Answer

Explanation: The impedance looking into the source of M

_{1}is 1/g

_{m}. V

_{in}experiences a potential divider before entering the source of M

_{1}. The voltage drop across R

_{s}is typically the voltage at the source and hence, it is equal to V

_{in}* R

_{s}/ (R

_{s}+ 1/g

_{m}).

2. What is the input impedance of the following CG stage?

a) 1/g_{m}

b) 2* R_{s} || 1/g_{m}

c) R_{s} || 1/g_{m}

d) R_{s} || 2/g_{m}

View Answer

Explanation: The input impedance can be calculated by performing a small signal analysis at the input node. We need to set V

_{g}and V

_{dd}to 0V and apply a small input voltage at the source. Now, the impedance looking into the source is 1/g

_{m}and R

_{s}is parallel to this impedance. Hence, the total input impedance is R

_{s}|| 1/g

_{m}.

3. If Channel Length modulation is neglected, what is the voltage gain from the source to the drain for the CG stage shown below?

a) g_{m} * R_{d} * {2R_{s} / (R_{s} + 1/g_{m})}

b) g_{m} * R_{d} * {R_{s} / (R_{s} + 2/g_{m})}

c) g_{m} * R_{d} * {2R_{s} / (R_{s} – 1/g_{m})}

d) g_{m} * R_{d} * {R_{s} / (R_{s} + 1/g_{m})}

View Answer

Explanation: The voltage gain from the source of M

_{1}to the drain of M1 can be found out from a small signal analysis and it’ll turn out to be g

_{m}* R

_{d}. But the input voltage is a result of the potential divider between R

_{s}and 1/g

_{m}. Hence, the overall voltage gain is g

_{m}* R

_{d}* {R

_{s}/ (R

_{s}+ 1/g

_{m})}.

4. What is the input impedance for the following circuit?

a) r_{o}

b) 1/g_{m}

c) R_{d} || r_{o}

d) Infinite

View Answer

Explanation: The input to the CG stage is placed at the source of M

_{1}. The impedance looking into the node of M

_{1}is simply 1/g

_{m}. Hence, the input impedance is 1/g

_{m}. R

_{d}|| r

_{o}is the output impedance if channel length modulation is present.

5. If channel length modulation is neglected, what is the voltage gain for the following circuit from source to drain?

a) g_{m} * R_{d}

b) g_{m} * r_{o}

c) g_{m} * (r_{o} || R_{d})

d) -g_{m} * R_{d}

View Answer

Explanation: In absence of channel length modulation, r

_{o}=0. The gain is simply g

_{m}* R

_{d}. It should be noted that the CG stage doesn’t invert and hence the voltage gain is not -g

_{m}* R

_{d}.

6. If channel length modulation is present, what is the output impedance of the following circuit?

a) R_{d}

b) R_{d} || r_{o}

c) r_{o}

d) 0

View Answer

Explanation: In presence of channel length modulation, r

_{o}appears to be in parallel to R

_{d}. Hence, the total output impedance becomes R

_{d}|| r

_{o}. In the absence of channel length modulation, the output impedance is R

_{d}only.

7. If channel length modulation is neglected, what is the voltage gain for the following CG stage?

a) R_{d}/(1/g_{m} – R_{s})

b) R_{d}/(3/g_{m} + R_{s})

c) R_{d}/(1/g_{m} + R_{s})

d) R_{d}/(2/g_{m} + R_{s})

View Answer

Explanation: The above circuit is quite similar to the CS stage with degeneration. But the CG stage doesn’t invert and after performing a small signal analysis, the voltage gain comes out to be R

_{d}/(1/g

_{m}+ R

_{s}).

8. If channel length modulation is present. what is the overall output impedance of the following CG stage?

a) R_{d} || {R_{s}*(1+g_{m} * r_{o}) + r_{o}}

b) R_{d} || {R_{s}*(1+g_{m} * r_{o}) + 2r_{o}}

c) R_{d} || {R_{s}*(1+g_{m} * r_{o}) – r_{o}}

d) R_{d} || {R_{s}*(2+g_{m} * r_{o}) + r_{o}}

View Answer

Explanation: The impedance looking into the drain of M1 would be similar to that of a CS stage with source degeneration. That implies the impedance is R

_{s}*(1+g

_{m}* r

_{o}) + r

_{o}. But this impedance is parallel to R

_{d}. Hence, the overall output impedance becomes R

_{d}|| {R

_{s}*(1+g

_{m}* r

_{o}) + r

_{o}}.

9. The current gain of a simple CG stage is approximately ___

a) Infinity

b) unity

c) twice

d) 0

View Answer

Explanation: The input to a CS stage is at the source of M

_{1}. This current simply flows into the channel and flows out of M

_{1}. Approximately, we can say that the overall current gain is unity since the gain contributes very low current.

10. The voltage gain of a simple CG stage is greater than that of a follower.

a) True

b) False

View Answer

Explanation: The voltage gain of a follower is always less than that of a CG stage. This can be proven by a small signal analysis that the voltage gain for a follower is R

_{s}/(1/g

_{m}+ R

_{s}) while that of the CG stage is g

_{m}* R

_{d}. Hence the above statement is true.

11. If channel length modulation is neglected, what is the voltage gain of the following circuit?

a) – {g_{m1} * R_{d} * g_{m2} * R_{d1}}

b) g_{m1} * R_{d} * g_{m2} * 2R_{d1}

c) – {g_{m1} * R_{d} * 2g_{m2} * R_{d1}}

d) g_{m1} * 2R_{d} * g_{m2} * R_{d1}

View Answer

Explanation: This is a cascade of a CG stage preceding a CS stage. For the CG stage, the voltage gain is g

_{m}* R

_{d}. But after this stage, the signal gets amplified by the CS stage with a factor of –(g

_{m2}* R

_{d1}). Hence, the overall voltage gain is the product of both the factors ie –(g

_{m1}* R

_{d}* g

_{m2}* R

_{d1}). Note that since channel length modulation is absent, r

_{o}is not present in the expression of gain.

12. If channel length modulation is present, what is the voltage gain of the following circuit?

a) g_{m1} * (R_{d} || r_{o1}) * g_{m2} * R_{d1}

b) – {g_{m1} * R_{d} * g_{m2} * 2(R_{d1} || r_{o2})}

c) – {g_{m1} * (R_{d} || r_{o1}) * g_{m2} * (R_{d1} || r_{o2})}

d) g_{m1} * 2R_{d} * g_{m2} * R_{d1}

View Answer

Explanation: This is a cascade of a CG stage preceding a CS stage. For the CG stage, the voltage gain is g

_{m}* (R

_{d}|| r

_{o1}). But after this stage, the signal gets amplified by the CS stage with a factor of – {g

_{m2}* (R

_{d1}|| r

_{o2})}. Hence, the overall voltage gain is the product of both the factors i.e. – {g

_{m1}* (R

_{d}|| r

_{o1}) * g

_{m2}* (R

_{d1}|| r

_{o2})}. Note that the input impedance looking into M

_{2}is infinite ad hence the voltage gain of the CG stage is typically unaffected by the CS stage (for low frequency operations only).

13. If channel length modulation is neglected, what is the voltage gain for the following circuit?

a) – {g_{m1} * R_{d} * R_{d} / (1/g_{m2} + R_{s})}

b) – (g_{m1} * 2R_{d} * R_{d} / R_{s})

c) – {g_{m1} * R_{d} * R_{d} / (1/g_{m2} + R_{s})}

d) – {g_{m1} * R_{d} * R_{d} / (1/g_{m2} + 2R_{s})}

View Answer

Explanation: This is a cascade of a CG stage preceding a CS stage. For the CG stage, the voltage gain is g

_{m}* R

_{d}. But after this stage, the signal gets amplified by a degenerated CS stage with a factor of -R

_{d}/ (1/g

_{m2}+ R

_{s}). Hence, the overall voltage gain is the product of both the factors i.e. – {g

_{m1}* R

_{d}* R

_{d}/ (1/g

_{m2}+ R

_{s})}. Note that the input impedance looking into M

_{2}is infinite ad hence the voltage gain of the C.G. stage remains unaffected by the C.S. stage (for low frequency operations only).

14. If channel length modulation is neglected, what is the overall voltage gain of the following circuit?

a) – {g_{m1} * (R_{d} || 1/g_{m2}) * (R_{d1}/ (1/g_{m2} + R_{d}))}

b) – {g_{m1} * (R_{d} || 1/g_{m2}) * g_{m2} * 2R_{d1}}

c) – {g_{m1} * R_{d} * g_{m2} * R_{d1}}

d) – {g_{m1} * 1/g_{m2} * g_{m2} * R_{d1}}

View Answer

Explanation: This is a cascade of CS stage preceding a CG stage. The voltage gain of the first stage is – (g

_{m1}* R

_{d}|| 1/g

_{m2}). This is because the drain of M

_{1}is connected to the source of M

_{2}and the impedance looking into the source of M

_{2}is 1/g

_{m2}. Now, the source of the CG stage is connected to R

_{d}and hence the voltage gain due to this stage is affected by source degeneration and the voltage gain is R

_{d1}/ (1/g

_{m2}+ R

_{d}). The overall voltage gain is – {g

_{m1}* (R

_{d}|| 1/g

_{m2}) * (R

_{d1}/ (1/g

_{m2}+ R

_{d}))}.

15. If channel length modulation is neglected, what is the voltage gain of the following circuit?

a) g_{m2}/g_{m1}

b) – {g_{m2} * R_{d} * g_{m1} * R_{1}}

c) R_{d}/g_{m2}

d) 0

View Answer

Explanation: The impedance looking into the source of M

_{1}is 1/g

_{m1}. Hence, the product of this times the transconductance of M

_{2}will be the overall voltage gain i.e. g

_{m2}/g

_{m1}. Note that the gain is function of only the intrinsic parameters of the MOSFET and independent of other parameters.

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