This set of Microelectronics Multiple Choice Questions & Answers (MCQs) focuses on “Low Frequency Response of Stages of BJT”.

1. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) r_{π}

b) r_{π}+R

c) r_{π}-R

d) Infinite

View Answer

Explanation: The coupling capacitor has to behave like a short circuit at frequencies of interest. The impedance of the coupling capacitor is 1/CΩ & this should be less than the input impedance of the Q

_{2}, which is simply r

_{π}.

2. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) (β+1)R

b) r_{π}+(β+1)R

c) r_{π}-(β+1)R

d) Infinite

View Answer

Explanation: Q

_{2}is degenerated by a resistance of R. This will increase it’s input impedance by an amount (β+1)*R where β is the current gain.

3. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) (β+1)R

b) r_{π}+(β+1)r_{o3}

c) r_{π}-(β-1)r_{o2}

d) Infinite

View Answer

Explanation: Q

_{2}is degenerated by the output impedance of Q

_{3}. This will increase it’s input impedance by an amount (β+1)*(r

_{o3}) where β is the current gain. Note that r

_{o3}is assumed to be held at a value by a constant bias.

4. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) (β+1)r_{o3}

b) r_{π}+(β-1)(r_{o3}||r_{o4})

c) r_{π}-(β-1)r_{o2}

d) r_{π}+(β+1)(r_{o3}||r_{o4})

View Answer

Explanation: Q

_{2}is degenerated by the output impedance of Q

_{3}& Q

_{4}. This will increase it’s input impedance by an amount (β+1)*(r

_{o3}||r

_{o4}) where β is the current gain. Note that r

_{o3}& r

_{o4}is assumed to be held at a value by a constant bias.

5. If C_{1} is assumed to be a short circuit at a certain frequency, in an ideal situation, what is the small signal voltage gain of Q_{1}?

a) -g_{m}*(R_{1}||(r_{π}-(β+1)R))

b) -g_{m}*(R_{2}||(r_{π}-(β+1)R))

c) -g_{m}*(R_{1}||(r_{π}+(β+1)R))

d) -g_{m}*(R_{2}||(r_{π}+(β+1)R))

View Answer

Explanation: Q

_{1}behaves as a C.E. stage. It’s output impedance is (R

_{1}||(r

_{π}+(β+1)R). Note that the total resistance for Q

_{2}has increased due to degeneration. The gain becomes -g

_{m}*(R

_{1}||(r

_{π}+(β+1)R)).

6. If C_{1} is assumed to be a short circuit at a certain frequency, in an ideal situation, what is the small signal voltage gain of Q_{1}?

a) g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o4})))

b) g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o3})))

c) -g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o3}||r_{o4})))

d) -g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o3}||r_{o4}))

View Answer

Explanation: Q

_{1}behaves as a C.E. stage. It’s output impedance is (R

_{1}||(r

_{π}+(β+1)(r

_{o3}||r

_{o4}))). Note that the total resistance for Q

_{2}has increased due to degeneration by the two npn transistors. The gain becomes -g

_{m}*(R

_{1}||(r

_{π}+(β+1)(r

_{o3}||r

_{o4}))).

7. If C_{1} is assumed to be a short circuit at a certain frequency, in an ideal situation, what is the small signal voltage gain of Q_{1}?

a) g_{m}*(R_{1}||(r_{π}+(β*1)(r_{o2})))

b) g_{m}*(R_{1}||(r_{π}+(β-1)(r_{o4})))

c) -g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o3}||r_{o4})))

d) -g_{m}*(R_{1}||(r_{π}+(β+1)(r_{o1})))

View Answer

Explanation: Q

_{1}behaves as a C.E. stage. It’s output impedance is R

_{1}||(r

_{π}+(β+1)(r

_{o1})). The formulae for calculating the output impedance for the MOSFET and the BJT are different. However, the voltage gain becomes -g

_{m}*(R

_{1}||(r

_{π}+(β+1)(r

_{o1}))).

8. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) r_{π1}+(β+1)*(1/g_{m3})

b) r_{π2}+(β+1)*(1/g_{m5})

c) r_{π2}+(β-1)*(1/g_{m5})

d) r_{π1}+(β+1)*(1/g_{m2})

View Answer

Explanation: Q

_{2}is degenerated by the output impedance of Q

_{5}. This will increase it’s input impedance by an amount (β+1)*(1/g

_{m5}) where β is the current gain. Note that 1/g

_{m5}is assumed to be held at a value by a constant bias.

9. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) r_{π2}+(β-1)*(1/g_{m5}||1/g_{m6})

b) r_{π2}+(β+1)*(1/g_{m5}||1/g_{m6})

c) r_{π2}+(β-1)*(1/g_{m5}+1/g_{m6})

d) r_{π2}+(β+1)*(1/g_{m5}+1/g_{m6})

View Answer

Explanation: Q

_{2}is degenerated by the output impedance of Q

_{5}. This will increase it’s input impedance by an amount (β+1)*(1/g

_{m5}||1/g

_{m6}) where β is the current gain. Note that 1/g

_{m5}& 1/g

_{m6}is assumed to be held at a value by a constant bias. The three terminals of each transistor being connected to one another, they are in parallel.

10. What happens to Q_{5} for a low V_{IN}? Assume that C_{1} is shorted.

a) High

b) Low

c) Moderately High

d) Moderately Low

View Answer

Explanation: If V

_{IN}is low, the input to the base of Q

_{2}is expected to be high if C

_{1}is reasonably short. Thus, the base of Q

_{3}follows the base of Q

_{2}and is expected to be approximately high and the transistor is behaving as a C.E. stage.

11. The frequency of the input voltage is Ω. What is the input impedance of Q_{2} which allows us to decide a value for C_{1} such that the impedance of C_{1} is less than the input impedance at the frequency of interest?

a) r_{π2}+(β-1)r_{π3}

b) (β+1)r_{π2}+r_{π3}

c) r_{π2}+r_{π3}

d) r_{π2}+(β+1)r_{π3}

View Answer

Explanation: Q

_{2}is degenerated by the input impedance of Q

_{3}. This is simply r

_{π}. The overall input impedance becomes r

_{π2}+(β+1)r

_{π3}.

12. If the transconductance of Q_{1} is provided to be g Siemens, what should be the factor by which the capacitance of the coupling capacitor is related to the inverse of its transconductance such that the input is shorted to the base of the transistor?

a) Capacitance much less than g

b) Capacitance much more than g

c) Capacitance equal to g

d) Frequency of operation not mentioned

View Answer

Explanation: The impedance of the coupling capacitor will have to be less than the input impedance of Q

_{1}. The input impedance of Q

_{1}is r

_{π1}.This is inversely proportional to g. The impedance will have to be less than 1/g and hence the capacitance will have to be much less than g. It is to be assumed that C

_{2}shorts R

_{1}to ground and is a bypass capacitor.

13. If the effect of the degenerating resistance is to be reduced, what should be the value of the capacitance such that it gets shorted to ground at low frequencies?

a) less than 1/g

b) greater than 1/g

c) equal to 1/g

d) equal to 2/g

View Answer

Explanation: The effect of the degenerating resistor is to increase the input impedance, we need to make sure that r

_{π1}dominates the expression of input impedance (β+1)*1/wC

_{2}+ r

_{π}and hence (β+1)*1/wC

_{2}< r

_{π}ie less than β/g

_{m}.

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