# Network Theory Questions and Answers – m-Derived T-Section

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “m-Derived T-Section”.

1.The relation between ZoT and ZoT in the circuits shown below.

a) ZoT = ZoT
b) ZoT = 2 ZoT
c) ZoT = 3 ZoT
d) ZoT = 4 ZoT

Explanation: The relation between ZoT and ZoT is ZoT = ZoT where ZoT is the characteristic impedance of the modified (m-derived) T-network.

2. The value of Z2 in terms of Z1, Z2 from the circuits shown below is?

a) Z2=Z2/4 m (1-m2)+Z2/m
b) Z2=Z1/4 m (1-m2)+Z1/m
c) Z2=Z2/4 m (1-m2)+Z1/m
d) Z2=Z1/4 m (1-m2)+Z2/m

Explanation: As ZoT = ZoT, √(Z12/4+Z1Z2)=√(m2 Z12/4+m Z2). On solving, Z2=Z1/(4 m (1-m2))+Z2/m.

3. The relation between Z and Z in the circuits shown below is?

a) Z = 2 Z
b) Z = 4 Z
c) Z = Z
d) Z = 3 Z

Explanation: The characteristic impedances of the prototype and its modified sections have to be equal for matching. The relation between Z and Z is Z = Z.

4. The value of Z1 in terms of Z1, Z2 from the circuits shown below is?

a) Z1=(m Z2(Z2 4 m)/(1-m2))/m Z1(Z2 4 m/(1-m2))
b) Z1=(m Z1(Z2 4 m)/(1-m2))/m Z2(Z2 4 m/(1-m2))
c) Z1=(m Z1(Z2 4 m)/(1-m2))/m Z1(Z2 4 m/(1-m2))
d) Z1=(m Z1(Z2 4 m)/(1-m2))/m Z1(Z1 4 m/(1-m2))

Explanation: As Z = Z, √(Z1Z2/(1+Z1/4 Z2))=√(((Z1 Z2)/m)/(1+(Z1)/(4 Z2/m))). On solving, Z1=(m Z1(Z2 4 m)/(1-m2))/m Z1(Z2 4 m/(1-m2)).

5. The value of resonant frequency in the m-derived low pass filter is?
a) fr=1/(√(LC(1+m2)))
b) fr=1/(√(πLC(1+m2)))
c) fr=1/(√(LC(1-m2)))
d) fr=1/(√(πLC(1-m2)))

Explanation: ωr2 = 1/(LC(1-m2)). So the value of resonant frequency in the m-derived low pass filter is fr=1/√(πLC(1-m2)).
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6. The cut-off frequency of the low pass filter is?
a) 1/√LC
b) 1/(π√LC)
c) 1/√L
d) 1/(π√L)

Explanation: To determine the cut-off frequency of the low pass filter we place m = 0. So fc=1/(π√LC).

7. The resonant frequency of m-derived low pass filter in terms of the cut-off frequency of low pass filter is?
a) fc/√(1-m2)
b) fc/√(1+m2)
c) fc/(π√(1-m2))
d) fc/(π√(1+m2))

Explanation: If a sharp cut-off is desired, the frequency at infinity should be near to fc. The resonant frequency of m-derived low pass filter in terms of the cut-off frequency of low pass filter is fr=fc/√(1-m2).

8. The expression of m of the m-derived low pass filter is?
a) m=√(1+(fc/fr)2)
b) m=√(1+(fc/f)2)
c) m=√(1-(fc/fr)2)
d) m=√(1-(fc/f)2)

Explanation: As fr=fc/√(1-m2). The expression of m of the m-derived low pass filter is m=√(1-(fc/fr)2).

9. Given a m-derived low pass filter has cut-off frequency 1 kHz, design impedance of 400Ω and the resonant frequency of 1100 Hz. Find the value of k.
a) 400
b) 1000
c) 1100
d) 2100

Explanation: The value of k is equal to the design impedance. Given design impedance is 400Ω. So, k = 400.

10. Given a m-derived low pass filter has cut-off frequency 1 kHz, design impedance of 400Ω and the resonant frequency of 1100 Hz. Find the value of m.
a) 0.216
b) 0.316
c) 0.416
d) 0.516

Explanation: m=√(1-(fc/fr)2) fc = 1000, fr = 1100. On substituting m=√(1-(1000/1100)2)=0.416.

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