# Network Theory Questions and Answers – Poles and Zeros of Network Functions

This set of Basic Network Theory Questions and Answers focuses on “Poles and Zeros of Network Functions”.

1. The coefficients of the polynomials P (S) and Q (S) in the network function N (S) are ________ for passive network.
a) real and positive
b) real and negative
c) complex and positive
d) complex and negative

Explanation: The coefficients of the polynomials P (S) and Q (S) in the network function N (S) are real and positive for passive network. On factorising the network function we obtain the poles and zeros.

2. The scale factor is denoted by the letter?
a) G
b) H
c) I
d) J

Explanation: The scale factor is denoted by the letter ‘H’ and its value is equal to the ratio of ao to bo.

3. The zeros in the transfer function are denoted by?
a) 3
b) 2
c) 1
d) 0

Explanation: The roots of the equation P (S) = 0 are zeros of the transfer function. The zeros in the transfer function are denoted by ‘o’.

4. The poles in the transfer function are denoted by?
a) x
b) y
c) z
d) w

Explanation: The roots of the equation Q (S) = 0 are poles of the transfer function. The poles in the transfer function are denoted by ‘x’.

5. The network function N (S) becomes _________ when s is equal to anyone of the zeros.
a) 1
b) 2
c) 0
d) ∞

Explanation: The network function N (S) becomes zero when s in the transfer function is equal to anyone of the zeros as the network function is completely defined by its poles and zeros.
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6. The N (S) becomes ________ when s is equal to any of the poles.
a) ∞
b) 0
c) 1
d) 2

Explanation: The network function is completely defined by its poles and zeros and the network function N (S) becomes infinite when s in the transfer function is equal to anyone of the poles.

7. If the poles or zeros are not repeated, then the function is said to be having __________ poles or ________ zeros.
a) simple, multiple
b) multiple, simple
c) simple, simple
d) multiple, multiple

Explanation: If the poles or zeros are not repeated, then the function is said to be having simple poles or simple zeros and the network function is said to be stable when the real parts of the poles and zeros are negative.

8. If the poles or zeros are repeated, then the function is said to be having __________ poles or ________ zeros.
a) multiple, multiple
b) simple, simple
c) multiple, simple
d) simple, multiple

Explanation: If there are repeated poles or zeros, then function is said to be having multiple poles or multiple zeros and the network function is stable if the poles and zeros lie within the left half of the s-plane.

9. If the number of zeros (n) are greater than the number of poles (m), then there will be _________ number of zeros at s = ∞.
a) n
b) m
c) n-m
d) n+m

Explanation: If the number of zeros (n) are greater than the number of poles (m), then there will be (n-m) number of zeros at s = ∞ and to obtain (n-m) zeros at s = ∞ the condition is n>m.

10. If the number of poles (m) are greater than the number of zeros (n), then there will be _________ number of zeros at s = ∞.
a) m+n
b) m-n
c) m
d) n

Explanation: If the number of poles (m) are greater than the number of zeros (n), then there will be (m-n) number of zeros at s = ∞ and to obtain (m-n) poles at s = ∞ the condition is m>n.

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