Directions:

In the following question there are two statements, one labelled as 'Statement (I)' and the other as 'Statement (II)'. You are to examine these two statements carefully and select the answers to these items using the code given below.

Statement (I):

A transfer function is a function which relates the current or voltage at one port to the current or voltage at another port.

Statement (II):

If the function has one or more poles in the right-half plane, then the function is non-minimum phase.

Question

Question

This question was previously asked in

UPSC ESE Electronics & Communication 2022 Official Paper

Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
Statement (I) is true but Statement (II) is false
Statement (I) is false but Statement (II) is true

Answer 1

Key Points

The transfer function of a control system is defined as the ratio of the Laplace transform of the output variable to Laplace transform of the input variable assuming all initial conditions to be zero.

G(s) = C(s)/ R(s)

here,

C(s) → Laplace transform of output (Voltage or current)

R(s) → Laplace transform of input (Voltage or current)

A proper rational transfer function is a minimum phase transfer function if all of its zeroes lie in the left half of s-plane. It is a nonminimum phase transfer function if it has one or more zeros in the right half of the s-plane.
As transfer function is just a ratio of output and input expression it does matter whether it is minimum or nonminimum phase system.

Hence, option (2) is correct.