Electronics Engineering (ELEX) Board Practice Exam

Given a transfer function G₂₁(S) as s/(s+1), what is the transfer function Z₂₁(S) in the circuit?

1. s

2. 2s

3. s²

4. 1/s

The correct answer is: 2s

To determine the transfer function Z₂₁(S) in the given circuit, we start with the provided transfer function G₂₁(S) = s/(s+1). This function typically represents the relationship between the Laplace transforms of the output and input signals in a linear time-invariant system. In control theory, the transfer function Z, which is often used to represent an effect on the system output due to the input and potential feedback, can be derived from G. If G₂₁(S) is known, the relationship often can indicate how it may relate to Z in specific configurations or applications, such as in feedback systems or when examining the overall system structure. For the transfer function G₂₁(S) = s/(s+1), one common approach to obtain a corresponding Z function is to manipulate or double the numerator. This is because in many control system applications, particularly those involving inputs that can effectively 'scale' the output, Z may represent a modified version of G. The doubling of 's' results in Z₂₁(S) = 2s, which maintains a similar behavior but with a different gain factor. This reflects a linear increase in the system response. Therefore, the correct transfer function Z₂