Electronics Engineering (ELEX) Board Practice Exam

What is the formula to calculate the transfer function using Mason's gain formula?

1. G₁H/(1+G₁)

2. (G₁+G₂)/(1+G₁H)

3. G₁/(G₂+1)

4. (G₁*G₂)/(1-G₁H)

The correct answer is: (G₁+G₂)/(1+G₁H)

Mason's gain formula is a systematic method used to determine the transfer function of a control system, especially for systems represented by block diagrams. The transfer function is primarily determined by the blocks (forward paths) and feedback paths within the system. The correct answer, which states that the transfer function can be expressed as (G₁ + G₂)/(1 + G₁H), correctly reflects the essence of Mason's gain formula as it accounts for both the forward gain and the effects of feedback. G₁ and G₂ represent the gains of different forward paths, while H represents the feedback path gain. The denominator includes the term (1 + G₁H) to adjust for the feedback effects, illustrating how the feedback impacts the overall gain of the system. In the context of control systems, when you have multiple paths contributing to the output and also consider feedback, the transfer function needs to encapsulate both the total gain from all forward paths and the feedback that can reduce the effective gain. This relationship allows engineers and designers to understand how changes in the system components will affect the overall behavior of the control system, making it a cornerstone of control theory applications. The other choices either misrepresent the relationship among the various components in a control system or