The transfer function C(s)/R(s) for the signal flow shown in figure is [Figure description: A signal flow graph. R(s) enters with gain 1 to a first node; a forward path G1 goes along the middle to a second node, then gain 1 to C(s). Above, a second forward path G2 arcs over from the first node to the second node, with a self-loop -H1 on the arc's top (at the first/top node of G2). Below, a feedback path -H2 returns from the second node back to the first node.]
- A. [G1(1 + H1) + G2(1 + H2)] / [1 + H1 + G1H2 + G1H1H2]
- B. [G1(1 - H1) + G2(1 - H2)] / [1 + H1 + G1H2 + G1H1H2]
- C. [G1(1 + H1) + G2] / [1 + H1 + G1H2 + G2H2 + G1H1H2]
- D. [G1(1 + H1) + G2] / [1 + H1 + G1H2 - H1H2]
Answer: C. [G1(1 + H1) + G2] / [1 + H1 + G1H2 + G2H2 + G1H1H2]
Explanation: Applying Mason gain formula to the signal flow graph: forward paths and non-touching loops yield [G1(1 + H1) + G2] / [1 + H1 + G1H2 + G2H2 + G1H1H2].