Discussion
For the following ladder network :
its block diagram is :
- A.
- B.
- C.
- D.
Answer: B
The block diagram is (B).
Call the voltage across the shunt R, V2, the current in the first series R, I1, and the current in the second series R, I2. Writing the network as cause and effect, with G = 1/R and Z = 1/(sC):
\[ \begin{aligned} I_1 &= G\,(V_1 - V_2) \\ V_2 &= R\,(I_1 - I_2) \\ I_2 &= G\,(V_2 - V_3) \\ V_3 &= Z\,I_2 \end{aligned} \]
That needs three summing points in a chain, with blocks G, R, G and Z in that order, and three feedback paths: V2 (after R) back to the first junction, I2 (after the second G) back to the second junction, and V3 (after Z) back to the third. Diagram B is exactly this.
A has only two summing points and no feedback of V3. C puts Z before G, so it applies an impedance to a voltage difference, and its feedback paths come from the wrong places. D starts with R instead of G, which would multiply a voltage by a resistance. The printed diagrams carry no plus or minus signs; the signs above come from the network equations.
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