Question

The \(a_{ij}\) is the ___ of the branch directed from node \(x_i\) to \(x_j\) in signal flow graph. (Note: The blank is after "is the". Assuming it asks what \(a_{ij}\) represents.)

• A. Resistance
• B. Impedance
• C. Admittance
• D. Transmittance

Hint:

Signal Flow Graph (SFG) components:
Nodes: Represent variables.
Branches: Directed lines connecting nodes.
Branch Transmittance (Gain): The multiplicative factor associated with a branch.
\(a_{ij}\) is the transmittance of the branch from node i to node j.

Answer 1

The Correct Option is D

In a Signal Flow Graph (SFG):
Nodes (or vertices) represent system variables (signals).
Branches (or edges) represent the functional relationship between the variables at the connected nodes. Each branch has a direction and an associated gain or transmittance. The term \(a_{ij}\) (or \(t_{ij}\) or \(g_{ij}\)) represents the transmittance (or gain) of the branch directed from node \(x_i\) (source node) to node \(x_j\) (destination node). This means that the signal at node \(x_j\) contributed by the branch from \(x_i\) is \(a_{ij} \times x_i\). \(x_j = \sum_{k} a_{kj} x_k\) (signal at node \(x_j\) is sum of signals from all incoming branches). Resistance, Impedance, and Admittance are terms primarily used in electrical circuit analysis, though they can be represented in SFGs if the system variables are voltages/currents and the transmittances are appropriate electrical quantities. However, the general term for the branch gain in an SFG is "transmittance". \[ \boxed{\text{Transmittance}} \]