Question

The scattering matrix for a N - port network can be written as [s]

[ s₁₁, s₁₂ ... ... s₁N ]
[ s₂₁, s₂₂ ... ... s₂N ]
⋮
[ sN₁, sN₂ ... .. sNN ]
(i) If all the matrix coefficients are known how would you find coupling to port q from port p ?

Answer 1

The coupling to port q from port p in a N-port network is determined by the scattering matrix coefficient spq, which indicates both the strength and phase shift of the wave transmitted between the two ports.

Step-by-step explanation:

To find the coupling to port q from port p in a N-port network using the scattering matrix, you would look at the corresponding element spq in the scattering matrix.

The coefficient spq represents the complex amplitude of the wave that is transmitted to port q from port p. If these coefficients are all known, the magnitude of spq gives the coupling strength between the ports, while the phase of spq provides information about the phase shift that the wave undergoes during this transmission. It is important to note that in a reciprocal network, the coefficient spq is equal to sqp, meaning the coupling from port p to q is the same as from q to p.