Four linear two-ports are specified by parameter matrices

Four linear two-ports are specified by parameter matrices. Reciprocity tests: \(z_{12}=z_{21}\); \(y_{12}=y_{21}\); \(AD-BC=1\) for the chain matrix that uses the leaving current \(I_2'\); and \(h_{12}=-h_{21}\). Symmetry tests (in addition to reciprocity): \(z_{11}=z_{22}\); \(y_{11}=y_{22}\); \(A=D\); and, for the hybrid set of a reciprocal network, \(h_{11}h_{22}-h_{12}h_{21}=1\). - Network P has \(z_{11}=12.0\,\Omega\), \(z_{12}=4.00\,\Omega\), \(z_{21}=4.00\,\Omega\), \(z_{22}=8.00\,\Omega\). - Network Q has \(y_{11}=50.0\,\mathrm{mS}\), \(y_{12}=-20.0\,\mathrm{mS}\), \(y_{21}=-30.0\,\mathrm{mS}\), \(y_{22}=40.0\,\mathrm{mS}\). - Network R has chain parameters \(A=3.00\), \(B=8.00\,\Omega\), \(C=1.00\,\mathrm{S}\), \(D=3.00\). - Network S has \(h_{11}=50.0\,\Omega\), \(h_{12}=0.200\), \(h_{21}=25.0\), \(h_{22}=2.00\,\mathrm{mS}\). (a) For each of P, Q, R, and S, determine whether the two-port is reciprocal. Quote the numerical test used. (b) For every network that is reciprocal, determine whether it is symmetrical. (c) Convert the chain parameters of network R to \(z\)-parameters and confirm your conclusions of parts (a) and (b) from the \(z\)-matrix.

Apply the reciprocity test that belongs to the given parameter set; do not convert until part (c).