Multi-Port Network: Z- and Y-Parameters
This chapter deals with distributed media with some spatial variations where there are multiple input sources and multiple output observation points. The most common scenario is a 2D conductor slab with multiple ports, where the ports are stimulated by a voltage/current source and the goal is to find the ports current/voltage values, respectively. Putting aside scattering parameters (which are dealt with in the next chapter), the current chapter focuses on three methods: flat RLC grid, impedance (Z-)parameters, and admittance (Y -)parameters. In the flat-grid method we simply discretize the slab into RLC elements, do KVL/KCL for all nodes and branches, and then solve for all voltages and currents. For Z-parameters we derive the impedance matrix by selectively stimulating each port with a current source and observing voltage at all ports. Once the impedance matrix is ready, all that has to be done is to multiply it by any new current vector to give us all port voltages. Similarly for Y -parameters we derive the admittance matrix by selectively stimulating each port with a voltage source and observing current at all ports. Once the admittance matrix is ready, all that has to be done is to multiply it by any new voltage vector to give us all port currents. Of course each of Z-and Y -parameters could be frequency dependent, and hence will build on spectral methods. We wrap the chapter by illustrating the relation between the Z- and Y -matrix.