Multiport Parameter Matrices
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Multiport Parameter Matrices
For a one-port device, we know that we can express the relationship between V and I in either
impedance (Z = R + jX) or admittance (Y = G + jB) forms. We make the choice based on the
nature of the network that comprises the one-port, typically choosing Z for series elements and
Y for parallel elements.
For a two-port we have a wider range of choices, always restricted to two equations defining
the four variables, V1, I1, V2 and I2.
We can express the relationships in z,y,h, g or ABCD parameters:
V1 = z11 I1 + z12 I2
V2 = z21 I1 + z22 I2
I1 = y11 V1 + y12 V2
I2 = y21 V1 + y22 V2
V1 = h11 I1 + h12 V2
I2 = h21 I1 + h22 V2
I1 = g11 V1 + g12 I2
V2 = g21 V1 + g22 I2
V1 = A V2 + B I2
I1 = C V2 + D I2
We can determine the values of the various parameters by measurements that are made under
the conditions that constrain other parameters to be zero. For example, using z parameters, we
can set I2 = 0 by open circuiting the output of the two-port. This allows us to measure z11 in the
first equation and z21 in the second. Similarly, we can constrain
I1 = 0 and measure z12 and z22. Other parameter sets require short-circuit loads at the ports.
Many active devices will oscillate with such a load, and hence can't be measured under those
conditions.
However, a true wideband short or open circuit directly at a port is very difficult to obtain at
microwave frequencies, while a matched load can be constructed over a very broad frequency
range. Although the matched termination does not constrain either V or I, it does create a
situation for which there is no reflected wave regardless of the length of the transmission lines
used.
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