Questions on two-port network

[promach]

For z-parameter model:

a) How to derive the two equations in the screenshot below which are retrieved from https://en.wikipedia.org/wiki/Impedance_parameters#Impedance_relations ?




b) Why is output impedance, Zout computed with input node shorted to ground ?



For Y-parameter model:

a) As shown below , why "Though allowing simpler algebra, the Y model does not provide intuitive results." ?




b) As in http://rfic.eecs.berkeley.edu/~nikne...ct4.pdf#page=6 , why " y21 =gm - y? " ?

[T3sl4co1l]

a. Literally, just write down the port voltages and currents, and rearrange into the canonical impedance form.  (Any other two-port form can be reached by rearranging the equations as well.)  Recall the definition of a vector and a matrix in a system of equations.

b. The picture says it's computed for input node connected to Zs.

Tim

[promach]

The screenshot is for question (a)

[danadak]

Keep in mind the Z of an ideal V source is 0 and of a current source infinity.

Makes for quick shortcuts when configuring two port for calculations.


Regards, Dana.

[The Electrician]

Often the situation is idealized by assuming the input of the network is driven by a voltage source.  Voltage sources have zero output impedance, so when the input node is driven from a voltage source, this is the same as shorting the input node to ground as far as impedance seen at the input node is concerned.

You might need to show Fig. 8.51(a) to help us see what might be more intuitive about the G model equations.

[promach]

[The Electrician]

I don't see immediately why the Y model would be easier algebra but less intuitive.  It might be necessary to work out the result using the Y model; perhaps then it would be obvious.