What are two-port networks all about?

[Avichal]

I do not understand two-port networks. Why are they so useful?
My book says that for a two port network current incoming and outgoing at each port must be equal. Why is that? Okay, even if they are equal how does that help us? How are we able to neglect all the inner circuit and just focus on the ports and still get the values of voltage and current so easily?

 

[yungman]

Two port network can be very useful. But there are many two port networks depend which one you are referring to. Without knowing what two port network your are referring to, there is no way I can comment on that.

 

[Studiot]

I do not understand two-port networks. Why are they so useful?
My book says that for a two port network current incoming and outgoing at each port must be equal. Why is that? Okay, even if they are equal how does that help us? How are we able to neglect all the inner circuit and just focus on the ports and still get the values of voltage and current so easily?

Are you quite sure? Under what circumstances does your book say this?

Why are they so useful?

Because
Two port networks can be assembled in cascade to analyse circuits.
The offer a format that can be represented by a pair of simultaneous linear equations that can be written as a matrix and the matrices multiplied in cascade.

Further by choosing one of the ports as common to input and output they can be used to represent many three terminal devices such as transistors.


for example

v₁ = z₁₁i₁ + z₁₂i₂
v₂ = z₂₁i₁ + z₂₂i₂

subscript 1 refers to input and 2 refers to output

This is the impedance version and clearly shows different input and output currents and voltages.

 

[Avichal]

Are you quite sure? Under what circumstances does your book say this?

Yes we can write voltage and current at the ports in terms of the parameters. We don't need to solve the whole circuit right?

v₁ = z₁₁i₁ + z₁₂i2
v₂ = z₂₁i₁ + z₂₂i2

subscript 1 refers to input and 2 refers to output

This is the impedance version and clearly shows different input and output currents and voltages.

That's what I want to know. How do we get these equations?

 

[Studiot]

Quote by Studiot
Are you quite sure? Under what circumstances does your book say this?

Yes we can write voltage and current at the ports in terms of the parameters. We don't need to solve the whole circuit right?

I am sorry how is this an answer to my question?

If your book genuinely says this (yes) for all circumstances, change your book soonest.

 

[Avichal]

I am sorry how is this an answer to my question?

If your book genuinely says this (yes) for all circumstances, change your book soonest.

It doesn't say for all conditions. It has some restrictions:-
(1) Incoming and outgoing current must be equal at each port
(2) Circuit must be linear
(3) There should be no independent sources present

So if the circuit meets all these conditions how can we derive the following equations:-
v₁ = z₁₁i₁ + z₁₂i₂
v₂ = z₂₁i₁ + z₂₂i₂

Thank you

 

[Studiot]

Well then pleaase tell us what circumstances you (your book) is talking about.

What circuit is it considering?

 

[Avichal]

Hmm could you just tell me what all circumstances this concept is valid and how do we get those equations
Sorry for the confusion
Thanks a lot

 

[Studiot]

I don't like to contradict a textbook; they can be wrong, but in my experience most issues arise through misreading or misreporting what they say.

A two port network is the classic 'blackbox' theory.
You do not need to know what goes on inside the box.
The blackbox contains two pairs of terminals labelled input and output and unknown works inside.
Each pair of terminals forms a port.
All its properties are characterised by the relationships between variables of interest measurable at the two terminal pairs or ports.
There may be (or may not be) interaction between the input and output terminals. That is what the current at the input may or may not affect the current at the output.
A blackbox may (but does not have to) contain an energy source.

All this leads to the the equations I wrote.
The first term of each describes the interaction between curennt and voltage at each port, without regard to the other port.
The second term of each describes the interaction of the input port with the output port.

 

[Avichal]

Okay, so z₁₁, z₂₁ and others are all just constants. Do they have a physical meaning?

And why so many parameters, apart from the impedance parameters there are y (admittance), t, g and other parameters.

 

[Studiot]

Yes the z parameters are impedances.

z₁₁ is the input impedance

z₂₂ is the output impedance

z₁₂ is the forward transfer impedance

z₂₁ is the reverse transfer impedance, which may or may not be equal to z₁₂

You can write the equations is 5 other ways with admittances, and with what are known as mixed parameters.

 

[Avichal]

Well thanks a lot - I got the basic why, how questions all cleared up from you.
No idea where would I be without PF!

 

[Studiot]

Time for tea and chocolate biscuit.