# Talk:Two-port network

## parameters definitions

${\displaystyle Z_{ab}={\frac {V_{a}}{I_{b}}}{\bigg |}_{I_{!b}=0}}$

where !b means the value that b isn't (ie if b=1, !b=2, and if b=2, !b=1).

${\displaystyle y_{ab}={\frac {I_{a}}{V_{b}}}{\bigg |}_{V_{!b}=0}}$

where !b means the value that b isn't (ie if b=1, !b=2, and if b=2, !b=1).

It's more common to use a conventional complement operator. For example,
${\displaystyle y_{ab}=\left.{\tfrac {I_{a}}{V_{b}}}\right|_{V_{\tilde {1}}}}$
or
${\displaystyle y_{ab}=\left.{\tfrac {I_{a}}{V_{b}}}\right|_{V_{\neg 1}}}$
or
${\displaystyle y_{ab}=\left.{\tfrac {I_{a}}{V_{b}}}\right|_{V_{\hat {1}}}}$
or
${\displaystyle y_{ab}=\left.{\tfrac {I_{a}}{V_{b}}}\right|_{V_{\bar {1}}}}$
etc... —TedPavlic (talk) 20:23, 19 January 2009 (UTC)

## combining 2 port networks

When talking about cascading networks or putting them in series and parallel, we really should have diagrams (No Worries 23:18, 22 April 2007 (UTC))

## Partial derivations of voltages and currents in defnition of h parameters

I've made some research - preparing for labs of transistor characteristics and I used here specified definition of h parameters. My professor said me that it is not applicable to AC analysis and regime. For AC it must be partial derivation of those voltages and currents. --Čikić Dragan 13:39, 3 December 2007 (UTC)

Two-port parameters are for linear networks, so partial derivatives are not necessary. Of course you can always perform a linear approximation of a nonlinear network and then find the two-port associated with the linearization. -Roger 15:53, 3 December 2007 (UTC)
I think Čikić Dragan is talking about small signal h parameters, Roger, which are indeed defined as the derivative by transistor manufacturer data sheets due to the essential non-linearity of semiconductors. They also use large signal parameters which are going to be rather non-linear. This is the difference between hFE and hfe for instance. But I think this is something for the transistor circuit articles rather than here. SpinningSpark 17:48, 4 May 2008 (UTC)

## Scattering parameters subsection

It is unclear to me whether this subsection belongs here, because the variables V1+, V1−, … etc. appear unrelated to the two-port definition in terms of V1, I1, … etc. If there is some discussion that clarifies this relationship, OK, put this discussion in the subsection. If not, this subsection should be placed separate from the two-port article, and the "two-port" description should be amended. In addition, there is no definition provided for the S-matrix. This subsection also requires references. I'd recommend Choma and Chen, Chapter 3, isbn 981-02-2770-1 ; World Scientific (2007). The article Scattering parameters should be cited as a

Main article: Scattering parameters

I have removed the present subsection to the talk page (see below) until it is ready for prime time. Brews ohare (talk) 18:49, 13 March 2008 (UTC)

### Under construction

#### Scattering Matrix for a 2 Port Network

V1+         -----------------           V2+
o-----------| 2 Port        |-----------o
| Network       |
o-----------|               |-----------o
V1-         -----------------           V2-
${\displaystyle \left[{\begin{array}{c}V_{1-}\\V_{2-}\end{array}}\right]=\left[{\begin{array}{cc}\gamma &\mathrm {T} \\\tau &\Gamma \end{array}}\right]\left[{\begin{array}{c}V_{1+}\\V_{2+}\end{array}}\right]}$.

Where ${\displaystyle \gamma /\Gamma }$ is the reflection coefficient, and ${\displaystyle \tau /\mathrm {T} }$ is the transmission coefficient.

The scattering matrix

${\displaystyle \mathbf {S} =\left[{\begin{array}{cc}S_{11}&S_{12}\\S_{21}&S_{22}\end{array}}\right]}$.

I'm not sure if there's any benefit to giving this form, especially since it seems pretty much the same as this one. -Roger (talk) 03:30, 19 March 2008 (UTC)

## Combinations of two-port networks

I have a problem with this section. I do not believe it is true that the Z matrices can be simply added for series connected networks. Here is a counter example, take this simple network of two resistors;

${\displaystyle Z_{11}=2\Omega \,\!}$

Connecting two of them together like this gives the expected result;

${\displaystyle Z_{11}=2\Omega +2\Omega =4\Omega \,\!}$

But what about this one. Still the same two circuits with ports still connected in series but now;

${\displaystyle Z_{11}=2\Omega \,\!}$

Or this one. Now we have;

${\displaystyle Z_{11}=3\Omega \,\!}$

Same two circuits connected in the same configuration and three different answers. Only one of them agreeing with,

${\displaystyle [Z]_{1}+[Z]_{2}=[Z]\,\!}$

Does not get much simpler than a two resistor network. The statement cannot possibly hold for the general case. Or am I missing something obvious?

SpinningSpark 02:01, 25 March 2008 (UTC)

I have found a text-book which divides two-port interconnections into correct and incorrect depending on whether or not output current flows between them (everything above is incorrect except the first case). Solves the problem with output transformers, but then that means the model in not useable for dc/lf on incorrect circuits. Seems obvious that a great deal more needs to be written in this article to bring it up to standard on this point. SpinningSpark 17:22, 4 May 2008 (UTC)
I also have a text book which states the need to use ideal transformers, to prevent the short circuits. Ideal transformers work at ALL frequencies, even DC, as it is really about removing the unintended short circuit introduced.

Good points. The "two port" representation is a state space reduction from the real network equations Vx=Zx Ix which in this case would be 4x4 . A way to look at the assumption made in the reduction is that the current flowing into the input top node is balanced by the current flowing out of the bottom node of the input; similarly for the output. Your connections to your diagrams violate this. Balance can be reinstated by a transformer or hybrid representation with the ground broken. It's the ground loops that kill you:)

A more direct observation would be to write: Vt,Vb, etc.. for the voltage of top, bottom, etc... network and

Vt=Zt It , Vb=Zb Ib then Vt+Vb=Zt It + Zb Ib and =(Zt+Zb) I? if and only if It=Ib

In other words a lot of different circuits reduce to a particular two port Z; but the mapping is not invertible. Only special circuits will allow you to add Zt+Zb.

The two port representation is good for source and loading analysis, but is limited. A four node representation should be doable but is a lot more difficult to deal with. As always, it behoves you to understand your tools and keep your fingers out of the moving machinery:) Rrogers314 (talk) 14:27, 30 August 2008 (UTC)

Old question but still worth answering: In order to add the Z matrices of two interconnected two-ports you have to verify that the connection between them satisfies Brune's tests. --Ferengi (talk) 13:28, 13 February 2011 (UTC)

The Brune test is sufficient, but not necessary [1]. Networks exist that fail the Brune test but with matrices that still correctly add. Also, the reference you are pointing to appears to give an incorrect definition of the Brune test: all the circuits above would pass the test as stated by Bakshi so he is clearly wrong. The correct test is shown here. SpinningSpark 16:23, 13 February 2011 (UTC)

## Equals - triangle

Ted, what do you mean by that symbol? Why will plain equals not do? SpinningSpark 18:46, 19 January 2009 (UTC)

The ${\displaystyle \triangleq }$ is a conventional symbol representing "equal by definition." Some texts use ${\displaystyle {\stackrel {\text{def}}{=}}}$ instead, but ${\displaystyle \triangleq }$ is a little more compact. It's often important to be clear about whether a relationship is a definition or is a theoretical consequence. For example, when an entry is dense with math, sometimes it's unclear to see why something is "=" to something else. When you tell the reader that it's equal by definition, then the reader doesn't have to comb through the reset of the entry to see whether or not the equality is a mistake. —TedPavlic (talk) 20:15, 19 January 2009 (UTC)
Ok, but I think that is unusual enough that it should be explained in the article. The alternative symbol is self-explanatory and I am used to := but the triangle I have not seen before and I am sure it will confuse a lot of others as well. SpinningSpark 21:38, 19 January 2009 (UTC)
Changed all to the stackrel variety. There are some more attractive alternatives (including a very nice looking := symbol that properly lines up the centers of the : and =), but Wikipedia's class-Z LaTeX support doesn't include them. If their backward distro would support the mathtools package entirely, the math on these pages would look MUCH better... But apparently it's too much to ask for them to support amsmath even. Oh well... How do things look now? —TedPavlic (talk) 01:06, 20 January 2009 (UTC)

## All are bmatrix now – change to pmatrix if want

To make the article consistent with itself, I've chosen (arbitrarily) to change all vectors and matrices to be grouped using a LaTeX bmatrix (i.e., "bracketed matrix") environment. If people feel like parentheses are a better convention to use, then change every bmatrix to pmatrix (i.e., "parenthetical matrix") and you'll be set. For example, in Vim (as an external editor) execute:

:%s/{bmatrix}/{pmatrix}/g

and save the page. Note that I've gone ahead and changed every "choose" to a proper matrix environment, and so this global change will definitely touch everything. —TedPavlic (talk) 20:27, 19 January 2009 (UTC)

## Networks with more than two ports

The article states that the following representations are necessarily limited to two-port devices:

• Hybrid (h) parameters
• Inverse hybrid (g) parameters
• Transmission (ABCD) parameters
• Scattering transfer (T) parameters

This is not correct for ABCD and T parameters. A multiconductor transmission line can be modeled by a 2n-port matrix, where there are n input and n output ports. A 2n-port matrix is a 2x2 matrix where each element is an nxn matrix. 2n-port ABCD matrices can be multiplied for cascading two multiconductor transmission lines for example. I can't find any introductory text on this, but this might help: http://books.google.com/books?id=uO5HiV6V8bkC&pg=PA316

--Bmachiel (talk) 13:29, 24 November 2010 (UTC)

Feel free to update the article. But can chain parameters be extended to the general case n-port? I suspect (but do not know for sure) that such extensions are limited to special cases such as the one described where the ports can be divided into two equal groups - in this case the two "ends" of a multi-port transmission line. SpinningSpark 11:30, 19 December 2010 (UTC)

## Definition of 2-port network in linear case

"Any linear circuit with four terminals can be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions."

From this statement, it appears that it is more difficult for a linear circuit to qualify as a 2-port network than a nonlinear circuit, since there is an extra condition: not containing an independent source. — Preceding unsigned comment added by 84.227.254.143 (talk) 17:07, 31 March 2014 (UTC)