What is the ABCD matrix of a short stub and open stub transmission line?

[skatefast08]

How do you get an ABCD matrix of a stub for a single stub matched network? I know that the regular ABCD matrix for a transmission line is:

How would you express this equation for a stub?

I want to create a total s-parameter response graph on Matlab for a microwave pre-amplifier using single stub matching and i need to know the abcd matrix for each component; such as in the order of: stub, transmission line, transistor, transmission line, stub (with 50 ohm input and output terminations).

 

[pancho_hideboo]

Simply ABCD matrix for shunt element.
F={{1,0}, {1/Zstub,1}}

 

[skatefast08]

Simply ABCD matrix for shunt element.
F={{1,0}, {1/Zstub,1}}

I mean in terms of theta? theta = beta*l(length of stub)

 

[pancho_hideboo]

I mean in terms of theta? theta = beta*l(length of stub)

Surely understand Zstub.

 

[PlanarMetamaterials]

Surely understand Zstub.

I believe you want the input impedance of the stub in this case. There is a classic formula here.

 

[pancho_hideboo]

There is a classic formula here.

Zstub is Zsc or Zoc.

https://en.wikipedia.org/wiki/Stub_(electronics)#Short_circuited_stub

 

[skatefast08]

That's what I was thinking too, I just wanted to double check. I was also wondering if I can get the impedance of the series tline by using the Zoc equation? For a short stub tline I would use the Zsc but convert that to admittance instead, since its a shunt, right?

 

[volker@muehlhaus]

I was also wondering if I can get the impedance of the series tline by using the Zoc equation?

Have a look at the link in #5 in section "Input impedance of transmission line"

 

[skatefast08]

Have a look at the link in #5 in section "Input impedance of transmission line"

I want to exclude ZL though, I just want to know the impedance of just the transmission line without the load. wouldn't that be Zoc?

 

[volker@muehlhaus]

know the impedance of just the transmission line without the load

From your wording, I'm not sure if you want the characteristic line impedance (ZL) or the input impedance of the line with the other end open (Zoc) or something else.

 

[pancho_hideboo]

That's what I was thinking too, I just wanted to double check.

I don't think you can understand even very basic things correctly.

I was also wondering if I can get the impedance of the series tline by using the Zoc equation?

I can not understand what you want to mean at all.

For a short stub tline I would use the Zsc
but convert that to admittance instead,
since its a shunt, right?

Wrong, although I can not understand what you want to mean at all.

There is no difference between open-stub and short-stub.

Difference exists for shunt-stub and series-stub.
See https://www.edaboard.com/showthread.php?371705#4

ABCD matrix(=F matrix) for series-stub is F={{1,Zstub}, {0,1}}.
ABCD matrix(=F matrix) for shunt-stub is F={{1,0}, {1/Zstub,1}}.
Here Zstub=Zoc for open-stub, Zstub=Zsc for short-stub.

That's all.

I want to exclude ZL though,
I just want to know the impedance of just the transmission line without the load.
wouldn't that be Zoc?

Wrong.
Surely learn very basic things.

 

[skatefast08]

This is what I was thinking in the picture I a drew, which is attached below. The question mark is in the picture. Can I set up the equation like that to get Zin(total), which includes the stub, the length of the main line, and ZL(load impedance)? if you think its incorrect how would you implement Zin(total) ?

 

[pancho_hideboo]

if you think its incorrect how would you implement Zin(total) ?

Of course, very very wrong.

Surely learn very basic mathematics.

 

[pancho_hideboo]

Second and Third Matrix are both wrong.
Surely learn very basic theory of kindergaten level circuit.

Since you want to treat ZL as F-Matrix, Zin=A/C

That's all.

Again surely learn very basic theory of kindergaten level circuit and kindergaten level mathematics.

 

[skatefast08]

Second and Third Matrix are both wrong.
Surely learn very basic theory of kindergaten level circuit.

Can you help me figure out the 2nd and 3rd matrix if they are wrong?

Since you want to treat ZL as F-Matrix, Zin=A/C

What is A/C? alternating current?

 

[PlanarMetamaterials]

Again surely learn very basic theory of kindergaten level circuit and kindergaten level mathematics.

I believe that's what skatefast08 is trying to do. Surely learn some manners?


The reason the second matrix is incorrect is because you've applied the equation for a TL stub, and not the general expression for a TL. You might want the matrix for an unterminated TL here (hint: it has a function of Bl in every term). The last matrix is not correct, since the single load isn't represented by a matrix at all! (see here).

A better approach is to simply compute the input impedance of the stub, and the input impedance of the main line (both at the location of the stub), and then the input impedance is those values in parallel.

Good Luck!

 

[pancho_hideboo]

The last matrix is not correct,
since the single load isn't represented by a matrix at all!

No.
ZL can be treated as F-matrix for shunt element.

First Matrix has to be for shunt element.
Second Matrix has to be for TLine.
Third Matrix has to be for shunt element.

But skatefast08 apply followings.
Second Matrix is for series element.
Third Matrix is for series element.

Completely wrong.
I don't think skatefast08 can understand even very basic things.

What is A/C? alternating current?

Can you understand F-Matrix surely ?
F={{A,B}, {C,D}}.

You treat RL as F-matrix.

 

[volker@muehlhaus]

kindergaten

kinderwhat? Surely learn manners and spelling.

 

[pancho_hideboo]

kinderwhat? Surely learn manners and spelling.

Enter "kindergaten" in Google Search.
Google corrects it.

 

[volker@muehlhaus]

Enter "kindergaten" in Google Search.

If you insult other forums members in my language, surely use correct spelling.