Transmission Lines - S Parameters

[fourierpwn]

Hi, could someone please me help understand how to approach this question:

A transmission line with a characteristic impedance of 50 ohms is connected to a load. The load impedance is (30 +𝑗60) ohms. Calculate the dB value of S11 at the load.

The answer is -1.99dB, though I don't understand how to calculate this. 

[jpb]

S11 is just the fraction of the energy that is reflected - this classic HP app note explains it very well:

http://cp.literature.agilent.com/litweb/pdf/5952-1087.pdf

[Howardlong]

Another approachable text is Chris Bowick's RF Circuit Design, very approachable for engineers in practical terms, and thankfully free of unnecessary academic fluff.

It seems to be available in PDF if you google it.

[rfeecs]

Your answer seems to be wrong.  Off by a factor of 2.

S11 is the complex reflection coefficient.

Convert complex impedance to reflection coefficient, take the magnitude.  Just Google it.

Magnitude is 20*log(mag(S11)) because S11 is a voltage ratio.

[danadak]

Maybe useful -


http://fermi.la.asu.edu/ccli/applets/tran/tran.html


Regards, Dana.

[Howardlong]

To the OP:

If you look on pages 115 and 116 of Chris Bowick's RF Circuit Design book there's an example of how to do this with a Smith Chart.

Alternatively, here's the way we're more likely to do it nowadays, with the math(s) behind it: http://chemandy.com/calculators/return-loss-and-mismatch-calculator.htm

[fourierpwn]

S11 is just the fraction of the energy that is reflected - this classic HP app note explains it very well:

http://cp.literature.agilent.com/litweb/pdf/5952-1087.pdf

Thank you for the app note. I understand what S parameters are, though I don't see how they got this answer.

Another approachable text is Chris Bowick's RF Circuit Design, very approachable for engineers in practical terms, and thankfully free of unnecessary academic fluff.

It seems to be available in PDF if you google it.

Thanks. I actually have a copy of this book already! 

Your answer seems to be wrong.  Off by a factor of 2.

S11 is the complex reflection coefficient.

Convert complex impedance to reflection coefficient, take the magnitude.  Just Google it.

Magnitude is 20*log(mag(S11)) because S11 is a voltage ratio.

Yes, I agree. This is why I posted the thread. I don't see how they got that answer.

For now I think I'll just assume that the given answer is wrong.

Thanks for the replies.

[G0HZU]

Back in the days of QuickBasic I wrote a little program for this kind of thing and transferred it across to MSDOS back in the 1990s.

You can see it in the black DOS window in the image below. The background is an old copy of Eagleware Genesys showing the analysis of your load impedance and it seems to agree with my ancient DOS program.

It gives a result of -3.979dB for S11. You might also find some of the other analysis info in the image to be useful?

[fourierpwn]

Back in the days of QuickBasic I wrote a little program for this kind of thing and transferred it across to MSDOS back in the 1990s.

You can see it in the black DOS window in the image below. The background is an old copy of Eagleware Genesys showing the analysis of your load impedance and it seems to agree with my ancient DOS program.

It gives a result of -3.979dB for S11. You might also find some of the other analysis info in the image to be useful?

What a nifty little program!

While I am familiar with Genesys, I have never used it...

Thanks for the taking the time to check the result for me. 

Edit: I just did a quick sim. in AWR and produced the same results as you.

[G0HZU]

It's late and I'm tired and I don't have a microphone here but try this silent youtube vid that shows how to get the magnitude of the reflection coefficient and then the return loss for your chosen load impedance using a simple excel sheet.

Hope it's OK. It will probably fail if you put zero in for the real part but you get the idea how it works. The opening few seconds show part of the initial start screen of my old DOS program.

https://www.youtube.com/watch?v=eZmV4CeXobg&feature=youtu.be

Note that I haven't done this vector based algebra since I wrote that program over 20 years ago so there are probably bugs in the way I've done it from memory. I always use a computer for this stuff. I do remember that I had to do some extra computation in the program to get the angles to display correctly for all possible load impedances.

[fourierpwn]

It's late and I'm tired and I don't have a microphone here but try this silent youtube vid that shows how to get the magnitude of the reflection coefficient and then the return loss for your chosen load impedance using a simple excel sheet.

Hope it's OK. It will probably fail if you put zero in for the real part but you get the idea how it works. The opening few seconds show part of the initial start screen of my old DOS program.

https://www.youtube.com/watch?v=eZmV4CeXobg&feature=youtu.be

Note that I haven't done this vector based algebra since I wrote that program over 20 years ago so there are probably bugs in the way I've done it from memory. I always use a computer for this stuff. I do remember that I had to do some extra computation in the program to get the angles to display correctly for all possible load impedances.

Mate, you went above and beyond the call of duty with that post. I highly appreciate your effort!

I think it say safe to say that we can conclude that the given answer is incorrect 

Thanks again!