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Design >> RF Design >> smith chart
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Message started by raja.cedt on Oct 1^st, 2011, 7:48am

Title: smith chart
Post by raja.cedt on Oct 1^st, 2011, 7:48am

hello,
i was trying to solve a problem in RF design book in th lee. The problem is about smith chart for lossy transmission line, so i have started by assuming z0=a+ib, but some different curves i am getting. have any one tried this? otherwise can any one give me suggesion how to start

Thanks,
raj.

Title: Re: smith chart
Post by rfcooltools.com on Oct 13^th, 2011, 5:30pm

Raja,

Adding a complex component to the tline will not give you loss, for a single frequency you could look at it as a starting angle on a tline of a impedance |a+jb| arg(a+jb) or a tline of characteristic impedance in series with an inductor at a single frequency.
Be careful using this over frequency its even less of what you are looking for, since complex numbers always have a frequency component tied to the complex number. 1/sC or s*L etc.. One way to approximate a lossy tline is to break it into smaller sections where you can approximate the loss by adding a resistor to an AC ground and or a series resistor often as your needs require.
To be even more accurate a lossy Tline has several lossy mechanisms. The three dominant are dc resistance loss due to frequency dependent dielectric constant Er(f). And finally skin effect which is basically a resistor R=Rdc+Rse*sqrt(f/fo) where fo is the frequency where the skin effect starts effecting the resistance.

http://rfcooltools.com

Title: Re: smith chart
Post by vp1953 on Oct 13^th, 2011, 6:40pm

Hi Raja,

I do not think you can use a regular smith chart for this purpose - you would have to create some sort of a special version of the smith chart which would have different characteristics than the standard smith chart (eg as you traverse a length of the transmission line, you cannot use a constant reflection coefficient circular contour - it would have a spiral like contour). There is a minimal discussion of this at

http://www.mendeley.com/research/power-reflection-coefficient-analysis-complex-impedances-rfid-tag-design/

and also the paper referred to in there (kurakowa), though this is a far simplified case than your scenario. There might be some other and better references on this topic. I think the best approach is that advocated by rfcooltools which is to use discrete valued resistors to model the loss.

Title: Re: smith chart
Post by 3dsmithchart on Oct 25^th, 2011, 7:06am

Dear Raja and dear vp1953, most of the rf programs use to the kurowava formulation, however if you would use any formulation given you have to think that (az+b)/(cz+d) is a mobius tranformation that maps lines to circles or circles into circles. the smith chart is the result of (z-1)/(z+1) applied to a grid shape. if you use the complex normalization impedance you still get (z-1)/(z+1) after simplifications but you might get a module bigger than 1 since z is not anymore in the RHP. You cannot see this in the rf tools since mostly they use another formulation: the kurowava
On the site http://www.3dsmithchart.com/ you have a free tool that generalizes the Smith chart on the Riemann sphere and you may solve this pb too with a trick. It is based on a 2011 new concept introduced by my colleagues and myself in a June MWCL paper.