Smith Chart: Calculating Impedance with Loss/Leakage

[Magna Visus]

Hello guys,

I am using the Smith Chart to calculate impedance in lines, adapted lines, and lines with a stub in parallele (Short circuit).

I understood how to get Zin using the chart, first calculate reduced impedance, draw the circle, etc...

Now I have a question regarding this, and hopefully someone can clarify this.

If we have leakage/loss (γ=α+jβ and α non null) I have been told that I need to calculate how much loss in db/λ I have and then translate the old zin (reduced Zin) vertically by this same amount in oder to get the new zin, is this correct?

Thanks.

 

[anorlunda]

ping @sophiecentaur . Another spring cleaning thread.

 

[sophiecentaur]

ping @sophiecentaur . Another spring cleaning thread.

I think the Smith Chart is more convenient to use for lossless lines. I should imagine that the way to deal with a lossy line would be to take a number of short sections of line with lumped components added to give an equivalent value for the loss in each section of line. (using the sort of method that the OP describes, adding an appropriate Impedance or Admittance then rotating the chart by a small phase angle (That would need to be less than λ/8). This would produce a spiral of points, heading towards the centre of the chart.

 

[anorlunda]

Thanks Sophie, that us the last of the EE spring cleaning threads.

 

[sophiecentaur]

Thanks Sophie, that us the last of the EE spring cleaning threads.

My answer was a pragmatic one for someone who wants to use the Smith Chart. It would be easier to use other numerical methods these days. The Smith Chart was a great tool and it is still a great way of showing graphically / qualitatively how matching stubs etc. work. It will show, approximately (and understandably) the effect of losses and it teaches 'the student' about hopping from impedance into admittance and back again in a way that I couldn't begin to replace. I only ever used it in that way - with easy values - but I had a colleague who was dynamite with the chart. AND he used it to produce things that WORKED.