# Re: S - Y Parameter conversion with Smith Chart

From: Roy Lewallen (w7el_at_eznec.com)
Date: 07/30/04

```Date: Fri, 30 Jul 2004 16:29:42 -0700

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I sense some confusion about s and y parameters. S parameters aren't
impedances -- they're dimensionless transmission or reflection
coefficients. They do have a real and imaginary part (or magnitude and
angle) like an impedance, but that's as far as the similarity goes. You
can overlay a Smith chart on a polar plot of reflection coefficient
(e.g., s11) and directly read the normalized impedance which causes that
reflection coefficient. But what you read from the Smith chart isn't the
the reflection coefficient -- that is, it's not the s parameter. When
you reverse the Smith chart, you get the admittance causing the
reflection coefficient, but this still isn't a y parameter. If you
invert an s parameter, you still have a dimensionless number.

Y (admittance) parameters are a different critter, are measured
differently than s parameters, and have the dimensions of admittance.
Transformation from s to y or vice-versa isn't simple. For example,

y11 = {[(1 - s11)(1 + s22) + s12s21] / [(1 + s11)(1 + s22) - s12s21]}/Z0

(See, for example, Gonzalez, _Microwave Transistor Amplifiers, Analysis
and Design_.) From this you can see that in order to find y11, you not
only have to know s11, but also s12, s21, and s22. So it's simply not
possible to convert from y11 to s11 if s11 is all you know.

Roy Lewallen, W7EL