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I know that, for example, \$X_L=2\pi f L\$ will calculate reactance of an ideal inductor, but can this be calculated for a real component model? Given the S-Parameter values at some frequency from an S2P file, can you calculate the reactance of the component at that frequency?

For example, in Mag-Angle format, this 120 nH inductor has the following S-parameter values at 100MHz as seen in its .s2p file:

S-Param \$\|S\|\$ Phase \$\angle\$ in degrees
\$S_{11}\$ 0.588600478 50.2086462
\$S_{21}\$ 0.770096917 -35.9648121
\$S_{12}\$ 0.770096917 -35.9648121
\$S_{22}\$ 0.588600478 50.2086462

Reactance for 120nH at 100MHz should be somewhere near here, but I want to know the component's reactance based on the S2P model:

\$2\pi×(100×10^6)×(120×10^{−9}) \approx 75.36 \Omega\$

Questions:

  • Is it possible to calculate the (probably complex) reactance based on the S-Parameters above?
  • If so, how?

See also: Can admittance (Y) be used to calculate reactance when L and C values are calculated from the Y12 and Y11 parameters like normal as X=XL-XC?

KJ7LNW
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1 Answers1

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Maxim Tutorial 2866, equation 2; along with other sources; cover this. Essentially:

$$ Zin = Zo \left( {1+S_{11}} \over {1-S_{11}} \right) $$

where Zo is your measurement system impedance, generally 50 Ω.

If my arithmetic is right, \$ Zin = 55.1 + j76.3 \$.

qrk
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  • Interesting, so reactance is completely reflection-based? So, input impedance the same as reactance? Is S11 the only s-parameter responsible for reactance? – KJ7LNW May 21 '22 at 03:45
  • S11 is the reflection coefficient. Reflections happen because of impedance mismatch between the source and the system under test. The inductor data supplied shows it's an imperfect inductor, i.e., it has a significant real (lossy)component at the frequency under test. – qrk May 21 '22 at 18:44
  • Is S11 the only s-parameter responsible for reactance? – KJ7LNW Jul 30 '22 at 00:15
  • @KJ7LNW S22 can be used to find the impedance of the output of the network. – qrk Jul 30 '22 at 05:05