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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?

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1 Answer 1

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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 \$.

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  • \$\begingroup\$ Interesting, so reactance is completely reflection-based? So, input impedance the same as reactance? Is S11 the only s-parameter responsible for reactance? \$\endgroup\$
    – KJ7LNW
    May 21, 2022 at 3:45
  • \$\begingroup\$ S<sub>11</sub> 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. \$\endgroup\$
    – qrk
    May 21, 2022 at 18:44
  • \$\begingroup\$ Is S11 the only s-parameter responsible for reactance? \$\endgroup\$
    – KJ7LNW
    Jul 30, 2022 at 0:15
  • \$\begingroup\$ @KJ7LNW S22 can be used to find the impedance of the output of the network. \$\endgroup\$
    – qrk
    Jul 30, 2022 at 5:05

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