# How are S-Parameters and Reactance related, can one be calculated from the other?

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?

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 \$$.

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