My original question sought to understand the relationship between S-parameters and reactance. In the process of trying to figure that out, this second question arose. The actual question is at the bottom, and first here is some background:
According to this video, Y12 can be used to find L, R, and Q as shown in this frame:
Additionally (and correct me if I am wrong), C can be calculated from Y11 as:
\$C = \frac{Im(Y_{11})}{2 \pi f}\$
Given L and C values calculated from the admittance matrix as shown above, reactance is calculated as:
- \$X_L=2\pi f L\$
- \$X_C=\frac{1}{2\pi f C}\$
- \$X = X_L - X_C\$
Using S2P measurements of this 120 nH inductor to create a Y matrix from the S parameters using the equations above will yield the following values:
L=120.243566 nH
C=-20.970845 pF (ok, so negative capacitance is inductance, but is this right?)
R=5.084455
Q=14.859263
\$X_L=75.551260\$
\$X_C=-75.893435\$
\$X=X_L-X_C = 151.444695\$
When I run this calculation at different frequencies for different parts I always get a \$X_C\$ and \$X_L\$ that is nearly the same, but negative so \$X \approx 2X_L\$. When I run this against an S2P representing a 10pF cap I get the same behavior but reactance is negative instead of positive (as expected).
Questions:
- Why does \$X_L \approx -X_C\$?
- Is it expected that \$X_L\$ and \$X_C\$ calculated from S2P files should be similar?
- The \$X_L\$ and \$X_C\$ numbers are so close that it makes me doubt the math somewhere along the line and triggers these follow-up questions:
- Is the reactance for this component only \$X_L\$ using the admittance calculations above, or is it really twice that as \$X=X_L-X_C\approx 2X_L\$ as you would expect?
- C=-20.970845 pF: Ok, so negative capacitance is inductance, but is this the correct capacitance value for calculating \$X_C\$?