Estimating the R and L Values in the Transition Region
Q3D Extractor estimates the inductance and resistance values in the transition region. The estimate is based upon the DC and AC asymptotes.
An equivalent circuit model (shown below) is used to interpolate between the DC and AC solutions:
where:
- Rdc and Ldc are the DC RL values
- Rac and Lac are the AC RL values at frequency fac
- f is the frequency
This circuit has the correct limiting behavior at low and high frequencies. At intermediate frequencies, it has a frequency-dependent impedance:
The effective resistance R(ω) and inductance L(ω) can be extracted from the real and imaginary parts of this impedance.
When there are multiple conduction paths in the problem, all of the elements in the above circuit become multi-port devices, but the same basic procedure applies.
The interpolation scheme described above is not a solution of the underlying physics, but rather is intended as a rough estimate of the behavior at intermediate frequencies. A more rigorous solution can be obtained by employing a finite element field solver, such as Maxwell Field Solver, to solve the eddy current equation within the conductors.