5.3 Validation of the trace introduction by HFSS

An empirical validation of the proposed trace introduction method
with (5.6) and (5.9) is carried out by
HFSS^{®} simulations. HFSS^{®} is a FEM based
three-dimensional full wave simulation tool from Ansoft^{®}
[76].

A first HFSS^{®} enclosure model with a trace, depicted in
Figure 5.5(c), is simulated with ports at the source and the load positions
of the trace and three measurement ports at the slot. In a second HFSS^{®}
model, presented in Figure 5.5(d), the trace is removed and ports are
defined between the bottom and the cover plane of the enclosure in the same positions as
the trace load and source ports in the first model. The enclosure cover has been removed
in Figure 5.5(c) and Figure 5.5(d) to enable a view of the
inside. The enclosure with cover is depicted in Figure 5.5(b), and
Figure 5.5(a) depicts the bounding box, with absorbing boundaries at
the surface, that surrounds the enclosure in the simulation models.
Lumped ports are defined in HFSS^{®} on rectangular surfaces which are
small compared to the wavelength of the highest simulated frequency.
HFSS^{®} calculates the S-parameter matrix of the ports, which is
transformed to a Z-parameter matrix. Proven convergence of the HFSS^{®}
simulation is given through a monotone decrease of S-parameter results differences from
two consecutive adaptive mesh refinement iterations. For the model in
Figure 5.5(c) the transfer impedance from the trace source port to a
measurement port at the slot is

where , and are the Z-parameters of this HFSS

and

where is the trace width and is the trace height above the ground plane. Equation (5.11) with the adjustment function (5.12) approximates the exact conformal mapping solution from [78], [79], for the characteristic impedance of a thin sheet trace in air. The approximation uncertainty is below 0.03% for 1000.

For the purpose of simulating traces on a real PCB, the dielectric material of the PCB has to be considered with appropriate formulations [77], [80]. A comparison of the transfer impedances from both models validates the trace introduction method without any further simplifications, as there would be, if the cavity model were to be used instead of HFSS

(a) Enclosure model inside a bounding box. | (b) Enclosure model with cover. |

(c) Model with a trace (cover removed). | (d) Model with ports (cover removed). |

Load: 0 Ohm, magnitude. | Load: 0 Ohm, phase angle. |

Load: 1e9 Ohm, magnitude. | Load: 1e9 Ohm, phase angle. |

Load: 50 Ohm, magnitude. | Load: 50 Ohm, phase angle. |