The imported 2D-DXF CAD model was converted to a 3-D structure in CST MWS by extruding the metal profile to create a thickness of 35 microns and adding a substrate thickness of 1.6mm as shown in Figure 1 (right). The desired output quantity for this loop antenna was the complex input impedance for the coil without any other circuit elements, such as a tuning capacitance to adjust the resonance. The inductance of the antenna is defined by its coil-geometry and the capacitance is determined by the dielectric properties of the substrate FR4. Tolerance variations in FR4 thickness and dielectric constants are well documented in ,  and . A study was performed in order to demonstrate the impact of manufacturing tolerances on the resonance drifts. Figure 2 shows published measurement data  for real and imaginary dielectric constant variations versus frequency. ...
The dielectric constant and the dielectric losses have a significant impact to the magnitude and phase of the complex impedance values. To best fit the measurement data of the dielectric, a second order Debye curve-fit was applied to the complex material. The sample points and their related fitting curves are shown in Figure 3. The model was initially solved using the frequency domain (FD) with a tetrahedral mesh. In addition, some mesh constraints together with dummy elements have been used to reinforce a dense mesh in the vicinity of the wire traces. The model contains approximately 156.000 second order tetrahedrons. To further validate the results, for the same geometry a hexahedral meshtype with sugbrid option has been selected and the time domain (TD) solver was used to calculate the reflection parameter S11. Tetrahedral and hexhedral meshes are shown in Figures 4 and 5 respectively.
The reflection coefficient S11 data can be converted into a complex impedance curve which is more convenient for illustration purposes. The complex input impedance at 13.56 MHz was of particular importance for comparison purposes with measurements.
To demonstrate the sensitivity of the substrate thickness and permittivity, an FD-solver/tetra-based mesh parameter-sweep has been performed for a thickness variation of 1.6mm -/+ 0.13mm and a permittivity variation of the real part (eps') in the range of -/+ 0.15. As seen in Figure 6, the resonance peaks vary greatly for the above mentioned tolerances. Furthermore, for the nominal eps' and thickness curves, a comparison between time-domain and frequency-domain results has been added to the plot in Figure 6 (right). The deviations between these different solvers and meshtypes are a lot smaller than the shift caused by the tolerances of FR4.
The real part of the input impedance Re(Z11) can easily be converted into an admittance Y = 1/Z11 = G+jB for a better curve representation. This is shown in Figure 7 (left). The imaginary part of the impedance Im(Z11) is also shown in this Figure 7 (right).
Additional measurement data taken from  reveals, that simulation and measurements best fit at a tolerance set of delta_eps' = +0.15 and delta_thickness = -0.13 mm. Figure 8 shows the measurements for Re(Z11) and Im(Z11) and in Figure 9, the complex admittance Y11=1/Z11.
Conductance (G) and the susceptance (jB)- slope can be used to compute the Q-factor of the antenna.Convenient post processing templates within CST MWS, can be used to derive a susceptance versus frequency plot. Figure 10 shows plots and equations for calulating the Q factor.
As well as the integral parameters, CST MWS can be used to calculate the near fields. Visual current distributions and magnetic field radiation plots give a better insight into the models behaviour and aid in quantifying and understanding the model further.
The RFID example presented here demonstrates the capability of CST MWS Frequency Domain Solver using tetrahedral meshes. A parameter study was performed with respect to tolerances of the substrate to demonstrate the sensitivity of the input impedance for the more challenging case of an untuned RF-ID coil.
 P. Klaus, L.Kuenzle, Zuercher Hochschule Winterthur: Projektarbeit PA2 Bar06/01: "3D EM Simulation einer 13.56 MHz RF-ID Antenne"