CST – Computer Simulation Technology

RFID Reader-Coil, 13.56 MHz

Radio Frequency Identification Systems (RFID) are widely used nowadays and allow advanced solutions for a variety of applications in the area of authentication, ticketing, access control, supply management, parking, payment, vending,etc. The example presented here is a RFID Reader Coil "P81" from Legic Identsystems AG,  www.legic.com , and was modeled and solved using the frequency domain solver of CST MICROWAVE STUDIO® (CST MWS). The sensitivity of the computed complex input impedance with respect to substrate tolerances is computed and was compared to measurement data. (With courtesy and permission of Legic Identsystems AG, Switzerland)

Figure 1: (left) Photo and (right) 3D- Model of the RF-ID tag used for simulation. A part of the pin probe was also modeled

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 [1], [2] and [3]. A study was performed in order to demonstrate the impact of manufacturing tolerances on the resonance drifts. Figure 2 shows published measurement data [4] for real and imaginary dielectric constant variations versus frequency. ...


Figure 2: Measured dielectric properties of FR4: eps' (left) and eps" (right). Blue dots indicate measure points, a regression curve is plotted in red.

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.

Figure 3: Dispersion fit Debye 2nd Order Model was used representing the permittivity versus frequency

Figure 4: Mesh details of the tetrahedral Mesh used for the Frequency-Domain Solver in CST MWS. (left) Surface mesh, (right) cross-sectional view at the 4 traces

Figure 5: Details of the Hexagonal Mesh used for the Time Domain Solver of CST MWS. Subgridding allows refined meshes around the conductors

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.

Figure 6: Real Part of the Input Impedance: The axis marker depicts the Re(Z11) at 13.56MHz (left); Close-up look at the frequency drift (right) 

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).

Figure 7: (left) Conductance curves , (right) Imaginary Part of the Input Impedance. The axis marker at 13.56 MHz reflects the reactance (jwL)

Additional measurement data taken from [4] 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.


Figure 8: Measured Impedance Z11: real Part (top) , imaginary Part (bottom). 

Figure 9: Admittance Curves for the real Part of Y11 (top), imaginary Part of Y(11) (bottom).

Figure 10: Q-Factor calculation derived from Susceptance jB and Conductance G for the nominal setup

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.

Figure 11: Surface current distribution of the coil and magnetic field strength along a vertical cutplane


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.



[1] http://www.pcb-pool.com/download/spezifikation/deu_EP_84_FR4__kupferkaschiert____MSC_Ditron_DB.pdf  

[2] http://www.bungard.ru/downloads/iec249_e.pdf

[3] http://www.andus.de/Leiterplatten/Impedanz/e_impedanz.htm

[4] P. Klaus, L.Kuenzle, Zuercher Hochschule Winterthur: Projektarbeit PA2 Bar06/01: "3D EM Simulation einer 13.56 MHz RF-ID Antenne"



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