Design of MF RC500 Matching Circuits and Antennas

The following abbreviations are used:
ASK Amplitude shift keying
EMC Electro-Magnetic Conformity
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Calculation of the Antenna’s Coil Inductance
The precise calculation of the antenna coils inductance is not practicable and for the practical use not recommended. We recommend designing an antenna either with a circular or rectangular shape. For these a formula for a first estimation of the inductance is as follows:
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l1………….. Length of the conductor loop of one turn
D1 ………… Diameter of the wire or width of the PCB conductor respectively
K …………. = 1,07 for circular antennas = 1,47 for square antennas
N1 ………… Number of turns
ln …………. Natural logarithm function

Actual values of the antenna inductance depend on various parameters.
–antenna construction (Type of PCB)
–thickness of conductor
–distance between the turns
–shielding layer
–metal or ferrite in the near environment

Additionally, the number of turns N, which is needed for a certain size and a given inductance can be calculated. Figure 9-1 shows the number of turns needed for the antenna versus the antenna radius for a circular antenna. At a radius of 5cm the number of turns changes.

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Figure 9-1. Antenna radius versus inductance and number of turns

Estimation of the Coils’ Resistance
The operating frequency of MIFARE® is 13.56 MHz. In this frequency range it is not enough to describe the antenna coil with its DC resistance RDC. The skin effect can not be neglected. The relevant depth can be
calculated at 13.56 MHz and copper material to 18μm.
It is not practicable to calculate the complete AC resistance of the antenna coil RANT in general. The antenna’s resistance depend on several factor as material, dimensions of the wire, number of turns, shape
and shielding concept.
As a first estimation to tune the antenna without an impedance analyser the following formula should be used.
Note: The formula is the result of tests made with designed antennas. It is recommended to use an impedance analyser for an exact determination of RANT.