Design of MF RC500 Matching Circuits and Antennas

W SHORT RANGE SOLUTION
The second proposal to build up a 50Ω antenna uses only one driver stage, TX1 or TX2. In Figure 3-8 the complete impedance transformation and the receiving part are shown. The EMC filter based on L0 and C0 has the same structure as mentioned in the design hints for directly matched antennas. The combination of the components L0, C0 and C1 have the structure of a T- filter. This filter transforms the output driver resistance to the 50Ω resistance of the coaxial cable. The capacitance C1b is optional. It is recommended to use this tuning possibility for the first tests to find the optimum value for C1.

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Figure 3-8. 50 Ω Short Range solution: 50 Ω impedance transformation using one driver stage
To provide the functionality of the EMC filter a compromise between a matching to 50 Ω and the filtering has to be found. Table 7 shows the results of the tuning procedure.
Table 7. Values for the impedance transformation

Components Value Remark
C1a 69pF – 2% NP0 material
C1b 0-30 pF NP0 material

Note: To achieve the best functionality the used capacitors and inductors should have at least the performance and the tolerances of the recommended ones.

ANTENNA MATCHING CIRCUIT FOR 50 Ω ANTENNAS
The design of an antenna that matches the 50 Ω cable has to fulfil several requirements. Firstly The antenna coil itself has to be constructed and its inductance has to be measured or estimated using the formula to calculate the antenna’s inductance. This formula can be found in Annex A. Such an antenna is a low ohmic device. To connect this coil to an 50 Ω cable an impedance transformation has to be done. Additionally it needs a resonance circuitry to generate the highest voltage at the operating frequency of 13.56 MHz .

Determination of the Antenna’s Equivalent Circuit:
The reader antenna coil can be described with the equivalent circuit shown in Figure 3-9. The antenna exists of the winding itself. This winding has an inductance LANT. Additionally, this winding has the serial impedance RANT to describe the ohmic losses and a parallel capacitance CANT to describe losses both between windings and between the connectors.

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Figure 3-9. Equivalent circuit of an antenna coil

It is recommended, to measure the antennas equivalent circuit with an impedance analyser. Connect the antenna loop (when using shielded antennas connect the shield to ground) and measure the shown equivalent circuit. The value for the coil’s capacitance Cant can be neglected for the calculation of the quality factor and the tuning of the antenna.
Note: : If an impedance analyser is not available, use as starting value the calculated values for the inductance and resistance. To estimate these values formulas are given in Annex A. The operating frequency of MIFARE® is 13.56 MHz. At this frequency the ohmic skin effect losses can not be neglected, that is why it is not correct to use only the DC resistance of the coil. Please use the estimation in Annex A to find a start value for the impedance Rant. It is recommended to check the complete design later by measuring the quality factor. If necessary the starting value will have to be changed and the complete tuning procedure has to be redone.

Quality Factor
For the following part it is presumed that the values for the antenna’s inductance LANT and resistance RANT are known. It is recommended to measure LANT and RANT with impedance analyser. If the estimation is made using the formula to calculate to values, please note that these values are only starting values to calculate the Q-factor.
The antenna’s quality factor is an important characteristic for the correct tuning of the antenna and the achievable performance. The quality factor of the antenna defined as:

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Depending on the geometrical design of the antenna Q usually is in the range of 50…100, in the following it is shown that this value has to be reduced for a proper data transmission. As mentioned in chapter 2.3.2 the baudrate of MIFARE® is 105.9 kHz/sec and the data transmitted from the RWD to the card are Miller-coded with a pulse length of T=3µs.
Using the definition for the bandwidth B

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And definition for the time – bandwidth product  B × T ≥ 1

The required Q- factor can be calculated as Mifare DESFire EV1 2K Pre-printed cards,NXP MF3ICD21 Cards,HF 13.56MHz Mifare DESFire 2K Contactless Cards.

Due to tolerances of the components it is recommended to use a value of 35 for the Q-factor. It is required to reduce the Q-factor using an additional external resistance REXT. Figure 3-10 shows how to connect the external resistance REXT.

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Calculation of the Capacitors for the Matching Circuit
Figure 3-11 shows the recommended circuit to match the antenna coil to 50 Ω. The matching is done using a serial and parallel capacitance. The input resistance Z should match to 50 Ω.

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CS and CP should be SMD types with NP0 dielectricum for best temperature stability. It is recommended to split up CP in a fixed value and a trimmer (C’p) with a maximum value of 10… 20 pF.