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The challenge in enabling a device to communicate via NFC lies in the filter and matching network for the NFC antenna. Part 1 of this article introduced the theory of complex conjugate impedance matching. This part focuses on the application of impedance matching to an NFC output circuit. A combined wireless power/NFC coil from Würth Elektronik is chosen as an example.

Let’s begin with the structure of a typical NFC output circuit. An NFC IC usually has a differential output and an impedance of 50 Ω between the output pins TX_{1} and TX_{2}. These pins are connected to a circuit consisting of a filter network, a matching circuit, attenuation resistors and an NFC antenna. The output of the NFC IC is differential to provide resistance to electromagnetic interference. A typical differential NFC output circuit is shown in **Figure 4**.

To simplify the understanding of the NFC output circuit components, the differential circuit can be converted into a single-ended circuit. **Equations (8)** and **(9) **can be applied to calculate the matching capacitors C_{A} and C_{B}. The transformation calculations are performed as in reference 6 (see bottom of the page) and the resulting single-ended circuit is shown in **Figure 5**.

**EMC filter circuit**

Since the output signal of the NFC IC has a rectangular shape, the harmonics must be filtered out. This is performed by the EMC filter network, which forms a second-order low-pass filter. The low-pass filter consists of the inductance L_{0} and the capacitance C_{0}. The cut-off frequency f_{C} of the EMC filter can be calculated with **equation (10)**.

The cut-off frequency f_{C} must be higher than the upper subcarrier, which for the highest possible NFC data rate (848 kbit/s) is 13.56 MHz + 848 kHz = 14.4 MHz. To illustrate the necessity of the filter, **Figure 6** shows an NFC load modulation spectrum with carrier and subcarriers.

In order to perform impedance matching, the impedance of the filter must be calculated using **equation (11)**.

**Impedance matching network**

The matching circuit, also called an impedance matching network, as shown in **Figures 5 **&** 6** (part 1), has two tasks. The first is to compensate for the inductive impedance of the antenna. The second is to implement the impedance transformation from the load impedance to the source impedance. For a loss-free transformation, all components should be reactive elements. In a cost-critical and space-critical environment such as in NFC circuits, it is desirable to keep the number of components to a minimum, so an L-matching topology should be used.

**Attenuation resistors and equivalent antenna circuitry**

The damping resistor R_{q} is an optional resistor that can be used to reduce the Q-factor of the antenna. Choosing the optimum value for R_{q} is a compromise. On the one hand, a small value increases the antenna efficiency of contactless power transmission; on the other hand, a high resistor value provides a higher bandwidth for modulation and reduces the antenna Q factor. The recommended range of values for the Q-factor is between 20 and 35^{8}. The resistor R_{q} should be used when the antenna Q-factor, which can be calculated using **equation (4)** (part 1), exceeds 35. If the value is higher, **equation (4)** (part 1) must be modified using **equation (12)**.^{5}

This results in the following formula for calculating the damping resistance value R_{q} (for Q_{L,mod} ≥ 35):

The last part of the output network is the equivalent antenna circuit described in part 1 of this series. This network was used for the simulations and calculations of the load impedance.

**Determination of the equivalent antenna circuit**

For the NFC antenna WE-WPCC WPT/NFC (item 760308101312), the following parameters were determined by measurement and calculation:

The values for L_{a} and R_{a} were measured at the intended operating frequency of 13.56 MHz.

**Determination of the complex impedance and the Q factor**

The complex impedance Z_{L} of the NFC antenna of article WE-WPCC WPT/NFC (760308101312) is calculated with **equation (3)** (part 1) by inserting the parameters of the equivalent antenna circuit determined in the previous section, resulting in the following complex impedance value:

Based on **equation (4) **(part 1)**,** this leads to a Q_{L} of 33. Since the Q-factor of the antenna is less than 35, the damping resistors R_{q} can be omitted.

**Calculation of the filter components and the complex impedance of the filter circuit**

For the cut-off frequency f_{C}, which can be calculated with **equation (10)**, a value of 14.8 MHz was chosen, which is higher than 14.4 MHz. For L_{0}, an inductance value of 470 nH is chosen, resulting in a C_{0} of 247 pF. The values L_{0} and C_{0} must be substituted into **equation (11)** to calculate the complex filter impedance. For R_{D}, the value of 25 Ω is inserted, which is the differential output impedance of a typical NFC IC with respect to the ground signal.

These values result in the following complex filter impedance:

**Calculation of the values of the matching components**

The matching reactances X_{B} and X_{A} can be calculated directly with **equations (8)** and **(9)**. For R_{S}, the real part of the EMC network must be used, which is 165.82 Ω. For the imaginary part of the source reactance X_{S}, the imaginary part of the EMC filter must be used, which is -45.46 Ω. For R_{L} and X_{L}, the real and imaginary parts of the antenna network must be integrated, namely 1.87 Ω and 62.53 Ω. The resulting matching reactances X_{A} and X_{B} can be converted into the corresponding differential matching capacitors C_{A} and C_{B} as follows:

**Table 3** gives an overview of the resulting reactance and capacity values.

The capacitor values for C_{A1} and C_{B1} are used for the matching; the values for C_{A2} and C_{B2} are neglected because C_{A2} gives a negative value. This results in the matching capacitors for the differential output circuit to:

**Calculation of the resulting input reflection factor**

To check whether the calculated matching capacitor values C_{A} and C_{B} result in a low reflection, the parameter S11 must be calculated at the output of the NFC IC. The smaller the absolute values, the lower the reflection and the better the circuit is matched to the 50 Ω output impedance of the NFC IC.

The complex input reflection factor S11 can be calculated with **formula (15)**.

where R_{D} = 25 Ω, which corresponds to the single-ended output impedance of the NFC IC. The parameter Z_{in}‘ depends on the input impedance Z_{in} (see **equation (5)**) and can be calculated with **formula (16)**.

The amount of S_{11} can be calculated with:

In high frequency technology, |S_{11}| is often given in a logarithmic scale and can be calculated as follows:

The resulting values of **equations (5)** and **(15)**–**(18)** are shown in **Table 4**.

The calculations are carried out with ideal components, without taking parasitic influences and tolerance influences into account. However, in reality the capacitors and inductors have tolerances and parasitic inductances and capacitances. Often, these parasitic values are used as part of the matching/filter network. In addition, the components of the antenna’s equivalent circuit are measured and therefore not precise, so they also have tolerances. Besides geometric and chemical variations caused by the manufacturing process, there are also unknown parameters of the surroundings or additionally attached ferrite foils for shielding. Any metal in the vicinity of the antenna can change the impedance of the antenna and therefore also the total input impedance. How much these variations affect the input impedance depends mainly on the value of the input impedance and the quality factor. In general, lower quality factors and higher values of input impedance are less sensitive to a variation in component values.^{5} Given these variations, additional iteration of the adjustment is necessary.

**Conclusion**

It has been described how a WE NFC antenna can be matched to an NFC IC. The determination of the matching capacitor values was calculated and the measurement and necessary matching of the input impedance to the source impedance was shown.

The basics of complex impedance matching theory were presented in the first part of the article and typical L-matching topologies were described. Matching reactances and the determination of the Q-factor were calculated. The different parts of the differential output network were analyzed, and the individual components of the filter and the equivalent antenna components were dimensioned.

**References**

1. C. Bowick: RF Circuit Design, 2nd Revised edition, Newnes, 2007.

2. K. Cartwright, Non-Calculus Derivation of the Maximum Power Transfer Theorem, Technology Interface, 8 (2), 2008.

3. M. Roland: Automatic Impedance Matching for 13.56MHz NFC Antennas, 6th International Symposium on Communication Systems, Networks and Digital Signal Processing, 2008.

4. Würth Elektronik eiSos: ANP057a, WE-MCA Multilayer Chip Antenna Placement & Matching, Application Note, 2018.

5. T. Baier: Automated Impedance Adjustment of 13.56MHz NFC Reader Antennas, Master Thesis, 2014.

6. A. Schober, M. Ciacci, and M. Gebhart: An NFC Air Interface coupling model for Contactless System Performance estimation, International Conference on Telecommunications (ConTEL), June 2013.

7. Rohde und Schwarz: Near Field Communication (NFC) Technology and Measurements, White Paper, 2011.

8. NXP Corporation: AN11564, Antenna Design and Matching Guide, Application Note, 2016.

*This article was originally published on **EE Times Europe**.*