# Antenna Matching

The process of antenna matching is essential for optimal application design and RF performance. In receive mode, the antenna is the part of the circuit that collects the signal from the environment and converts the electromagnetic energy back into voltage and current. The signals are very weak, and keeping the best signal quality is mandatory as minor losses could damage the signal. Therefore, the losses in the transformation must be kept as low as possible. In transmission mode, the antenna is the part of the circuit that converts the available current and voltage into an electromagnetic wave. As the radiated energy directly influences the achievable distance, the maximum energy must be available at the antenna to get the maximum range.

For these two reasons, it is necessary to have a suitable and optimized matching to the available source impedance. Some antennas have a system impedance of 50Ω and do not require additional matching. Consider the parasitic from the board based on the design.

The matching of a monopole antenna is very similar to the matching of an LNA. The impedance can be measured with the NWA and transformed step by step to the required system impedance.

The matching of a printed magnetic loop antenna must be done with a network analyzer as matching calculation becomes very difficult due to parasitic influences from the PCB and the components consideration. As the parasitics might be unknown, the network analyzer is the best option. The magnetic loop antenna is the cheapest solution for antenna design, as it is just a trace on the Printed Circuit Board (PCB) matched with two components. An example of such a PCB design is shown in the following figure.

Figure 1. Magnetic Loop Antenna Example

The typical loop antenna design in automotive applications uses capacitors to reduce the bandwidth of the system. In that case, the capacitor at the end of the loop generates a resonant circuit. Calculate the resonant frequency using the following equation:

Figure 2. Resonant Frequency of an LC Network
fr=12π*LC
Figure 3. Loop Antenna Inductance Calculation
L=μ2π*l*ln(8AlW)

Use the given inductor value to calculate the required capacitor value using Figure 3 and Figure 2. The Antenna trace on the reference application design has a calculated inductance of 50 nH. Assuming a target resonance, the capacitor value is calculated as 2.7 pF for a frequency of 434 MHz. The following figure shows the measured impedance with the calculated component value. The measured resonance frequency is at 428.5 MHz (marker 2).

Figure 4. Loop Antenna Resonance Frequency of the LC Network

Note: S11 does not give any qualitative information at this stage as the impedance at the resonance frequency is too small. This condition is not according to the maximum power transfer theorem; therefore, S11 returns almost no return loss.

In the next step, the resonance frequency must be transformed to the target system impedance of 50Ω. According the guidelines from Smith Chart, this is done with a shunt capacitor. As the shunt capacitor can also influence the whole frequency behavior of the resonant circuit, a calculation of the second capacitor becomes difficult. It is possible to use simulation tools to estimate the transformation. If such tools cannot be used, a good starting point for the value of the capacitors at the input of the loop antenna is 10 x Cout (10 times the value used for the other capacitor). For this example, the capacitor is 27 pF and the result is shown in the following plot.

Figure 5. Loop Antenna Matching 27 pF

This capacitor value transforms the formerly imaginary value to the complex impedance. As the value is still far from the target impedance, the capacitor's value must be increased further according to the guidance from Smith Chart.

Figure 6. Loop Antenna Matching 33 pF

Figure 7. Loop Antenna Matching S11 33 pF

As shown in Figure 6 and Figure 7, the real part of the impedance is further increased and the S11 is already at ~-6 dB, which means 75% of the energy is already used. With a further increase in the capacitor value, a further improvement is possible as shown in the following figure.

Figure 8. Loop Antenna Matching 39pF

Figure 9. Loop Antenna Matching S11 39 pF

With this almost real impedance, 99.4% of the energy is routed through the circuit and any further increase deteriorates the result. Even a change of the capacitor at the end of the loop antenna changes the primary resonance frequency that affects the performance too.

Note: The antennas are susceptible to environmental effects. Metal or other materials close to the loop can influence the resonance frequency; thus, special care must be taken regarding the environment during the matching.