# Optimizing HF (13.56 MHz) RFID reader antenna for the smallest RFID tag

I want to use currently the smallest (3.2x3.2 mm2) HF RFID tag from Murata LXMS33HCNK-171 together with RFID reader based on MFRC522 RFID frontend from NXP. In my application, the maximal distance between the tag and the reader antenna is max. 6mm and they are always in parallel planes, where tag can always be "inside" the reader's coil. For designing this I follow application notes from NXP mostly for antenna tuning guidelines, but I also follow AN710 from Microchip, where the theory is very well described.

The equation 7 derives the mutual inductance between the reader's and tag's antennas as:

where a and b are reader's and tag's coil diameters respectively. r is the distance between the coils. Later they show that the optimal reader's coil diameter is $$\a=\sqrt{2}r\$$. From this, it can be assumed that the bigger the radius of the tag's coil the higher M. So, for the fixed distance between the coils and the Ampere-turns, the only way to increase the mutual inductance would be to increase the size of the tag's coil.

What I am trying to understand is how the ratio of both coil's sizes influence for example near-field coupling and signal backscattering. For example, if the reader's antenna is much bigger than the antenna of the tag, is it true that the tag's antenna will not have so much influence on the reader's antenna? In other words, should reader's and tag's antennas be of nearly the same sizes?

Yes, the coupling of two RFID coils is best when the coils have the same sizes. But coupling is not everything when tryping to maximize the reading distance.

Basically you have two things to consider: The RFID reader antenna has to generate enough field intensity at a given point in space (typically H_min=1.5 A/m) to power the tag and second, the tag antenna has to generate enough load for the receiver part of the RFID reader to "hear" the tag (load modulation).

A small RFID reader antennas generates more field intensity in its center, but this increased intensity drops faster with increased distance compared to a big RFID reader antenna. So a given tag might work well with a small RFID antenna at very low distance, whereas it would not work at all with a big antenna.

So for a given tag, there exists an optimal RFID reader antenna size.

You can use a field simulator (like FEMM) to find the best reader antenna radius with max. H-field intensity at max. distance for your tag. But you still have the issue of load modulation to consider.

• But how to choose the correct reader's coild size? The inductance of the planar rectangular inductor reduces with size, which means also the magnetic field (taking the current constant). So if I reduce my coil, the field will be weaker, although the current should be higher so I am a bit confused here. Feb 3, 2020 at 8:19
• No, you are wrong. Although the inductance decreases with coil size, the magnetic field intensity does not. And less winding distance means more current, not the same. This is a rather complicated optimization task. In the end, you might want to try and test different configurations. Feb 3, 2020 at 10:46
• WHat I wanted to say is that with the same amount of current the lower inductance will produce the weaker magnetic field compared to the higher inductance coil. Although it is not relevant cause we are not exciting those coils with the current source. Feb 5, 2020 at 8:29

From this, it can be assumed that the bigger the radius of the tag's coil the higher M.

No, because we're talking about mutual inductance and, what’s good for one coil applies to the other so, if the optimal coil diameter is $$\r\sqrt2\$$ for one coil then that applies to the other coil too.

In other words, should reader's and tag's antennas be of nearly the same sizes?

Yes they should. Increasing the number of turns helps too.