TRF7970A Antenna Matching Quality Factor with sloa135a

Eric/Ralph

the steps are the following, please don't overlook the details: 

first you need the j + XL of the coil , then tune the resonant circuit, applying the Q killer (shunt resistor) to get correct Q (of the entire circuit!)

the resulting smith chart is:

additional note, this is a higher Q,  longer range applications, with tags that use single sideband of 424kHz  this is OK in some cases

for the tags which use 848kHz sideband response, the Q should be lower, this is still valid and in that case, using the same coil, it would look something like this

Eric -
i used 1Ohm here just for demo purposes, you are correct that normally a coil would be milliOhms (real), but this is another "fine adjust knob" to turn if you need it. (i.e. use thicker wire or traces for lower R to start, thinner for higher R to start) this technique is also more commonly used in inlay style tags, where you cannot afford to put a Q killer resistor, because they are commodities that have all the cost taken out of them that is possible, plus they are expected to be flat, flexible and possibly pass a mailing test.

you should always measure your coil first with network analyzer or even a low cost device which is operating at your center frequency (for example an MFJ-259C, or similar), then use the accurate measurement to then either calculate or use Smith Chart tool to get right down to close to what you need for components.