# External circuit to increase the series capacitance of a resonant circuit

I am working with a long-range reader and antenna coil for a low frequency (135 kHz) RFID application (please see the basic representation below.) The reader features some unknown source impedance, as well as a series variable capacitor forming the tuned LC resonance circuit with the antenna coil. The variable capacitor has a range of values which can be used to tune to resonance for a coil with given inductance.

Simple model of the Reader and Antenna coil. External circuitry is a placeholder to represent the potential solution to the issue and is not actually present in the circuit currently:

My question occurs when the antenna loop inductance is out of range for the capacitor to resonate at the desired frequency. For example, let's say the inductance is a very low value, requiring a higher capacitance than the reader can supply. Obviously, the answer would be to increase capacitance, one must place a capacitor in parallel so the capacitances sum. What happens when I don't have access to the reader? (That is, I cannot reliably bypass the variable capacitor with one of my own). If I place a capacitor in series, the total capacitance will be reduced so I am stuck on how/if it's possible to extend the range of loops with various inductance values. I also need to ensure that the solution is able to drive the antenna at a high enough current. Is there something I can put in-between the antenna coil and the reader (denoted "EXTERNAL CIRCUITRY" as a placeholder in the shown schematic) that can achieve something like this? Perhaps a high impedance buffer of some sort (without sacrificing too much drive current?)

Any ideas?

• Do you have control over the loop antenna? Can you add an extra turn or turns to the loop antenna? That will increase its inductance while keeping its dimensions small. Commented Jan 17 at 17:28
• You are absolutely right that adding loops is an option! I can add loops generally, however, in one instance I was using a 6 AWG wire that would be impractical to loop more than a couple times due to cost, footprint of the large wire, etc. I am more asking this question for additional suggestions and circuits I can use in the case that loops are not able to be easily added to the antenna and increase the inductance. Commented Jan 17 at 17:40

Since this is an impedance matching problem, the ideal solution is an impedance matching transformer.

For example, if you use a 2:1 transformer, the impedance and therefore inductance seen by the reader will increase by a factor of 4 (turns ratio squared). The drive voltage available to the antenna will halve, and the drive current will double, which is exactly what you need for a low-inductance antenna coil.

simulate this circuit – Schematic created using CircuitLab

The transformer should be able to handle high frequency signals at low loss, so you'll need to use a ferrite core. An ungapped RM-type core is likely a good bet, for example RM12. You can get complete transformer assembly kits for these cores from TDK (consisting of the core halves, a coil former, insulating washers, and clamps to hold the assembly together).

You'll of course have to compute the properties of the transformer so that it can handle the involved signal voltages and frequencies, for which I recommend using this online transformer calculator. You'll also need to ensure that the magnetizing inductance of the transformer's secondary is much larger than the inductance of the antenna coil (i.e. by at least a factor of 10).

By varying the turns ratio, you can do (almost) arbitrary impedance transformations.

• Wow! Thanks for the great information! I'm a little bit unfamiliar with transformers and their effect on input/output impedance in a circuit, especially in RF. Do you have any resources/articles on this by chance that you can share? Commented Jan 17 at 17:36
• @tomhebe 135kHz luckily isn't quite RF yet - at these frequencies, a properly-built signal transformer will still behave almost exactly like an ideal one. Here's a derivation of why impedance is transformed: electronics.stackexchange.com/a/587424 And the Wikipedia article also goes into a lot of depth: en.wikipedia.org/wiki/Transformer (Most of the non-ideal stuff shouldn't be particularly relevant to your application.) Commented Jan 17 at 18:42
• Thanks again! I am curious if you would suggest a similar approach when the impedance adjustment needed is very slight? For example, if multiplexing multiple antennas and some feeds are longer than others causing a small increase to their inductance and detuning them from resonance. These antennas would have slightly worse performance than the antennas with the shorter feed length presumably. Would you also suggest a transformer for this type of design problem, or some other topology? Commented Jan 18 at 17:47
• @tomhebe In this case you'd choose the impedance of the antennas in such a way that it's within the range that the RFID chip can compensate for by tuning its internal series capacitor. Alternatively, you could add small inductors in series with the antennas that have shorter cables. Commented Jan 18 at 19:06