# Maximum tolerance for a loop trace-antenna's capacitor

While going through the document at https://www.silabs.com/documents/public/application-notes/AN639.pdf I have read from "Figure 13. Loop Antenna Simulated Mag(Zin) vs. CP1" below that even a 2% tolerance for Cp1 results in a Zin of about 200 - 250 Ohm for the 434 MHz frequency range that I am heading for. The desired Zin is 500 Ohm.

I am not sure if this is the case but as I understand it this will cause a good fraction of the power to be reflected back into the IC. If so, could I have a maximum tolerance level for Cp1 so that my transmitter will not require full power in order to cover a mere few meters ? (in ohter words, for my transmitter not to perform poorly)

• anytime Q=350, component tolerance on f and Zin is going to be very tight. as it is inverse to the Q. Dont forget dielectric tolerance of 10% ... go for the 55mm square and 15dB return loss and work out the tolerances. Otherwise, just use a 1/4 lambda wire. which will work for that range and tune length Commented Aug 9, 2017 at 1:34
• @TonyStewart.EEsince'75 Ok, is the dielectric with the 10% tolerance the PCB's dielectric ? If it is, isn't most of the electrical field radiated by this antenna formed between its two sides of the loop, so air would be the dielectric ? What is a '55 mm square' ? Commented Aug 9, 2017 at 10:34
• FR4 is inside the loop and this also affects self resonant freq. with e~4 +-10% . Datasheet shows dBi gain is max for 55mm square loop -3dBi ? as I recall, which is an indication of losses. Coupling to free space impedance affects far field levels with air as a diectric. The velocity factor for tuning L of V.F. 0.82 is prrof of this interaction. Commented Aug 9, 2017 at 14:25
• Don't expect to find a standard-size capacitor to tune this structure without having to add some PCB trim capacitance. As the app-note (and Tony) imply: calculate, build, measure....probably will take more than a few iterations. Commented Aug 9, 2017 at 14:41
• Okay, thanks you both,but I am not going to go through all the theory and test iterations. I shall stick with the given design which has all been set up optimally. My question was related to that final tuning cap Cp1. Let me rephrase it: How much power will I lose if instead the optimum 500 Ohm impedance I ended up with a 250 Ohm impedance ? How would I calculate that ? Commented Aug 9, 2017 at 15:29

Here a 55mm square loop gives the highest gain using 0.8mm FR4

Reducing area 50% correlates with ~3dB loss each time from this.

The author's calculation of v.f.= 0.82c is an indication of FR4 dielectric effects on wavelength and C values required.

Contrary to what the author says, the shunt capacitance controls a parallel resonant pole and not the series zero.

Here is my simulation.

You can play with the values and aim at peak to get a reading. Note how phase changes abruptly at series resonance.

THe 1 Ohm ground shunt measures current and the Out before the cap measure transfer function while moving out to the 1 Ohm measures Zin. Q here is about 320 or 42.73dB gain limited by Series ESR and sense R ratio as well as X(f) for a crude approximation... set to 434 MHz.

Here showing the effects of a shunt C with a notch in radiated power by parallel resonance which comes closer to series f with larger C values.