Matching network for small loop antenna
I have designed a electrically small square antenna on a piece of 0.8mm FR4 substrate (not great for this application I know) operating at 2.4 Ghz. The antennas circumference is 40mm (1/20 of 0.125 wavelength to get the radius then multiplied by 2pi to get the circumference). The antenna has a gap which acts as a capacitance to form a RLC circuit to achieve resonance so the imaginary part of the impedance is zero. The required goal is to make two and use them as near field antennas and then measure the distances that can be achieved. As expected the radiation resistance and ohmic resistance are very low, about 2 ohms give or take but still very low. I want to match the antenna to a 50 ohm line and have tried quarter wavelength transformers and single stub matching to try to achieve this but the dimensions i need for these methods seem huge for the overall size of the antenna. I have thought about using another small loop to couple the antennas together for the matching. Any other ideas or help would be appreciated.
Many Thanks
You can excite the 0.125lambda loop with another loop (as you mentioned). You may ground the middle of the loop and use a tap on the loop (delta match).
Other option is to open the loop in the middle, connect one end to ground and one end to ground via a capacitor. You can feed across the capacitor. From a simple lumped circuit approach, the ratio of capacitance between the open ends and the capacitor inserted, determines the impedance transformation.
If the Q-factor of the resonator is good, both delta match and capacitor in the middle does introduce only minor common mode current. You may know that it is good to keep common mode excitation low as this increases far field radiation.
Thanks for the quick reply, much appreciated.
I will try out your suggestions on my loop, have you got any good materials or thoughts on the mathematics involved (Capacitor values, Delta match lengths, etc) or shall I just google it and see what i can find?
Thanks again
As a first guess you can assume the current uniformally distributed along the loop wire. Use the radiation resistance formula for small loop antennas. As you tune it via the capacitance between the "high voltage" ends of the loop, a source in series with the loop will see this resistance (so it is a real value). In reality the impedance will be higher as your loop is not very short w.r.t. lambda, so current distribution will not be uniform, hence more far field radiation is produces.
Just let us assume a value of 5 Ohms. So when you interrupt the loop in the middle and put a source, its sees (for example) 5 Ohms. When feeding in the middle, the common mode voltage is lowest. You can use a standard L network to transform this to 50 Ohms at 2.45 GHz. Values will be in the range of 1 nH (series component), 4 pF (parallel to 50 Ohms source component).
So your 50 Ohms source will look into 4 pF (parallel) and a series L of 1 nH, this all in series with 5 Ohms radiation resistance. The capacitor can be just an SMD component. The inductor you make by increasing the capacitance between the high voltage ends a bit, this results in an inductive component in series with 5 Ohms. This has the same effect as making the loop somewhat longer to get 1 nH increase in inductance.
The other methods (inductive coupling and delta match) are mathematically very elaborate as you may to guess coupling coefficients via some very approximate calculations. I used both methods, but mostly I make a guess from experience, look to the S11 curve and based on that I know what to do.
You can reduce the far field radiation by dividing the tuning capacitance (end capacitance) over two opposite places. This makes the current distribution more uniform. I used this method in many inductive applications. It is also used in MRI antennas.
P.s. I actually want as little far field radiation as possible (always going to get some), that's why I chose the small loop design because of its low radiation resistance. I am designing a near field antenna so I just want the antenna to radiate in the reactive near field. I understand if two antennas are resonant at the same frequency then the magnetic/inductive coupling between these antennas will be very strong.
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Brilliant, thanks for your time. I will give it a go on the simulator and post my results.
For a visual presentation, best is to put your antenna into a simulator, feed it via localized port and view the current distribution. You will see that current near the ends is less then in the middle. So the current in the middle of the loop is not counteracted by the current on the opposite side of the loop.
When you distribute the tuning capacitance along the loop, the current distribution will be more even. Vicinity of a ground plane may also change the far field radiation. You may even feed your loop at the edge of a ground plane where the ground plane is one side of the loop.
I'm back, I went with a simple L matching network in the the end using an inductor in parallel and a capacitor in series at the input. I didnt wanna spend anymore time on the matching network really so just went with a lazy option. Would be very hard to manufacture because of values, tolerances and the bandwidth is terrible. But thats fine, wont be building it anyway now. Thanks for all your help!
So you matched to the one of the open ends? If so how did you handle common mode issues (as you want to reduce far field radiation)?