# Optimal antenna configuration for edge-on power transfer

I need to build a MHz antenna that can power an RFID chip that responds to mag field perpendicular to the plane of a loop antenna, e.g, using STL transmitter with a small receiver loop in same plane as the transmitter. I'm confused about the benefit of extra turns on the transmitter.

For a given a loop with area $$A$$ and perimeter $$C$$ then I can estimate a radiation resistance per unit area (for one coil) $$R_{r0}$$ and radiation loss per unit circumference, $$R_{l0}$$. Assume that I have a capacitor to cancel out inductance at resonance, then I only need to worry about total resistance which seems likely to be $$R_{r0} A^2 N^2 + R_{l0} C N$$. Regardless of efficiency, then $$P_{in} = I^2 R_{total}$$ i.e. $$I^2 N^2 A^2 (R_{r0} +R_{l0}*C/A^2/N)$$. I think the mag field in the plane parallel to the loop is (for small transmitter loop) $$-\beta^2 I N A \exp(j \beta r)/r$$.

Putting that all together says that for fixed $$P_{in}$$ then assuming that I can always impedance match then I should try to minimize $$R_{r0} + R_{l0} C/A^2 / N$$. I.e. increase as many turns as I can and prefer circles to decrease $$C$$ relative to $$A$$.

And then with regard impedance matching, if I can crank up $$N$$ then I can make $$R_{total}$$ equal to 50 ohms, or whatever I want.

So why do STL's usually have just one or two loops?! Or did I make a mistake in the math...

One potential mistake that I see is that I do need $$NC$$ to be less than $$\lambda /3$$. So for a circle set $$N = \lambda /3/(2 \pi r)$$ and then minimize $$R_{r0}+R_{l0} 12 \pi^2 r^2 / \pi^2 / r^4 / \lambda$$.

Ah... so you set $$N=1$$ to make $$r$$ as big as possible. Did I get it right?

But if $$r$$ is constrained for some reason then you should increase $$N$$ until $$NC = \lambda / 3$$. Yes?

• What's STL? Are you sure the ham radio Stackexchange site is really where you wanted to post this? General questions about radio technology are on topic here, but RFID really really stretches the term "general" a bit. Commented Nov 26, 2023 at 2:57
• Small Transmitting Loop, Marcus. Commented Nov 26, 2023 at 4:21
• Hi Marcus, I'm struggling with building a magnetic loop antenna and figured that the team here has built many such devices successfully. I can't even get mine to work with a software simulation, which got me intrigued/confused about how those things work in the first place. And I haven't even placed an order for my first butterfly capacitor yet! :-) Commented Nov 26, 2023 at 5:45

I've designed and optimized an HF tag reader antrnna, and done plenty of reading about small loops. To tackle just your final question:

The number of turns in a loop, the resonating capacitor, and the feed arrangement are merely items of convenience for the builder. You are free to use any arrangement that results in a current flowing around a circle; multiple turns of wire is one such arrangement.

It turns out that for one particular use case, HF radio communications, given the limitations of electrical conductivity, capacitor losses, transformer losses etc, one particularly efficient arrangement is to have a single turn loop, as fat as possible, in series with a very low loss capacitor. This is easily and cheaply matched to 50 ohms by exciting it with a small loop inside it or nearby. To use the same amount of metal to form multiple turns would make the loop less efficient, because practical capacitors are far, far lower loss than conductors or inductors.

There are many small transmitting loop calculators online, some quite sophisticated, you can try out various permutations there.

In the case of tag reader antennas, (which are also optimized for transmit efficiency) there are some other pressures which dominate. First, is that a reasonably large bandwidth is required to allow modulation of the transmitted and received signal; if the antenna is too efficient this requires resistors in the matching network! Also, it is highly preferred to print the antenna on a circuit board rather than make it out of a metal tube. Finally, they usually have to operate in the presents of a metal back plate, maybe with a ferrite shield, which further reduces their efficiency. These factors drive an HF tag reader to be a multiple turn printed circuit board loop, resonated with some capacitors and resistors, connected directly to the 50 ohm or 110 ohm cable, possibly by a capacitive divider.

I think you will find for tag readers that bandwidth is the the hardest requirement. Even radio hams ran into the bandwidth problem eventually, if a loop is made large and fat enough.

• Yeh, but as I stare at the math above, if it is correct, then I think a design approach would be to first make the loop as big as you can in the space available, and then crank up the number of turns if, and only if, the perimeter is not reaching something bigger than 0.3 lambda, or so. After which point the turns will all start cancelling each other out. I'm happy with one turn. I was distracted by the "I * N * A" in the transmitted field. I am looking into PCB's and copper tubes. No decision on that yet. Commented Nov 26, 2023 at 7:01