quixotron

Hi guys, I tried posting this in the other forums but a screen comes up saying I don't have the privleges or the admins blocked me or something.

So:

I am working on a UHF small loop antenna. I want to model it as its equivalent square loop antenna. Note: I am working on a small inductively coupled loop, not those huge 3 m loops for radio operators and DXing.

The book I am using is Antenna Theory: Analysis and Design 3rd Edition by Constantin Balanis, great book. Also Antennas by John D. Krause

1: How do I know it qualifies as a small loop?
Balanis gives the stipulation that the radius of the circular loop must be less than lambda/(6*pi) which in my case it is.

2: what is the geometry of my antenna?

It consists of a small circular loop on a dielectric board (I think its FR-4) the antenna is not solid wire, it consists of conductive pcb trace, probably etched copper or conductive ink. The circular trace is then connected to two additional traces ending in a female sma connector. There is no ground, the traces connect to the hot wire and negative terminal of the sma to complete the circuit.
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3. Now to model both designs. I need to compute the external inductance of the loops. I can find these on an impedance analyzer and compute it, which I did for the circular loop. I want to solve for the inductance analytically, and subsequently I can modify my loop geometries/change dimensions for the square.

Note: internal inductance is neglected.

Balanis gives two equations that approximate the inductance values.

La=unot*a *[(ln (8*a/b))-2] eqn 5-37a // circular loop

a=radius of loop
b=radius of wire, in my case width/2 of trace.

I found this circular indutance, equated it to the square loop inductance formula and I extracted the parameters so I can build a square loop of the same inductance.

La=2*unot*a/pi *[ln (a/b)-0.774] // square loop

4. Now this handles the values for the antenna. The races that connectto the sma and the loop have their own inductances and contribute to the overall inductance. I need to find that.

Originally, I thought I could model it as another circular loop, given the length of the traces. I found the perimeter/circumference and then found the radius. I computed the inductance of the traces as a circular loop. As a first order approximation it wasnt too bad becoz the sum of the circular loop plus the traces =X nH. My exerimental value for the loop was Y nH on the analyzer. A percent error of 10.5% not bad for a rough guess.

However, I decided to be more scientific in my approach, so i tried to model the traces as two parallel wires. In Microwave Engineering 3rd edition, Pozar stated:

L= mu/pi * cosh^-1 (D/2A)

D is the separation distance between the wires center
A is the radius of the wire.

I have traces so I used the halfwidths as the radii, respectively. However, the results were way too large. So I have to model the traces as something else.

I read that some EMC books used flux calculations to derive the inductance values, but that is a bit tedious in computation time. There is also some 3-D model answers, but I just need a fairly accurate approximation.

5. My question is: Has anyone done work similar in this area, and if so could one provide some reference texts or articles or something to assist me? I like my first order guess. I'll go with that just to run a rough em simulation.

Am I leaving out some details? Yes. I would not like to divulge them if neecessary. I'd like to just discuss the physics.

If anyone can help me, I'd be most apprecitive.

Thanks.

RadioRon

The demarcation between "small" and "not small" can be a bit fuzzy, but many use one tenth wavelength circumferance as a rule of thumb but if your radius is as you say, your circumferance is approx one third wavelength. Unfortunately, I don't think this qualifies as a small loop for simplification and analysis purposes. The general idea behind defining a small loop is that the voltage and current distribution is roughly constant throughout the loop, but at one third wavelength this will not be true.

Yes, that is pathetic but at least you put in a bit of effort. A photo would be considerably more useful. I get the impression that the original designer meant for the parallel traces to be a balanced transmission line. The loop itself is a balanced structure, so this makes sense. Putting an SMA at the end of it without a balun doesn't make sense. Is the SMA your idea or was it already on there? In light of this, perhaps you could model the parallel wire part as a transmission line and model the loop separately. It would be interesting to learn if the length of the parallel wires is tuned so as to affect impedance matching to the loop. This may be the case. If you can determine the impedance of the loop, the rest will become apparent using a simple linear circuit simulator or a few minutes with a Smith Chart.

When you say "both designs" it isn't clear what you mean, so I presume you mean the actual circular loop and the square loop approximation that you would prefer to work with. By the way, what is the reason you prefer the square loop? Unfortunately, I haven't done any analytical look at loops for a long long time so cannot comment on your math. However, as your loop is large enough, you may also simulate it with some confidence in the results. My experience is that 3D and MOM EM simulators have difficulty with small loops, but one of your size may be OK. I recommend a quick trial with EZNEC+ which is a MOM simulator that is easy to use and quick (and very inexpensive when compared to the big name 3D EM simulators) and then compare to your measured values for the circular loop. Beware that there are many pitfalls in measurement though. For example, you would need to make the measurement at the feedpoint of the loop, not at the ends of those parallel lines, or you have to back out the effect of that parallel transmission line from your measurement (which you could easily do by rotating phase as the line will be relatively lossless).

Again, my math is too old, but I endorse the idea of modelling these lines as a balanced transmission line of classic two wire form. Typically, when I work with transmission lines, I don't pay as much attention to the inductance and capacitance of the line but more to the characteristic impedance and the length of the line. These are the parameters that will quickly tell you how the line is affecting your impedance.

I do have some friends who have done detailed work on small loops in the last year and could perhaps put you in touch if needed. Their experience will translate well to larger loops such as yours and they also would have looked at it analytically I think. Personally, as a working engineer I typically only review the analytical approach for a quick approximation and then move to either measurement, simulation or both. And beware the results of either as there are many pitfalls. PM if further interest.

Extra note: I start all antenna reviews with "Antenna Engineering Handbook" edited by Richard C. Johnson (older versions edited by Jasik), Mcgraw-Hill. This is a compendium of papers but very well edited to provide a broad coverage of practical antenna forms backed up with basic theory. A decent starting point for many antenna questions.

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RadioRon

quixotron

Right, in HF-lower UHF band the currents in a loop antenna undergo phase shifting and usually require a compensation device to bring the currents back into phase. My loop antenna operates in the upper uhf band(800-1000Mhz) My radius is less than 15 mm. So my loop qualifies as a small loop antenna. Sorry for being a bit stingy on roviding additional information.


1: You have to forgive me for not putting up a picture of the item itself. The net doesnt have small pictures of uhf loops readily available. I will say that the circular loop is a tapped capacitor loop antenna. The capacitors shift the bandwidth of interest and the resistor acts as a D-Queing device. I found an excellent introductory papper on small loop antennas on microp-chip.com.

2: The sma was already on there. It connects to a 1/4" piece of coaxial cable. I am tempted to model the loop itself, but I am afraid of ignoring the parasitic effects if the two parallel traces. When I determined the inductance of the circular loop antenna, I modeled it as a parallel circuit of a capacitor and a resistor/inductor series part. But now that you mention it, I presume the orginal design of the traces was to mtch the input impedance to the 50 ohm line as well as tweaking the resonant frequency. I have to ask some EMC guys abiut this, problem is they work with suppressing radiation not intentionally to radiate.

Agghh. You got me! I am using a 3-D MOM em simulator. It doesnt not like circular shapped objects. Only rough polygons. I can estimate a circle with a N-side polygon. However, multiple comonent parts will result in multiple current elements to compute the fields and mesh equations. One time I simulated a coaxial cable, and it reported it required 17K MB of memory and 6500 current elements. I couldn't simulate it, unless I used the large problem solver. MOM does not, i repeat does not, like dielectric surfaces. Only very simple structures are applicable.

This is why I need to model a square loop. I could do it for Ansoft HFSS, but it costs a lot of money.

Right. again i'm worried though that the lines inductance plays a key role. When I computed the inductance of the loop I included the lines. I didn't measure from the feedpoint. See, the whole loop is just a continuous pcb trace fashioned in a circular loop with the two arallell traces ending in the source point, the female sma.

Yeah thats a good book. The problem though is that the engineering handbook, balanis and kraus are encyclopedias. They do not treat antenna types with exasperating detail. I had to buy a few books on just patch antennas and probably loops themselves.

I am a working Rf engineer and a hamster myself. Glad to meet you and thanks. I'll pm in a few.