Dr. Ulrich Rohde; Small portable loop antennas

A couple of classic texts if you need to dust off the E&M skills:
Purcell, E.M. (1985). Electricity and Magnetism. McGraw-Hill Press.
Griffiths, D.J. (1981). Introduction to Electrodynamics. Cambridge University Press

 

Check out Chapter 5 in Constantine Balanis's "Antenna Theory and Design." It has the complete treatment of the fields generated by a small loop antenna.

 

First, I am delighted to see Ulrich (N1UL) healthy and active, and as always, I wish him the best.

A bit surprised to see PDE's on the 'Zed, but we are a very richly diverse group as hams.

Onto the pdf summary: This is a very interesting exploration of small antennas, which benefits from a certain clarification posed below.

The radiation resistance of an (electrically) small loop is not defined by the area it occupies (the footprint).

That approximation has regimes of size where it is useful, but others where it is not.

This was debunked 25 years ago. I am sure the authors can find the reference, given QEX's history(and its various forms).

The fallacy arises from the carry-over of optics (see, for example, 'Optics' by Born and Wolf) into the radiation of electrically small radiators. For very electrically large radiators, the area of the radiating aperture defines the radiator. Thus it is defined in the physics that 'area characterizes radiation resistance'.

This carry over notes that electrically small antennas have an 'effective aperture' in order to produce a continuity of description where Fourier optics breaks down, with fractions of a wave number. In other words, the radiation resistance of the antenna is not defined by its area, but we can turn the equation around and say that the dipole has an 'effective aperture' which is different from its actual aperture (area).

This manifests as a good example with the obvious fallacy that a thin wire dipole's area does not produce the 73 odd ohm radiation resistance. If that were true, then a flat, thin wire dipole would have twice the radiation resistance if you doubled the width by two. Nope.

No doubt the notion of 'effective aperture' is a practical way of describing antennas, but, even with a dipole, the area of a dipole is not the same as its effective aperture. That tells us that the care should be emphasized when exploring antennas that are physically small, but electrically long (that is have more than one current max), in terms of relating their radiation resistance to their areas.

This issue is relevant to electrically small loops. In said loops, there is no 'area' which radiates, as characterized in the equations as the FOOTPRINT of the loop. It is the PERIMETER which RADIATES. Not the AREA of the footprint.

One does not map to the other.

As an analogy often posed, if you were to box in the area of Britain, and compare it to its perimeter , you would find that the roughness of the coast prevents you from making a relation between that area and the perimeter. (see, for example, Mandelbrot67Science.pdf (mit.edu) ) )In fact, the perimeter actually depends on the length of your ruler. So you can't just assume that 'perimeter' maps directly to 'area'.

Space filling curves can have near-infinite perimeters, but nearly zero areas.

In other words in electrically small loops, for a given 'area', the physical length and geometry of the radiating elements are both important in the antenna's radiation resistance. 'Area' does not hold these sensitivities constant.

Now: given that the near field dominates the issue, the question is, is there some point where even those sensitivities to geometry and perimeter length break down. Answer: of course! All very electrically small antennas meet a regime where more than one current max on the perimeter--electrically 'long' -- has no practical impact on changing the radiation resistance of the antenna. When this happens, the radiation resistance is so low as to be trivial compared to the dominant ohmic loss, and the antenna is more aptly characterized as a type of 'resonator'.

Hope this helps. The near field (the more general topic relating to small antennas) is a fascinating regime with many surprises uncovered when assumptions, geometries, and boundary conditions are explored. It is poorly understood (in general) and incompletely exploited.

73
Chip W1YW

 

I did not know this. Looking at section 10.9 of Schelkunoff's Antenna Theory and Practice, he claims that the radiation resistance is proportional to area squared. I thought that this was the case because the current in a small loop is uniform and therefore the fields in radiating current segments do not cancel to the extent they are separated by area inside the loop. I attached copies of the relevant pages to this messages.

By the way, if you would like to look at this book, it is available at archive.org

https://archive.org/details/antennastheorypr00sche

Can you cite a particular example where the radiation resistance of small loop is not proportional to its area squared?

 

Thank you, This is what I love about QRZ. It's now saved for future reference.

 

Yes, I am well familiar with that material. I have this book too. Indeed, I have a library of about 500 antenna books--larger than R.C. Hansen's before it was donated to Oklahoma. And yes, there was a study in 1996 in Comm Quart that showed that exactly. The authors may wish to dig it out given the involvement of editorship with QeX.

You may show it for yourself. Use an electrically small fractal, moderately lacunar, loop and simulate its radiation resistance , for a given footprint, as a function of decreasing frequency. Compare that to a square loop of the same footprint. Calculate the enclose area of the fractal loop. Calculate the enclosed area of the square. Why don't they produce the same curve with frequency, nor the same slope?

The current is not uniform : the fractal is electrically long for a larger range of frequencies than the square or circular loop. Thus the formula is a misleading approximation.

Eventually, as the frequency approaches zero, the radiation resistance becomes asymptotic for all loops.

We must be very careful not to take first order approximations as exact answers

In any case, when very electrically small, save for superconducting situations (which are dubious IMO), the ohmic loss so dominates over radiation resistance in very electrically small loops that the issue is --almost- purely academic. They all perform with equally bad performance.

IOW all pinhead sized loops have pinhead sized performance.

R.C. Hansen published a study in short loaded monopoles many years ago that may be helpful to some here. I do not have that reference handy, but others might. Since short monopoles seem to be the main topic, my only comment is to make sure that what radiates is, in fact, the short monopole, not the ground system nor the GP of the radio, its mike, and so on.

I am sure Ulrich corrects for those. But others often do not.
73
Chip W1YW

 

Is that a AN/PRC-117? If so, where did you get it?

I have in my collection the AN/PRC-: 10, 77, 80, 104, 113, 119, and 515.

I'd love to get a 117... 73s Hank

 

Negative

It's from Rohde & Schwartz. M3TR radio family

 

Where did you get a R&S M3TR? What are they costing, i'm afraid to even ask > $50K ?
I recognized it immediately. They are as good as the Harris line.
I'd like to get my hands on a R&S MR3000P
Have you seen the R&S backpack RDF pack? MP007 If memory serves me correctly.
They are amazing!

W5TXR

 

Perfect, I'll go buy a M3TR and a R&S test receiver. I need equipment with "outstanding characteristics" and obviously an engineering degree.

 

I wanted to find something useful about small ('magnetic') loops in this article. But I don't think I did. There is no method or other detail for how the efficiency of the loop was determined, nor, for that matter, what is precisely meant by 'efficiency' for the purposes of the topic under consideration (e.g. does it include environmental effects, etc? - see Prof. Underhill's materials on this).

In the end, it is better for potential loop users to build one and make determinations for themselves. From my own careful work, I know a magloop situated in a good location can exceed the performance of a wire dipole in an average, typical environment. I live on a clear hilltop overlooking the sea. Most others don't. Should I enjoy the benefits of the loop-and-environment combination, or somehow dumb the results down so that others who want to feel aggrieved about not living in such locations can feel better about themselves? Sadly, in ham radio, there is too much bravado and jealousy, and not enough shutting up and getting on with it.

 

Ulrich has always been generous with his time and resources in ham radio. I think you may have missed his point here.

Ulrich and Kai are saying that we can do legit measurements OTA . They are showing us that the PROCESS applies across our entire domain of ham radio. Essentially, in a kindly way, these folks are making a friendly attempt to elevate our expectations in what can be done experimentally OTA.

Now: some may benefit by being reminded what a 'vector potential' is; others may benefit by seeing the methodology of the experiments. What you find useful is up to you.

It does seem, sometimes, that the core passion for further advancement has been eclipsed in the amateur radio service. That would be a shame; it is deep within our roots.

I love KE4PT's motivation: "I would rub silk and amber across the terminals of a wet-noodle antenna if I thought that the sparks would get me a new DXCC entity."

73
Chip W1YW

 

To show the radiation resistance in both cases I have just now added a set of slides from my friend and colleague Professor Eibert, Technical University of Munich , which may help.
73 de Ulrich, N1UL.

 

RE: Fitzgerald Dipole/Loop analysis--

The issue comes down to the case where

P / lambda < < 1 (EQ 1)

where P is the perimeter length (= circumference for a circular loop)

In a space filling curve, such as a fractal, P can be very different compared to the circumference for a circular loop, in the same footprint, and that means the validity of the analysis is sensitive to equation 1 at a different transition value of lambda.

The assumption ka<<1 , for 'a' being a circular radius ,is just a special case of (EQ 1), and for that,

2* pi* a/ lambda <<1 (EQ 2.)

Try it yourself with EQ 1:

for a 1/10th wave by 1/10th wave footprint, 'a' =0.05 waves for a circular loop. For a fractal, it is easy to get P= 0.7 waves or more on that footprint.

Then try a smaller footprint....

73
Chip W1YW