Loop Antenna Dimensions

The purpose of the calculator is to give you a quick overview of the feasibility of "squeezing" a loop into your available yard or apartment space. The calculator yields a reasonable approximation of dimensions, to within 5% over the amateur bands, using typical wire gauges ranging from #12-18 AWG. (It does not calculate inductance, impedance, or even "Q" factor values since it is assumed that tuning will be accomplished using open feeds and a transmatching device, which should more than adequately compensate for the range of construction and materials variations as measured by these parameters.)

As a reminder, it always displays the "standard" input (feedpoint) impedance for a full wave loop, which of course will vary slightly depending on materials and location. And, a few extra features, a selector for dimension types, meters, or feet; and a mid-band calculation, have been added to the JavaScript code.

These measurements should be able to tell you at a glance if you have room for a loop! I hope so... loops make great antennas! (NOTE: You may deduct 29.3% (0.293) from all vertical lengths if you decide to slope the antenna away from the vertical plane by 45 degrees; see table below. Don't forget to include an additional height above ground for the lowest horizontal element when determining the total vertical dimension, usually six or seven feet for safety reasons, i.e., people.)

To see how the calculator works, click on the "Random Sample" Button. Or, enter a value in the Frequency (megaHertz) text box, the Band text box, or the Wire Length text box, and then click on "Calculate Dimensions" to see the values you are interested in...

Repeatedly pressing the "Mid-Band" button displays the wire lengths, and design dimensions, for the center frequency in each of the amateur bands in turn. (A single press for any given frequency, occurring within a valid amateur band, will also show its mid-frequency point for that band range. The symbols ">" and "<" indicate out-of-band conditions, hence no mid-band frequencies are calculated...)

Pressing the "Mid-Band" button after entering a wire length, will identify the lowest frequency loop, or largest antenna size, within an amateur band. (A subsequent press will calculate the actual mid-band dimensions for that band as usual.)

NOTE : Wire lengths for a mid-band frequency may prove to be the most practical since you may tune above or below to obtain full coverage over the entire band! (The probable exception here would be the 160m band. Tuning down from the mid-point might place a tuner box under considerable electrical "strain" and would not be recommended. So, you can't "cheat" at 160m, you will most likely need the full loop for its lower band edge frequency.)

For a broader discussion of antennas used in packet radio, please see Packet Radio Antennas. Here several types of popular VHF and UHF antennas will be listed...

Loop Calculator:

Enter Parameter(s) for Loop Calculations:
	Enter <Frequency> in Mhz:	<Band>:   Select:  Meters  Feet  Centimeters
1)	Antenna Dimensions in:
2)	Total <Wire Length>:		Height at 45 ° slope
3)	Length on a Square Side:	Length of the Diagonal:
4)	Rectangle 2:1, Horizontal:	Height of above Diagonal at 45 ° slope
5)	Rectangle 2:1, Vertical:
6)	Circular Shape, Diameter:
7)	Delta Loop, one Side:	Height (Base to Apex:)
8)	Typical Impedance:

A Few Operating Notes : The conversion factor, as applied in feet-to-meters calculations, is: 0.3048 The value used here for the cosine of 45 degrees is: 0.7071 The wire gauge, most frequently cited by the research articles, was: #14 AWG. (Please see "Construction Hints & Tips" below... ) Thanks to Steve, G0SGB for keeping me honest :) Geometry buffs might notice an equivalency between the side of a square and the height of the square's diagonal when sloped at 45 degrees. This implies that a vertical square loop has the same height as a 45 degree sloping diamond square loop. (Interesting :) For radio buffs, this means that you only need one support if you use the sloping diamond shape. Are these two antennas comparable in performance? A good research question! The sloper certainly has a larger "footprint" and possibly a significantly different radiation pattern.

Construction Hints & Tips:

"What Size Wire Should I Use?"

There are several factors to consider when choosing your wire gauge and type. As you know there is solid, stranded, covered or insulated, and bare. A general principle is: as you move up in frequency, wire size and type matter! As you move down in frequency, these parameters become much less critical, or even relevant! For example, for an 80m loop, the diameter of the wire compared to its length is going to be a very small ratio. And, it is this ratio that plays a key role in determining the inductance of the antenna. So even if you double or half the size of the wire, the outcome is not going to be significant enough to be concerned about at these very long lengths of wire...

However, for a loop approaching the microwave region, wire size and type become central to the design of the antenna! The formula noted above, for the length of the loop, is probably not going to be very accurate in this regard. Special formulas would be needed to take all the physical variations into account, and predict its performance. (Even fairly wide variations will probably be noticed in the 2m and 70cm regions as well, despite the fact that the standard length formula is often still recommended! You might consider using more appropriate formulas in these cases... )

So, to make a long story short, #14 AWG is probably a good "bet." In most of my primary sources; this is the gauge most frequently used in the HF region. For VHF, #10-12 seems to be very popular. But, follow your plans or specifications to the "letter" if you are working from schematics. (Here are some plans for a quad VHF antenna which is working here on 145.070.)

"What Type of Wire Should I Use?"

Again, the general rule still applies: the longer the antenna element, the less it matters; and the shorter, the more it matters! We all know that covered wire usually "appears" longer electrically than bare wire. But, there are practical considerations too. Covered or insulated wire holds up better when exposed to the elements. And sometimes the tough, plastic covering on the wire can help to act as a strain relief for the antenna if so constructed. For this class of outdoor suspended HF antenna, stranded wire is probably best since it will flex with the wind and not begin to work itself apart as solid wire would. And if the wire is covered (insulated), you won't need quite as much of it as if it were bare.

If you are putting up an indoor antenna in your attic, for example, you could probably use bare wire, either stranded or solid since there will be no wind loading to be concerned about. If you use bare wire, common sense dictates that you use good quality insulators as "stand offs" to prevent adjacent materials from overheating. (Very large currents can circulate in loop antennas, and wires can get quite warm!)

So generally for the HF bands, stranded wire, covered or bare, is a good choice. At VHF, you may use solid wire. This may even help in offering some extra support for your wire struts when on a beam or quad design. In most cases, there will be a minimum of flexing due to wind with solid wire. And, it may be covered or not. (If covered, then it will "appear longer" than if uncovered, and you may need to take this into account when trimming it up for resonance. In other words, the resonant frequency may be lower than indicated by the calculation.)

Supporting Your Loop Antenna

There are two types of support connectors that can be used for HF loop antennas at the insulators: fixed and floating. Fixed ensures that the wire will not slide through the insulator. You can use another short piece of wire to twist around both sides of the loop wire, thus "grasping" the insulator and preventing any movement. You might want to use this type of connection near or at your feedpoint. The other type speaks for itself; the wire is free to move through the insulator and is considered a floating connection. This might be the best type when using a horizontal loop that is supported by ropes tied to "potentially swaying" trees.

For VHF, all points of contact with the supporting struts must be securely fastened. I have used everything from electrical tape to heavy twine on indoor antennas, and plastic ties to small hose clamps on outdoor quads. Here is a problem with a wide range of solutions. Let you imagination be your guide...

Conclusions

Deciding to put up a loop antenna can be more of a logistical problem than an engineering problem in the initial phases of your project planning. I hope the calculator helps you with the logistical part, and gets you thinking about the engineering part. This page can be considered as a secondary source; so be sure to follow up on your leads to primary engineering sources: such as text books, Ham Radio publications, and professional journals; or computer programs that have been specifically designed for radio engineering and mathmatical analysis. A great deal is understood about loops, but there is probably much more to be discovered as well... Your experience in loop building, testing, and operating will not only benefit your own technical skill, but can offer valuable insight and understanding to the field of RF antenna design!

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(Courtesy KBNorton Computer Systems)