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• Antennas

# Loop Antenna Dimensions

### Determining Your Best Loop Design...

Have you been thinking about experimenting with a loop antenna, but are not sure you have enough space to put one up? Have you heard that loops come in many "shapes and sizes" and are confused about what might work best for you at your particular location? Would you like to see "at a glance" if you have room for a loop? The simple calculator below uses the well-known standard formula for determining the total wire length in feet for a single element (single turn), full wave loop antenna, (length = 1005/MHz). It also calculates measurements for:

• A square or diamond loop shape

• A rectangular shape with a 2:1 ratio, (where the horizontal is longer than the vertical length by a factor of 2)

• A delta or triangular loop shape

• A circular shape

in the HF and VHF Amateur Radio bands. NOTE: All results may be presented in either feet, meters, or centimeters. (See Hints and Tips below for suggestions about actual construction techniques...)

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.)

These calculations 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 calculator 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, the Wire Length text box, or select an entry from the drop down menu, 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
 Bands 160m 80m 40m 30m 20m 17m 15m 12m 10m 6m 2m 1.25m 70cm
1) Antenna Dimensions in:
2) Total <Wire Length>: Equivalent Dipole:        1/2 wave 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.)

"What are my options for supporting connectors?"

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...

"What wire types can be used for the transmission line?"

Almost any kind of wire can be used to feed the loop. Recall, the loop is a current "device," so you won't see high voltage nodes in the feed line, permitting less expensive coax or ladder line, as a result. Of course, if you are running the full legal limit, you want to be sure your line can handle the current load. So, your range of "ruggedness" can vary from light 300 Ohm TV ribbon to heavy 450 Ohm ladder line, from low power 50-75 Ohm coax to even hardline for higher power feeds, depending on your rf power output.

In all cases, it is assumed that an antenna tuner will be located between the transmitter and the feed line. Typical impedances for a full wave horizontal loop are about 102 Ohms, at the fundamental frequency. However, this may vary when using a vertical loop at harmonic frequencies, hence the need for a tuner. Many combinations of coax, ladder line, and baluns are feasible. For example, if you have a long run to your loop, you might want to begin with a short span of coax, then include a 4:1 balun before converting over to open ladder line for greater efficiency and less loss. Although not required, some amateurs position a 1:1 current balun right at the loop feed point similar to a dipole feed. This could make sense if the coax run is not too long. More detail can be found at Loop Antennas.

"How do I determine the loop's polarity?"
Conclusions

### Itemized Help:

Frequency

Enter a typical frequency as found in the amateur bands. Be sure to include the decimal point, such as: 14.200. Don't enter any labelling letters such as Mhz. The program is just looking for numbers here. You may enter frequencies outside the amateur bands, such as 0.500 Mhz or 1000 Mhz. However, there will be no output in the band box.

Then click on the button labelled "Calculate Dimensions." After the values have been displayed, you may also click on "Mid Band" which recalculates for the mid-point frequency. At any time, you may select dimentions other than feet which is the default, and recalculate. Calc

Band

Enter an amateur band, with or without the appending letter "m." For example, 17m or just 17. If no "m," it will be appended. The drop down box lists the amateur bands for the calculator. Click on your choice and then click on either the "Mid Band" or "Calculate Dimensions" button. All results, originating with a band choice, result in a mid-point frequency for that band. Calc

Wire Length

You may begin the calculations with a known length of wire instead of a frequency or band. For example, suppose you have a coil of wire which is 100 feet long. Enter this value in the "Wire Length" field and click on the "Mid Band" button. If it is within an amateur band, and thus useable, that band will be displayed in normal fashion, i.e., no "<>" marks which indicate frequency out of band. Pressing the "Mid Band" button again will display the actual mid-point frequency.

If it is out of band, then clicking on the "Mid Band" button continues to cycle through the values from the drop down Band List.

Do not use the "Calculate Dimenions" with this function... It is not relevant. Calc

Impedance

As a reminder, this field always displays the "standard" input (feedpoint) impedance for a full wave loop at the fundamental frequency, which is approximately 102 Ohms, depending on materials, location, and height above RF ground.

As has been noted, the impedance will vary significantly when the loop is worked on its harmonics. Thus, the need for a matching device, typically an antenna tuner. This rule applies regardless of the polarity of the antenna, horizontal or vertical. Harmonic frequencies change the input impedance. Calc

(Courtesy KBNorton Computer Systems)