Calculators, tools

Tools to calculate the following:

• frequency to wavelength for radio waves
• conversion of metric to Imperial (meters to feet and inches) lengths
• conversion of VSWR losses to dB losses
• conversion of impedance values to VSWR, return loss and mismatch loss
• conversion of reactance value to inductance or capacitance value
• addition or subtraction of two decibel (dB) values
• quarter-wave line matching transformer

Frequency / wavelength calculator

Metric to Imperial units calculator

• Convert decimal meters to feet and inches, or
• Convert decimal feet to meters

Simply type a meters or feet length into the appropriate field, and the corresponding value will be calculated as you type:

Convert VSWR value to power loss

Any value of VSWR higher than 1:1 can cause power loss due to reflected RF being dissipated in the feeder line. Use this to calculate how much power loss is due to VSWR:

Convert impedance values to VSWR, return loss and mismatch loss

Choose a system or coax cable impedance, input a complex load impedance, and calculate the following:

• Reflection coefficient
• VSWR
• Return loss
• Mismatch loss

System impedance:	Ω
Load impedance:	Resistive: Ω    Reactive: Ω
Reflection coeff.:
VSWR:	: 1
Return loss:	dB
Mismatch loss:	dB

Convert reactance value to inductance or capacitance value

Decibel calculator

Add or subtract two decibel (dB) values

Quarter-wave line matching transformer

The 1/4-wave line matching transformer, also known as a Q-section, is a section of feed-line having a specific impedance designed to transform an input impedance to a different output impedance.

This can be useful when connecting feedlines of different impedances: say, a length of 50Ω coaxial line to a length of 75Ω coaxial line.

The matching 1/4-wave section is connected in series between the input line and the output line, or load.

Shortening coil calculator

Building a 1/4-wave vertical antenna for the low HF bands can be problematic, since the full length required can be difficult or impossible for many to manage, especially when operating portable.  Fortunately, there exist a few methods by which the physical length of the radiator can be shortened, while still maintaining the desired frequency.  Here are two such methods:

• use inductive base loading  to electrically lengthen a much-shortened radiator;
• use capacitive top loading  to electrically lengthen a much-shortened radiator.

In the following calculations, we use the first of these two methods.

Part #1 - Calculate coil inductance

Part #2 - Calculate coil dimensions

We'll now use the inductance L_µH, which we have derived using the above calculator, to estimate the parameters of a coil which we can use to electrically lengthen a short vertical antenna for use in the lower HF bands.

Highly accurate estimates of such parameters can be made, but these involve very complex mathematical expressions ⁽¹⁾ , which are beyond the scope of this site.  Instead, we make use of much simpler expressions/formulas which will give results accurate to within 1 or 2 percent - easily good enough for the practical purposes of constructing an antenna for portable use.

We use the well-known formulas from H. A. Wheeler ⁽²⁾ for single- and multiple-layer air-cored helical coils. These formulas were derived empirically by Wheeler from inductance formulas and curves from the US Bureau of Standards, and published in October 1928.  It's recommended to use "enamelled" magnet wire for the coil windings, since this type of wire has a very thin but flexible insulation coating, allowing the coil windings to be as close-spaced as possible.

Coil former:  The relative permeabilities μ_r of plastics commonly used as coil formers are very close to unity (as for air), so that in electromagnetic terms, they behave identically to air for inductance calculations - they can safely be neglected.  For reference, some typical values are as follows:

• Air: 1.0000
• PVC: 1.0004
• Acrylic: 1.0005
• Nylon: 1.0006

Single-layer helical coil The first formula used here is for a single-layer air-cored helical coil: \[ L_{\mu H} = \frac{N^2 R^2}{9R + 10W} \] where LµH = coil inductance in micro-Henrys, N = number of turns of wire, R = coil mean radius in inches, W = coil width in inches. This formula is claimed to be accurate to within 1 percent for coils having W > 0.8R.

Fig.1 - Single-layer coil

Coil inductance:	µH	No. of turns: Est. wire dia.:  mm
Length units:	Metric Feet/inches
Coil width:	mm
Coil mean radius:	mm

Enamelled wire sizes:   ------
(Some wire sizes may not be readily available from your suppliers)

References

1.   Inductance Calculator at hamwaves.com - demonstrating how complex an accurate estimate of coil inductance can be.
   
   
2.   "Simple Inductance Formulas for Radio Coils", H. A. Wheeler, Proceedings of
   The Institute of Radio Engineers, Vol.16, No.10, October 1928 - scroll to p. 1398 for the article.

Wire cutting/adjustment table

When creating a new wire antenna, it is always advisable to add extra length - a couple of percent extra - to the calculated length. In this way, you ensure that the wire you cut for the antenna is, from the outset, not too short for its' intended purpose.

It's handy to know just how much wire to cut off, in order to arrive at the correct length - i.e. the length at which the antenna resonates at the intended frequency, or frequencies. The table presented here can help you to determine just that. Values in the table are based on a quarter-wave length of wire: thus, when adjusting a dipole for instance, the amount to be cut will be removed from each quarter-wavelength section, that is to say from each "arm" of the dipole.

Use the controls to choose your wire core diameter, and insulation thickness and type if needed: the table will be updated to reflect your choice.

Wire core:	0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 mm  diameter Include end-effect factor:
Wire insulation:	No insulation - bare wire 0.10 mm 0.20 mm 0.30 mm 0.40 mm 0.50 mm 0.60 mm 0.70 mm 0.80 mm 0.90 mm 1.00 mm 1.20 mm 1.40 mm 1.60 mm 1.80 mm 2.00 mm 2.20 mm 2.40 mm 2.60 mm 2.80 mm 3.00 mm thickness
Insulation type:	5PE, PolyethylenePTFE, Teflon ®PU, PolyurethanePVC, Polyvinyl chlorideSILR, Silicone rubber    Insulation correction factor:

To use the values listed, it will be necessary to first erect the antenna in its' intended configuration.  Attach a length of coax, and measure the VSWR on the band of interest with whatever you have available - an analog VSWR meter, or a VNA / digital VSWR device.  Note the frequency at the VSWR minimum, and estimate how far this deviates from the design frequency: this deviation we will call delta.

Find, in the table headers, the closest frequency discrepancy to this delta (you may wish to interpolate between two columns) and, in the row for the band of interest, read off the required adjustment in millimeters.  Given your choice of wire and insulation, this adjustment amount should be close to what you will need to cut from the wire, in order that the VSWR minimum frequency will be close to the design frequency.  Make your adjustment to the antenna, and measure the VSWR again.

Please note that the values listed in the table are intended only as an approximate guide to adjusting the length of your antenna - as with all things, caution is advised when cutting antenna wire to length.   If in doubt, take less off than the value derived from the table, and measure the VSWR again.

Table values calculation

Since we cut the wire section long, the first VSWR measurement will (hopefully!) be at a lower frequency than that desired.

Let the measured frequency of minimum VSWR be f_m , the desired resonant frequency be f₀ , and the measured
radiator length be L_m

Then, the antenna section length for resonance at the desired frequency

L₀ = f_m * L_m / f₀

Hence, the wire must be shortened by an amount

d_L = L_m - L₀

Another way of looking at this is as follows: for one side of a dipole, the difference in length between two pieces of wire cut for different frequencies f₁ and f₂ is given by:

d_L = k × c × (f₂ - f₁) / (4 × f₁ × f₂) ,

for a quarter-wavelength, where

• k = length-correction factor for the wire (depends on various parameters including end-effect and insulation type/thickness)
• c = speed of light

End-fed random wire antenna lengths calculations

End-fed random-length (EFRL) wires can be very effective multi-band antennas, but finding the right length for your own situation can be difficult.  Suitable lengths must conform to these criteria:

• the antenna must be non-resonant on any of the bands you want the antenna to cover;
• the length must be at least a 1/4 wavelength on the lowest frequency band you wish to use, and does not
  need to be longer than 1/2 wavelength on that band, although you may use a longer one if you wish;
• the antenna impedance should be moderate - in the hundreds of ohms - on all bands you wish to use.

There are many sources online which claim to have the length you need, or which present lists of lengths to try, and choosing between them can be challenging (see "Proposed lengths" section below).

Use this tool to chart lengths applicable to your own EFRL antenna setup: you will set dimensions and type of both wire and insulation, a choice of bands to be covered by your antenna, and a suitable length representing your garden/yard/field where the antenna is to be erected. Click the "Chart results" button to start the process: the program will identify the lengths to be avoided, and will show these in colored regions in the chart, the colors corresponding to frequency bands and their harmonics.  These colored areas mark lengths for the chosen bands at multiples of 1/2 wavelength, and hence lengths presenting feed-point high impedances leading to high voltages in matching devices. Any clear, non-colored, areas in the chart will mark lengths, or ranges of lengths, from which you can choose a length for your own use.  Also charted will be one or more of the "proposed" lengths listed in the table below.  Lengths may be read directly from the tooltip shown when the mouse hovers over the chart.

Wire core:	0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 mm  diameter
Wire insulation:	No insulation - bare wire 0.10 mm 0.20 mm 0.30 mm 0.40 mm 0.50 mm 0.60 mm 0.70 mm 0.80 mm 0.90 mm 1.00 mm 1.20 mm 1.40 mm 1.60 mm 1.80 mm 2.00 mm 2.20 mm 2.40 mm 2.60 mm 2.80 mm 3.00 mm thickness
Insulation type:	5PE, PolyethylenePTFE, Teflon ®PU, PolyurethanePVC, Polyvinyl chlorideSILR, Silicone rubber

Choose bands:	160m 80m   60m   40m   30m 20m   17m   15m   12m   10m	All None
No. of ½-waves:	1 2 3 4 5 6 7 8 9 10
Limit results to:	20 30 40 50 60 70 80 90 100 125 150 175 200 any  meters in length, maximum

(An example of a similar, but rather more modest, chart may be seen at Simple End Fed Antenna Calculations, by Mike AB3AP)

"Proposed" lengths
A few optimal lengths, or length-ranges, have been worked out by several operators, see e.g. The "Best" Random Wire Antenna Lengths...  some are listed here as a helpful guide (the length most often quoted online is probably the 71ft / 21.64m variant).  The values in the table will be plotted as dashed "proposed" length-lines in the chart: