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 for 1/4-wave verticals

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, or
• use capacitive top loading

to electrically lengthen a much-shortened radiator. In the following calculations, we use inductive base loading; capacitive top loading, using a so-called "capacitive hat" is beyond the scope of this site.

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 DC permeabilities μ_r of plastics commonly used as coil formers are very close to unity (as for air). However, at RF frequencies, some plastics can be lossy, especially PVC.  The best core is no core - an "air-core" coil is the least lossy core type.

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: Coil width:  mm Coil wire len.:  m RF resistance:  Ω
Coil mean radius:	mm
Coil wire diameter:	mm
Windings spacing:	Zero spacing 1/2-diameter spacing 1-diameter spacing 2-diameter spacing Wide spacing
Est. coil Q-factor:

If you intend to use enamelled wire in your coil (acceptable for the higher HF bands or VHF), you can take a coil wire diameter value from this dropdown list of standard enamelled wire sizes:

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

Part #3 - A note on radials lengths for shortened verticals

Once you have decided on the length of your shortened radiator section, you need to consider the lengths of the radials you will be using with your antenna.  Basically speaking, since radials act more like a loss-reduction system than tuned elements, any length of radials is better than no radials at all, and so shortened radials can be used with your coil-loaded short vertical antenna, but there will be a trade-off:

• shorter radials = easier to handle,
• but reduced antenna efficiency.

Shortening the vertical with a loading coil mainly fixes reactance (resonance), but it does not reduce the current that must flow in the "ground system".  Radials form the return path, or image plane, for current returning to your feed system, so shortening the radials will both:

• increase signal loss, and
• decrease the bandwidth of your antenna,

Keep this in mind when choosing a length for your radials: 0.25 λ is the optimum choice in terms of efficiency, but if space is at a premium, you may decide to use more radials, each perhaps a little shorter than the 0.25 λ optimum length.  There is no special radial-lengths rule to be applied here: ultimately, you make a choice, build your antenna, and test it.

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.

Single-band L-match calculator

Calculates an LC L-network to match a source impedance \(R_{\text{source}}\)  to a load impedance \(R_{\text{load}} + jX_{\text{load}}\)  at a single frequency.

An LC L-network provides an exact match at the design frequency, typically with limited bandwidth, whereas broadband
transformers (ununs, baluns) provide a more general but less precise match.

Key article takeaways  » » »

Two solutions are usually possible for each L-match calculation:

• a low-pass network (series L, shunt C);
• a high-pass network (series C, shunt L).

When two solutions are possible (as is most often the case), then both solutions give the same match, but with different voltage and current stresses.  For high-impedance loads, the low-pass solution is often preferred, since inductors suffer increasing resistive loss as current rises, whereas capacitors can tolerate high voltage with relatively low loss.  In addition, the low-pass solution provides a DC path to ground, which helps bleed off static charge.  The high-pass solution may be chosen where DC blocking is required.

Inductors in L-match networks may be air-cored or wound on toroidal cores.  Air-core inductors offer the lowest loss and are often preferred for single-band matching, while toroidal inductors (especially those using powdered-iron cores) provide a more compact and convenient solution for low-power portable or multi-band use.

The solutions presented here are most suitable for use in the following configurations:

• End-fed half-wave (EFHW) antenna - (single-band use)
• End-fed half-wave verticals
• Non-resonant wires at a chosen frequency
• Loaded or shortened antennas

Typical ranges of impedances Z for these antennas:

L-match calculator

Frequency:	MHz
System impedance:	Ω
Load impedance:	Resistive: Ω    Reactive: Ω
Coil quality (Qcoil):	100 150 200 250 Typical air-core coil
No solutions found for this configuration!

Solutions:

Low-pass solution Series L:  µH Shunt C:  pF L-match Q: Efficiency:  % Notes: • High voltage on capacitor • Passes DC	Low pass L match
High-pass solution Series C:  pF Shunt L:  µH L-match Q: Efficiency:  % Notes: • High current in inductor • Blocks DC	High pass L match

Reference

Table of L-match circuit Q values, listing applicable ranges and usages.

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 desired operating 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 desired operating 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.

Cut back, or fold back?

Assuming that the antenna wire starts out being too long, we need to shorten its length. We could do this in one of two different ways:

• fold back a section of wire to "see how that performs"
• cut the excess wire completely.

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 \(f_{0}\),  and the measured radiator
length be \(L_{m}\) :

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

Hence, the wire must be shortened by an amount

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 \(f_{1}\) and \(f_{2}\) is given by:

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: