Antenna designs 101

 by Mike S Mather ZL2CC

Forty metre dipole antenna design

The 40m band is an excellent DX band from New Zealand. Open locally during the day and world wide during night-time. Especially during the winter months. So let’s look at making a 40m wire antenna.

The basic formula for designing any wire dipole is usually given as;

468/MHz to give an answer in feet or

142/MHz to give an answer in metres.

While these formulas seem like they should give the correct dimensions for dipoles they are really more of an approximation. They will give an approximate total length for the antenna and should be on the long side of things. This is desirable as the real world situation means that the theoretical values will need adjusting. It is easier to shorten an antenna wire by folding back on itself than to lengthen it. If the antenna wire used is insulated this will also effectively lower the resonant frequency making a shortening of the length necessary. See the tables below.

The theory and discussions here are for the 40m band but are similar for any band.

The tables are for a 40m dipole antenna for a frequency of 7.150MHz where the formula will give an overall length of 19.86m. With reference below to the table of bandwidth against element diameter, this is a good centre frequency for 1 or 1.5mm wire. These wire thicknesses correspond to easily obtainable insulated electrical cable.

What height do I need to mount my antenna at? There is no optimum height for a horizontally polarized antenna. The more height the better is the usual maxim. However, look at the table below to see how the height above ground affects the impedance and the resonant frequency. Most New Zealand situations will be in the 12m to 20m heights and typical ground conditions. You will see that when in these conditions the resonant frequency has moved up to 7.200MHz. This means the antenna wire is too short and the impedance is 73 to 84 ohms also too high.

The impedance can be changed by angling the legs into an inverted V configuration but the length will need to be physically changed. Hence cut it long to start with. It can be temporally shortened by doubling the wire ends back on themselves and hand twisting along the length. Cut off and seal after all adjustments have been completed. Remember to adjust the leg lengths equally both sides.

The radiation pattern off a straight dipole depends on many things but in general if the dipole height is more than one wavelength above good ground it will be predominately broadside and tending towards omni-directional as the height decreases. In practise if you have the capability to mount a dipole at 40m height a better choice of antenna is required. Therefore, as your antenna is likely to be mounted around 12 to 14 metres high, then go for an inverted V configuration. This only requires a single support point and will improve the impedance as shown in the tables.

Height metres              (feet)	Frequency MHz	Typical ground Impedance	Perfect ground impedance
40         (132)	7.175	73.5	72
30         (100)	7.100	75	60
20          (66)	7.200	68	70
12          (40)	7.200	84	92
8            (26)	7.060	73	63
4            (13)	7.080	53	22
Free space	7.150		75

Table of frequencies against height above ground for antenna designed for 7.150MHz

Angle degrees	Frequency MHz	Impedance
180	7.150	73.5
160	7.160	72
140	7.170	67
120	7.200	59.5
100	7.260	49.5
90	7.290	43.5

Table of frequency and impedance against angle at apex of inverted V wire antenna

Thickness of insulation	Frequency MHz	Impedance
No insulation	7.150	73.5
0.05mm	7.010	71
1.3mm	6.890	69
2.5mm	6.740	66.5

Table of frequency and impedance against insulation thickness of antenna wire

Element diameter	Frequency MHz	Impedance	Bandwidth in kHz
1mm	7.160	74	290
1.6mm	7.150	73.5	310
5mm	7.120	72.5	355
10mm	7.100	72.3	400
25mm	7.055	72	445
50mm	7.010	72	500

Table of bandwidth, frequency and impedance against element diameter

To sum up:

From the above tables for the average ZL station;

At 12m height and typical ground will give an impedance of 84 ohms

Using electrical single ‘conduit’ cable of 1mm will give an impedance of 74 ohms.

But an apex angle of 120° will give an impedance of 59.5 ohms.

So, a wire dipole in inverted V configuration using 1mm insulated electrical ‘conduit’ looks very promising.

Use the formula to give you the wire length and cut it a little bit longer. Choose your method of support, hoist it up and adjust as required. This will take several attempts so don’t despair. Use an antenna analyser to set the antenna resonant frequency and impedance and start working the DX.