# Jimmy-rig FM: The half-wave dipole antenna

% Remco Bloemen % 2014-02-27, last updated 2014-03-04

Together with two friends I constructed an antenna for the Racal 9084 signal generator I posted about to see how much we could increase the range.

Of course, the whole thing had to be constructed on a shoe-string budget. Here’s how it went:

## Design

The goal is to create a simple antenna for approximately 94 Mhz. The dipole is on of the easiest to build, it just requires two conductors of a certain length. An often cited formula for deriving the total length of a half-wave dipole antenna is: $l = 0.95 \frac{1}{2} \lambda \approx \frac{142 \mathrm{[m]}}{f \mathrm{[Mhz]}} \mathrm{[m]} = \frac{142 \mathrm{[m]}}{94 \mathrm{[Mhz]}} \mathrm{[m]} = 1.51 \mathrm{[m]}$ So the antenna works out to be about one and a half meter.

Next is impedance matching so we can get the maximum power out of the transmitter without blowing it up. On wikipedia it is derived that the resistance of the antenna is about 73 Ω. The transmitter is designed for a 50 Ω load, so the matching is not that necessary.

However, it is necessary to convert the unbalanced (signal + ground) feed into an balanced (signal + negative signal) feed for the antenna. This can be done using a device called a balun. For this application we designed an autotransformer style balun like this:

By connecting the ground half way between the positive signal and negative antenna lead and placing the signal on the positive side a balanced signal is created.

But, if I were to connect the input signal directly to the positive antenna lead the effective load would change: the turn ratio would be 2:1, the impedance ratio 4:1 and the effective load would be about 18 Ω, much less than 50 Ω!

This is because the voltage and current depend linearly on the number of windings, so the impedance depends quadratically on the number of windings. The load over the antenna is about 72 Ω and has 2×N windings, this means the number of windings for the transmitter has to be about 1.7×N to create a 50 Ω load. This can easily be done by adding a 0.7×N windings to the right of the transformer, as shown in the diagram.

## Build

The antenna was cheaply constructed using steel-cored clothes line, tape, rope and electric tubing. I bet the radio frequency conductive properties of clothes line are very bad, but we’ll see. For the balun I salvaged a ferrite core from a broken computer power supply (I counted a total of twelve transformers and chokes in it, they are packed with them!). The power supplies operate at a few kHz and the ferrites are not designed for operation at a hundred Mhz, but we’ll see. I then wound three wires 20, 20 and 14 times and soldered the thing to a pcb with some nice connectors. All in all it took about one and a half hour to scavenge the parts and construct.

## Measurements

Since we are all three properly educated in physics andor technology we have a tendency to measure everything we can, this antenna is no exception. Unfortunately, we do not have an antenna analyser, or even a scope that goes to up to FM radio frequencies. Therefore we choose this poor-mans method:

1. Connect the antenna

2. Set a frequency

3. Start transmitting at 2.2 V (maximum)

4. Find the transmission on my friends mobile phone

5. Walk down the street until reception is failing

6. Measure the distance as the crow flies using Google earth.

Resuls:

Antenna Frequency Range

Piece of wire 94.5 Mhz 104 m Dipole antenna 94.5 Mhz 304 m Dipole antenna 88.5 Mhz 723 m

The pore range on the second attempt at 94.5 Mhz was mainly due to a much stronger dutch pirate radio which also transmitted on that frequency and overtook the reception. This did not happen on the bare-wire trial. We then tried again with 88.5 Mhz because it was in a large empty area.

The dipole has whopping increase of $10 \log \frac{723^2}{104^2} = 17 \mathrm{[dB]}$ over the bare wire! However, some of that can be attributed to the dipole sticking out a window, while the bare wire was inside the house and maybe the pirate interfered with the first measurement as well.

## Pictures of the antenna

TODO: Pictures

Salvaging a ferrite core, Salvaging a ferrite core form a broken computer power supply.

Diagram of the balun, Diagram of the balun.

Close up of the finished antenna, Close up of the finished antenna

The finished antenna, The finished antenna

Remco Bloemen
Math & Engineering
https://2π.com