# VK1SV 472 kHz small loop experiment

## Introduction

This experiment is about testing a small "magnetic" loop on 630m. A magnetic loop is a loop which is, compared to the wavelength, very small. The small loop produces electromagnetic radiation that starts as a magnetic field (rather than an electric field) and, when mounted vertically, is a directional antenna. Unlike a vertically mounted large loop, the small loop produces maximum field along the plane of the loop.

The radiadion resistance of a small loop is inversely proportional to the wavelength to the power 4. For 630m, this is a very large number! It is therefore expected that the radiation resistance will be very small. This is the bad news. The good news is that, unlike a Marconi type antenna, the losses in the small loop are likely to be a lot less, resulting in a relatively large current flowing through it. This is good because the radiated power is proportional to the square of the current.

This page will describe a crude experiment in making such a small magnetic loop for transmitting on 630m.

## Some numbers first...

The radiation resistance of a loop is given by the formula Rrad=(177*N*S/lambda^2)^2. For a loop with 0.7m^2 surface and 10 turns on 630 metres, we get a radiation resistance of 9.7 uohm (micro ohm). This is a very small number. For comparisson, a 7 metre vertical with no horizontal top loading, has a radiation resistance of 49 mohm (milli ohm). I selected to compare the small loop with a 7 metre vertical as the latter is an antenna that most amateurs with very limited space can probably accommodate.

If we feed 5 W to both antennas and we know the losses, we can calculate the radiated power. For the vertical, the losses (ground loss plus loading coil loss) in my case, are 33 ohm. A suitable transformer couples the 50 ohm transmitter and produces a calculated 0.39 A of antenna current. The resulting radiated power is about 7 mW. For the loop, the losses are the sum of the enviroment losses plus the R of the inductor. In my case, I used a ferrite impedance transformer to match the antenna to the 50 ohm transmitter which had a turns ratio of 7:1. This implies approximatelly 1 ohm of losses (the Rrad is indeed negligible compared to the losses). The resulting antenna current from the 5 W transmitter is 2.2 A which, as predicted, is higher than the current on the vertical. The calculated radiated power is 48 uW, which is two orders of magnitude lower than the vertical (over 20 dB!).

## Construction

The next step is the construction of the very small loop. I used LDF4-50A coaxial cable because it was available and it is rigid enough to retain its shape. The loop was formed by the outer conductor of the coax. The complete assembly was held a few centimetres off the ground and the turns were spread to form a solenoid of about 1.5 m length. The antenna was installed in my sunroom: A variable capacitor was placed in series with the loop. Extra capacitance from a fixed silver mica capacitor was added in parallel to the variable capacitor in order to reach the capacitance required (a bit less than 2 nF). Impedance matching was achieved by using a ferrite toroid with 7 turns (blue wire) connected to the transmitter and the loop going once through the toroid forming a single turn secondary, as seen below: Tuning was confirmed with an antenna analyser and was rather sharp. The final schematic of the system is as seen below: It is interesting to note that the schematic above is very similar to the schematic of a traditional Marconi antenna. In the Marconi case, the Rrad belongs to the capacitor formed by the antenna and the ground and not the inductor. In reality, in the Marconi antenna the loading coil will still have some radiation resistance but it will be negligible compared to the radiation resistance of the antenna.

## Results

The antenna was connected to my 5 W autonomous arduino WSPR transmitter and was left transmitting. The antenna was directed to VK2DDI, who is about 150 km from my QTH and has a world class receiving station on this part of the spectrum. The day before, David VK2DDI received my usual inverted L antenna (7 m tall, 10 m horizontal) about -12 to -15 dB S/N during the day and up to 10 dB better (but variable) during the night when the sky wave kicks in.

During the day, there were no reception reports for the loop. This is not surprising as the much lower radiated power would place the signal at David's location way below -30 dB which is limit of WSPR. In the evening though, there were four spots, with an S/N between -22 dB to -27 dB. This is roughly the expected S/N, assuming all other variables are not very far from their usual values. The antenna was located in the sun room which has a metal roof and metal frame. The transmitter was fed by an isolated power supply and there were no connection to the ground (either the electrical or the radio ground). My inverted-L antenna was detuned (shorted to the ground).

## Future work

Given the radiation resistance of the small loop is proportional to the squares of the area and number of turns, it is sensible that the experiment can be scaled up for better results. For example, a 10 turn, 3 m by 3 m square loop is connected to the same transmitter will result in a radiated power of 8 mW. This assumes the same losses, which may be not a realistic assumption. Increasing the number of turns rapidly increases the inductance, which makes it difficult to tune as it requires a tiny capacitance. Spreading the turns lowers the inductance, as inductance is inversely proportional to the length of the solenoid. It is clear that this will be an optimisation problem as well as a compromise problem...

73, Dimitris VK1SV