The ‘net abounds with articles describing easy to build low cost small transmitting loops (STL).

This article describes measurement of a STL for 4MHz using RG213 coaxial cable for the main loop and its tuning capacitance, and a smaller plain wire loop for transformation to 50Ω.

## Loop construction

The loop comprises a length of RG213 formed into a loop and the ends brought together at the top where the inner conductor of one side is connected to the shield on the other side. There are no other connections to the main loop which electrically is a large loop of braided circular conductor of 8mm diameter broken at the top and an open circuit stub of the same length as the loop circumference is connected across the open loop ends. The loop circumference was chosen to resonate with the stub at 4MHz, and is 3.7m.

A smaller loop of 2mm copper wire of about 800mm circumference was suspended inside the main loop and was connected to a coax adapter and onto an antenna analyser for measurement. This smaller loop was distorted to change its effective area and so obtain a perfect match (VSWR=1) close to 4MHz.

## Loop model

Above is the results of Reg Edward’s RJELOOP1 for a copper loop of the same dimensions in free space

Note the loop efficiency of just 1.49%.

## NEC model

A NEC-4.2 model of the copper loop was constructed. The 3.7m circular loop of 8mm diameter copper is located at a height of 1m above average ground, and tuned with a lossless capacitor.

Above is the gain plot from the optimistic model. The model gain is -13dBi.

Lets do some calculations based on the reported efficiencies above. Feed R at resonance was 0.0902Ω, and the radiation efficiency figure tells use that 1.407% of that is radiation resistance Rr, Rr=0.01407*0.0902=0.001269Ω. Loop loss (conductor only in this case) Rloop is (1-0.1631)*0.0902=0.07549Ω, and therefore equivalent ground loss resistance Rg is found by deduction from the total Rg=0.0902-0.07549-0.001269=0.001344Ω.

Note that Rr and Rg are sensitive to height above ground and the ground type.

Above is a plot of the VSWR and -ReturnLoss curves. The half power bandwidth is the difference between frequencies where VSWR=2.618 or ReturnLoss=6.9dB. The half power bandwidth is 3.75kHz.

## Our loop

We might expect that the effective RF resistance of the braided loop conductor is somewhat higher than that of the copper conductor (77mΩ).

Ground proximity can be expected to add some equivalent series resistance to the loop (13.44mΩ from the NEC model).

The input impedance of the 3.7m o/c stub of RG213 is calculated at 0.23-j98.44 Ω using TLLC (Duffy 2001), This adds 230mΩ to the total loop equivalent resistance.

Note the predicted half power bandwidth of 3.3kHz with total loop resistance of 78.3mΩ from RJELOOP1.

The NEC model gives a better prediction that includes ground loss and gives us the Directivity in proximity to ground, half power bandwidth of 3.75kHz and Directivity of 5.68dB.

## Measurement

The actual loop half power bandwidth was measured to estimate the actual efficiency. The loop was matched exactly at one frequency and a sweep of input impedance made with an AA-600 analyser.

Above is the VSWR plot from the AA-600. VSWR=2.6 bandwidth corresponds to the half power bandwidth of the loop itself, much wider than predicted for the copper loop in free space using a lossless capacitor, and that implies much lower efficiency. Measured bandwidth is 30kHz.

Above is a calculation of the loop efficiency, it is 0.18% which indicates a total loop resistance of 1.27/0.0018=706mΩ, 627mΩ higher than accounted for by the radiation resistance (1.2mΩ) and plain copper loop conductor loss(77mΩ).

## Radiated power

Q of the loop is 4000/30=133. The main loop inductor is 3.75µH and has reactance of 94Ω, and the main loop conductance is 1/(Q*Xl)=12.6kΩ. Peak voltage across the loop gap at 1W given by (2*P/G)^0.5=159Vpk.

Whilst the loop might withstand the voltage associated with 1kW continuous input (5kV), it would not withstand the dissipation of almost 1kW continuous power in the loop losses. It might well withstand 1kW PEP SSB telephony due to the low Average/PEP ratio, and that would radiate just 1.6W PEP. It is a QRP antenna, whichever way you go.

## References

- Duffy, O. 2001. RF Transmission Line Loss Calculator (TLLC). VK1OD.net (offline).
- Calculate small transmitting loop gain from bandwidth measurement