Wanted: magnetic loop for the 40-80-160 meter band with real power ©
Calculation, design and preliminary tests of the tuning system
(PA2ION, radio amateur)

Living in urban area often demands for extra challenges for antenna design for 'lower' HF bands. The compactness of the magnetic loop made it to be the candidate.
Calculations have been carried out for several magnetic loop antennas build with copper tubes having large diameter. It was focused on a loop of 3.18m diameter because it is the largest object that can be placed in the intended backyard.
The whole antenna system and controlled components should stay stable under long term outdoor conditions due to smaller bandwidth at lower frequencies.
For a moderate weight, better radiation efficiency the loop material should consist of red copper as plate material with thickness: 0.3-1mm and width: 15-20cm!

Preliminary ‘on air’ function tests have been carried out with a test system consisting of a tuning system developed to be combined with a plate loop (at the moment connected to a 1.54m magnetic loop from 16mm copper tube), home brew stepper electronics and a computer program. Tests both gave intended results and interesting learning facts.

Warning: avoid submersion in excessive electromagnetic fields during tuning tests and SWR measurements inside home: keep a distance of 3 meter from the antenna using a power input less then10 watt RF! Direct body contact with a radiating antenna may cause serious injuries and have lethal effect!


1.1. Radiation efficiency of magnetic loops
For gathering of parameters the “Magnetic Loop Antenna Calculator – v1.6 from KI6GD has been used. (www.standpipe.com/w2bri/software.htm)

Table 1: Calculation results for magnetic loops with 100W RF input

The calculation results for 100W RF input into a 3m loop are listed in table 1 (above)
Results in table 1 for a 3.18m copper loop with 40cm(!) perimeter for the 40-80-160m band score radiation efficiencies of 97%, 74% and 23% respectively. The results will be part of the discussions.

Figure 1. Perimeter or diameter effect of copper on radiation efficiency values

The figure shows up that the efficiency of a 3m loop diameter has fast droppings for perimeters lower then 100mm for both 40 and 80m band.

1.2. Results from the calculation: RF currents near loop capacitors

Mean current value (Coulomb per second) at the capacitors were calculated for a 100W RF signal:


Capacity (kV)

Capacity (pF)














Table 2. Mean currents at capacitors of a 3.2m loop (100W RF signal)

Results in table 2 show that large currents occur towards the capacities for both 80m and 160m band. Good contacts of electrical connections and low resistance (inside) capacitors are necessary to avoid energy loss. High voltages also will occur at capacitors!

1.3. Effect of antenna bandwidth at operations
Multiband application is one of the reasons why magnetic loops are used. Antenna and tuning capacitor(s) are both integrated within the construction: special measures are needed for accuracy and stability at large capacities at presence of small bandwidth.

The capacity tolerance of the antenna system for a specific frequency is defined as “the capacity unit that corresponds with the quarter of the bandwidth”.
Example from data of Table 3 at 7.090MHz:

Abs[(74.2 – 74.5) / (7.100 – 7.090)] * (34.2 / 4) = 0.26 pF



More then 50% signal loss will occur when working outside the bandwidth that might result in a lot of problems for transmitter, signal quality etc.

· Tuning is nearly optimized when the antenna capacity is set within the tolerance.

· Stability: no change of antenna capacity should occur during transmitting.

· At the 160m band the speech audio spectrum is wider then the bandwidth (=700Hz)

· Results of table 3 clearly indicate that for 160m band a poor tuning accuracy, a poor system stability and the modulation mode can give unacceptable results.

· Large capacities require a stable tuning system and antenna. The tuning device must be able to handle very small capacity increments.
Note that moving antenna parts change the capacity value:
Applied method: application of reduction gear connected with capacitors to get capacity increments of a quarter of the tolerance (this system: 0.05pF).

· Working with costly and delicate vacuum capacitors and for saving the vacuum capacitor against early wearing and leakage caused by frequently tuning:
Applied method: usage of a parallel air capacitor type of 20 pF (suited for high voltage by wide spaced blades).

· Risk of a large vacuum capacitors: to minimize damage & injuries by fast flying glass projectiles at an accidentual implosion.
Applied method: capacitor is wrapped firmly with several layers of polyester foil (mylar).


Figure 2. Conductor skin depth (x-axis) versus frequency (y-axis)
(picture from Wikipedia).

1.4. Effects of conductor thickness
RF currents do not flow through the full cross section of the conductor of the antenna.
At higher frequencies it is limited to the upper skin depth of the conductor.
Figure 2 shows skin depth – frequency relation for several metals.

It’s indicating that at 1.8 MHz skin depth for copper is about 0.1mm.
Copper plate with a thickness of 2 – 3mm is available. Application of thin material is reaching soon the limits of the antenna weight (10*0.20*0.003*8900 = 53 kg copper!).
Tests & SWR reading will prove the mechanical behaviour and strength of a prepared construction containing weighty soft copper at outdoor usage.

The hardness and strength of tin-bronze(95%Cu, 5% Sn) gives impressions to be an alternative for copper. It was found that conductivity values for bronze in manufacturing lists differ and are lower!

1.5. Conclusion

Calculation results show that a 3-band magnetic loop is very sensitive for capacity deviations and therefore it is requiring a high mechanical stability.

When looking on table 1 it can be observed that the higher weight of copper of the pathway between the opposite capacitor plates is improving the radiation efficiency by improved conductivity.
To understand this better see details below:

Example 160m band: calculation of energy ratio capacitor and transmitter output
The c
harge of a capacitor: Q = C * U

Example 160 band (1.81MHz) for an 3.18m loop:
Energy stored during one half period on the capacitor = Ec = 0.5*C*U^2 = 0.5*1427E-12*4.1*E3*4.1E3 = 12E-3 Joules
Energy from 100W RF at 1.81 MHz during one half period = Et = 100/2*1.81E6 = 28E-6 Joules

Energy ratio= (capacitor content)/(transmitter output) = 1: 429

That ratio of 1:429 (corresponding with 0,25% radiation efficiency!) shows the enormous importance of a very good loop conductivity when its perimeter is much smaller then a quarter of the wavelength: the not radiated energy temporarily is stored on the capacitor and this part of energy will flow back again over and over the loop during the next half periods. The process is repeated for many times and by that the total radiation efficiency for that energy portion will rise but .. also its pathway length alos is longer and longer with as a consequence that large importance of a very good loop and leads conductivity!

For understanding: the sum of the distances by repeatedly running over the antenna and RF energy to get an efficiency: 95 per cent is calculated to be over 10km at 1.8 MHz!
The graph in figure 3 (below) shows the calculated cumulative patterns of the radiation efficiency of our sample loop for the 40-80-160m bands.

Ron, PA2ION, August 2015