How a magnetic loop works
A small transmitting loop is a single turn of thick conductor, usually copper pipe, tuned to resonance by a capacitor across a gap. Its circumference is well under a quarter wavelength, so its radiation resistance is tiny, often a fraction of an ohm. Everything depends on keeping the loss resistance even smaller, which is why loops use fat pipe, welded or soldered joints, and low-loss capacitors.
Loss resistance Rl = (D ÷ d) × √(π f μ₀ ÷ σ)
Efficiency = Rr ÷ (Rr + Rl)
Here A is the loop area, D the loop diameter, d the conductor diameter and σ the metal's conductivity. RF flows only in a thin skin on the conductor's surface, so the loss depends on the surface area, not the cross-section. Doubling the pipe diameter halves the loss resistance.
Tuning capacitance C = 1 ÷ (4π² f² L)
The voltage is the danger
All the power you feed in is dissipated in a fraction of an ohm, so the current in the loop is many amps, and the voltage across the capacitor is thousands of volts. The calculator works it out as:
V = I × XL (RMS; the peak is 1.41 times higher)
A 1 m copper loop on 20m at 100 W puts nearly 6 kV RMS across the capacitor. Choose a capacitor rated comfortably above the peak figure, and never touch the loop or capacitor while transmitting. The voltage at the capacitor can cause RF burns and arcing even at modest power. Keep the loop well away from people, as the field close to it is intense.
Bandwidth and tuning
A good loop has a very high Q, so its bandwidth is narrow. On 40m it can be just a few kHz, and you'll need to retune when you move frequency. The figure shown is the half-power bandwidth, f ÷ Q, with Q halved because a matched loop is loaded by the transmitter. The 2:1 SWR bandwidth is a little smaller. A very narrow bandwidth is a sign of an efficient loop, and it also filters out strong signals off the tuned frequency, which helps with receiving.
What the calculator leaves out
These are the standard formulas for a single-turn circular loop. They ignore the capacitor's own loss, joint resistance, the proximity effect and losses in nearby objects and the ground, so a real loop is less efficient than the ideal figure. Add an extra loss in milliohms to see the effect: a few tens of milliohms makes a big difference to a small loop on a low band. For an octagonal loop, enter the diameter of a circle with the same area. The formulas are reliable up to a circumference of about a quarter-wave.
Questions
How efficient is a 1 m magnetic loop?
In 22 mm copper pipe, ideally about 68% on 20m and about 16% on 40m. Real loops lose a little more in joints and the capacitor.
What size capacitor do I need for a magnetic loop?
It depends on the loop and frequency. A 1 m loop needs about 51 pF on 20m and about 205 pF on 40m, so a variable capacitor of around 15 to 250 pF covers 40m to 15m.
What voltage rating does the capacitor need?
Several kilovolts at 100 W. A 1 m loop on 20m sees nearly 6 kV RMS, more than 8 kV peak, so a vacuum variable or a widely spaced air variable is needed.
Why is my magnetic loop's bandwidth so narrow?
A small loop has a very high Q, because its radiation and loss resistances are tiny compared with its reactance. Narrow bandwidth is normal and is a sign of low loss.