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Magnetic loop calculator

How it works

A magnetic loop is a single turn shorter than 0.15 λ, closed by a capacitor into a tuned circuit with a very high Q. It works in spite of its size, and the price is plain to see: a narrow bandwidth, a few kilovolts across the capacitor and tens of amps in the loop.

Ccoupling loop ≈ 1/5 of the diameterD 1 md 20 mm
The break at the top is the tuning capacitor; the small loop at the bottom couples to the feeder
Tuning
What comes out of it
Numbers to watch

📐 The formulas​

Inductance of the turn (r — loop radius, a — conductor radius):

L = μ₀ × r × [ ln(8r/a) − 2 ]

Tuning capacitance and reactance:

C = 1 / ( (2πf)² × L )        X = 2πf × L

Radiation resistance (A — loop area):

Rr = 31171 × (A/λ²)²          31171 = 320·π⁴

Loss resistance (P — perimeter, Rs — surface resistance):

Rs = √(π · f · μ₀ · ρ)        Rl = P / (2π·a) × Rs

What comes out of it:

Efficiency: η  = Rr / (Rr + Rl)
Q factor:   Qu = X / (Rr + Rl)
Bandwidth:  BW = f / (Qu/2)        ← matched loop
Voltage:    Uc = √( P × Qu × X )
Current:    I  = √( P / (Rr + Rl) )

Symbols:​

  • ρ — resistivity of the material: copper 1.724·10⁻⁸, aluminium 2.65·10⁻⁸ Ω·m
  • Qu — the unloaded Q; the bandwidth is worked out from the loaded Q, which is half of it
Where this calculator stops:
  • The formulas hold for a perimeter up to 0.15 λ. Between 0.15 and 0.25 λ the calculator warns you; above that the numbers are not trustworthy
  • Losses in the capacitor and in the joints are not accounted for, and in practice they eat several more percent of the efficiency
  • The ground and nearby objects are not accounted for: the real efficiency is lower than the calculated one
  • The calculation is for a single turn; a multi-turn loop has far greater losses at radio frequencies

🎯 In practice​

  • QRP from a balcony. A 1 m loop works from 14 to 29 MHz at a respectable efficiency.
  • A receive antenna in town. The deep null in the pattern lets you turn away from a local noise source.
  • A portable antenna. A loop needs no mast, no radials and no room for a wire.
Practical advice:
  1. Use a vacuum or butterfly capacitor with at least 1 mm of gap per kilovolt. Mica ones break down immediately.
  2. No soldered joints in the loop: at 20–30 amps they heat up and ruin the efficiency. Bend the tube in one piece.
  3. Thicker tube, lower losses. Going from 15 to 25 mm adds several percent of efficiency for nothing.
  4. The coupling loop is about 1/5 of the main loop diameter; the match is set by its size and position.
  5. Keep the loop away from ground and metal: below about a metre the efficiency drops noticeably.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Magnetic Loop Antenna Calculator: Capacitor, Efficiency, Q». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/mag_loop/ (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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