magnetic loop calculator

What this magnetic loop calculator does

A magnetic loop antenna is compact, highly selective, and excellent for restricted spaces. The hard part is that loop performance depends strongly on geometry, conductor size, and losses. This calculator gives practical first-pass values so you can design faster:

• Loop inductance and required tuning capacitance
• Radiation resistance (usually very small for compact loops)
• Conductor AC loss (skin effect approximation for copper)
• Estimated efficiency, loaded Q, and 3 dB bandwidth
• Approximate RMS and peak capacitor voltage at the entered power level

Inputs explained

1) Frequency

The operating frequency sets wavelength and the capacitor needed to resonate the loop. Higher frequencies require less capacitance for the same loop size.

2) Loop diameter

This defines loop area and circumference. Larger area usually improves radiation resistance and efficiency, but also changes inductance and tuning range.

3) Conductor diameter

A thicker conductor lowers RF resistance and increases efficiency. For high power operation, larger conductors and low-loss joints make a major difference.

4) Number of turns

Inductance rises approximately with N². Multi-turn loops are common for receiving, while transmitting loops are often single-turn for better efficiency and manageable losses.

5) Additional loss resistance

Real loops include contact resistance, capacitor ESR, coupling losses, and nearby object losses. This input lets you include those practical effects.

Formulas used in this tool

This page uses common engineering approximations for a circular loop:

• Inductance: L ≈ μ0 · R · (ln(8R/a) − 2) · N²
• Resonating capacitance: C = 1 / ((2πf)² · L)
• Radiation resistance (small loop): Rr ≈ 31200 · (N·A/λ²)²
• Skin depth: δ = √(2ρ/(ωμ0))
• AC conductor resistance: Rac ≈ ρ·l/(π·d·δ)
• Efficiency: η = Rr / (Rr + Rac + Rextra)

How to use the results

Start with your target band, then adjust loop diameter and conductor size to increase efficiency while keeping capacitance in a realistic range for your variable capacitor. If calculated capacitor voltage is high, improve spacing and insulation and consider vacuum variable capacitors for robust operation.

Practical build tips

• Use short, wide, clean electrical joints to minimize milliohm-level losses.
• Keep the tuning capacitor and loop conductor connection mechanically rigid.
• Maintain safe clearance around the capacitor—RF voltage can be several kV at moderate power.
• Avoid nearby conductive objects that absorb energy and detune the loop.
• For transmitting loops, verify temperature rise during long key-down operation.

Limitations and assumptions

This calculator is intentionally simple. It assumes a circular geometry, uniform conductor, copper skin-effect model, and small-loop behavior. It does not model nearby ground, supports, weatherproof enclosures, coupling loop optimization, or detailed capacitor ESR versus frequency.

Treat these outputs as design estimates, then confirm with measurement (VNA, SWR bridge, current probes, and thermal checks).