EQUATIONS USED

Notes:
The Magloop Antenna Calculator was developed to predict the characteristics of a small-loop (aka "magnetic loop" or "magloop") antenna, given physical dimensions entered via slider widgets.
It supports:

• circular, octagonal, hexagonal and square-shaped loops
• main loops made from either hollow round anodised-copper or aluminium conductors
• metric and imperial units
• magloops with 1-to-8 turns

I developed this multi-turn capable magloop calculator to take advantage of the touch-screens and high-speed of modern mobile phones, to allow users to get realtime feedback of the predicted behaviour of a magloop antenna.
-- 73 de VK3CPU

Inputs via the slider and radio widgets:

• ⌀a : Conductor diameter in millimeters (mm) or inches ("). (Measured between opposing conductor outer surfaces.)
• ⌀b : Loop diameter in meters (m) or feet ('). (Measured between the conductor centers.)
• N : Number of turns or loops.
• c/a : is the spacing ratio; based on 'c' being the inter-winding spacing for multi-turn loops measured between conductor centers, and 'a' is the conductor diameter. (Must be >= 1.1) A low-value will increase the resistance due to the proximity effect. (Ignore for single-turn loops.)
• Tx : The transmit power in Watts. This affects the predicted voltage across the capacitor (Vcap), and the RMS loop current (Ia).
• Re : Additional resistance due to external losses, due mainly from capacitor contact resistance and proximity-to-ground effects. Use Re=0.0 to assume the loop is in free-space with no capacitor losses (i.e. ideal conditions, with loop-related losses only). Adding Re will reduce antenna efficiency, Q, Vcap and Ia, while increasing antenna BW. According to [1] and [2], a 1 m diameter loop of 22 mm copper tubing at a height of 1.5 m above the ground operating at 7 MHz had a calculated capacitor contact resistance of ~190 mΩ and an additional ground proximity loss resistance of ~30 mΩ. Note that true ground losses are dependent on both frequency and height-above-ground.
• Metric or Imperial : selects the measuring system.
• Cu or Al : selects the type of metal conductor (annealed copper or aluminum).
• Circ, Oct, Hex or Sqr : selects the shape of the magloop.

Calculated parameters:

• L : Inductance in microhenries.
• A : Loop area in square meters or square feet.
• C : Effective capacitance of the loop in picofarads.
• peri : Perimeter of the main loop in meters or feet.
• c : Distance between windings, measured from the conductor centers in mm or inches.
• cond : Total required conductor length in meters or feet.
• Tuning Cap (pF): The capacitance required to bring the loop into resonance at the given frequency. Value in picofarads.
• Vcap (kV): The predicted voltage across the capacitance given the desired transmit power.
• BW (kHz): The predicted 3dB bandwidth of the magloop antenna.
• Efficiency (%): The percentage of input energy that is actually radiated and not lost as heat.
• R-radiation (Ω): The calculated radiation resistance of the loop in ohms.
• R-loop (Ω): The calculated resistance of the loop in ohms, due to the combination of material conductance, conductor length, skin-effect and proximity effects.
• Reactance (jΩ): The inductive reactance of the loop in ohms.
• Q : The antenna Q (quality) factor.
• Ia (A): The RMS loop current in amps.
• Perimeter (λ): Antenna perimeter size relative to the wavelength.

Usage hints:

Tap on legend items to disable or enable an output parameter. This can be used to declutter the chart.

Tap on a chart 'dot' to display a tooltip containing calculated output parameters for that frequency or band.

References:
[1]: B. Austin, A. Boswell and M. Perks, "Loss Mechanisms in the Electrically Small Loop Antenna" , IEEE Antennas and Propagation Magazine, 56, 4, August 2014, pp. 143.
[2]: A. Boswell, A. J. Tyler and A. White, "Performance of a Small Loop Antenna in the 3 - 10 MHz Band" , IEEE Antennas and Propagation Magazine, 47, 2, April 2005, pp. 5 1 -56.

Change history:
[28-Sep-21]
* Commenced development.