Small Transmitting Loop Antenna Calculator

Small transmitting loop antennas, commonly called "magnetic loops" or "mag loops," can perform surprisingly well when they are carefully designed and constructed. This online calculator can help you design, build, and test loop antennas for use in the HF amateur radio bands (about 1 to 50 MHz), and to answer "what if" questions until you arrive at a design that meets your needs.

Units of measurement:
      (feet and inches)    (meters and millimeters)

Loop material:


Loop shape:


Conductor length:
Practical lengths are about 0.08 to 0.2 wavelength.
feet
Conductor diameter:
At least 0.5 inch or 12 mm for copper and more for aluminum.
inches
Frequency
 megahertz
Transmitter power:
(Optional)
 watts

 

These results assume no losses from poor joints, capacitor contacts, nearby metal, or other construction and installation factors, all of which can degrade antenna performance.

RESULTS:
Antenna efficiency:
Antenna bandwidth:
Tuning capacitance required at this frequency:

Capacitor voltage:
Resonant circulating current:
Radiation resistance:
Loss resistance:
Inductance*:
Inductive Reactance:
Quality factor (Q):
Distributed capacity:
Loop area:
Loop antenna Side length:

Analysis:


Input Values:
Loop material:
Loop shape:
Length of conductor:
Diameter of conductor:
Frequency:
Transmitter power:

Source:
Small Loop Antennas in The ARRL Antenna Book: The Ultimate Reference for Amateur Radio Antennas, Transmission Lines And Propagation, 15th Edition, copyright 1988, pages 5-2 to 5-17

References:
The ARRL Handbook for Radio Communications

Resources:
  • Design your own tuning capacitor for use with this antenna with the
Capacitance Calculator (Capacitor Design)
  • AA5TB's Small Transmitting Loop Antennas web page

Equations
Radiation resistance, ohms
   RR = 3.38 × 10^-8 (f^2 A)^2
Loss resistance, ohms
   RL = 9.96 × 10^-4 √f (S / d)
Efficiency
   η = RR / (RR + RL)
Inductive reactance, ohms
   XL = 2 π f L × 10^6
Tuning capacitor, picofarads
   CT = 1 / (2 π f XL × 10^6)
Quality factor
   Q = (f × 10^6) / Δf = XL / (2(RR + RL))
Bandwidth, hertz
   Δf = (f × 10^6) / Q = (f1 - f2) × 10^6
Distributed capacity, pF (calculated for an octagon; approximate for hexagon or square)
   CD = 0.82 S
Capacitor potential, volts
   VC = √(P XL Q)
*Inductance
   Inductance for square, hexagonal, and octagonal loops is calculated using F. W. Grover's published equations. Inductance for circular loops is calculated using H. A. Wheeler's equation. Because different equations are used, the estimated inductance for a circle may be slightly lower than that for an octagon of the same conductor length and diameter.

Where:
   f = operating frequency, MHz
   A = area of loop, square feet
   S = conductor length, feet
   d = conductor diameter, inches
   η = decimal value; dB = 10 log10 η
   P = transmitter power, watts


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