Monopole & Small Loop
Two staple electrically-small antennas. A quarter-wave monopole over a ground plane is half a dipole — same current distribution, half the radiation resistance, and 3 dB more gain in the upper hemisphere. A small magnetic loop radiates through its magnetic moment, with a radiation resistance that scales as (circumference/λ)⁴ — tiny, which is why loops are low-efficiency but compact. Pick a type and frequency to size it.
Equations & Parameters ▸
\(\text{Monopole: } \ell=\dfrac{\lambda}{4},\ R_r\approx36.5\,\Omega,\ G\approx5.15\ \text{dBi}\)
\(\text{Small loop: } R_r=20\pi^2\left(\dfrac{C}{\lambda}\right)^4 N^2,\ G\approx1.76\ \text{dBi},\ C=\pi d\)
\(\text{Small loop: } R_r=20\pi^2\left(\dfrac{C}{\lambda}\right)^4 N^2,\ G\approx1.76\ \text{dBi},\ C=\pi d\)
| f0 | Frequency (MHz). |
| d | Loop diameter (m) — small loop only. Circumference C = π d. |
| N | Number of loop turns — small loop only. Rr scales as N². |
| Rr | Radiation resistance. Monopole is ideal over a perfect ground; loop assumes C ≪ λ. |
Reference: J. D. Kraus & R. J. Marhefka, Antennas for All Applications, 3rd ed., 2002. Monopole Rr = ½ × dipole (73 Ω).
Inputs
over ground plane
MHz
Bandm
loop onlyloop only
Results
Geometry
Wavelength λ—
Length / circumference—
Size in wavelengths—
Performance
Radiation resistance Rr—
Gain (ideal)—
Diagram