Antenna Calculations

This page collects the arithmetic needed to size antennas and reason about signal levels in SimTX. All formulas are standard radio engineering practice.

Wavelength

Wavelength in meters:

λ = 300 / f, with f in MHz.

Examples: 4.625 MHz → 64.9 m; 7.1 MHz → 42.3 m; 14.2 MHz → 21.1 m.

Resonant lengths

Practical wire antennas are slightly shorter than the free-space length because of end effects and wire thickness. Useful sizing rules (f in MHz, results in meters):

Antenna	Formula	Example at 7.1 MHz
Half-wave dipole (total)	143 / f	20.1 m
Quarter-wave vertical	71.5 / f	10.1 m
Full-wave loop (circumference)	300 / f	42 m
End-fed half-wave (wire)	143 to 150 / f	20 to 21 m
Longwire, Beverage (guideline)	2 × λ or more	84 m or more

In SimTX a wire length of 0 asks for the resonant length automatically; the formulas are mainly useful for setting explicit lengths and for understanding harmonic operation (a 40 m dipole for 3.6 MHz is also resonant near 10.8 MHz, three times the frequency).

Decibels

• Power ratio in dB: 10 · log10(P2 / P1). Doubling power is +3 dB; ten times power is +10 dB.
• Absolute power: dBm = 10 · log10(P in W) + 30. Examples: 5 W = 37 dBm, 100 W = 50 dBm.
• One S-unit on a receiver corresponds to 6 dB, or a factor of 4 in power. Going from 100 W to 25 W costs one S-unit; from 100 W to 5 W costs about 13 dB, two S-units.

Antenna gain

• Gain in this wiki and in the application is in dBi, decibels relative to an isotropic radiator.
• Gain relative to a dipole (dBd) is dBi minus 2.15.
• Effective radiated power combines transmitter power, feedline loss and antenna gain. Example: 100 W (50 dBm) into 1 dB of feedline and a 7.5 dBi Yagi radiates the equivalent of 56.5 dBm, about 450 W, toward the main lobe.

SWR, reflection and mismatch loss

Given a standing wave ratio S:

• Reflection coefficient: Γ = (S − 1) / (S + 1)
• Reflected power fraction: Γ²
• Mismatch loss: −10 · log10(1 − Γ²) dB

SWR	Reflected power	Mismatch loss
1.0	0 %	0 dB
1.5	4 %	0.18 dB
2.0	11 %	0.51 dB
3.0	25 %	1.25 dB
5.0	44 %	2.55 dB
10.0	67 %	4.81 dB

Mismatch loss alone is mild, but the transmitter's protection foldback adds further reduction above SWR 2.5, see SWR and Transmitter Protection.

Height in wavelengths

Convert antenna height to electrical height: h / λ. A dipole at 10 m is 0.24 λ high at 7.1 MHz (high-angle radiator, regional coverage) but 0.47 λ at 14.2 MHz (good low-angle lobe, long distance). This single number explains most of the difference in where a horizontal antenna performs well.

Path budget in one line

Received signal = TX power (dBm) + TX antenna gain (dBi) − TX losses (feedline, mismatch, foldback) − path loss + RX antenna gain − RX losses. The signal is usable when it clears the receiver's noise floor by the margin the modulation mode needs, see Propagation Basics.