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.
Use the formulas as starting values
No calculation is required for the first-transmission example. Use this page when changing frequency or comparing antennas.
For a dipole at 4.625 MHz, 143 / 4.625 gives about 30.9 m. Start around 31 m, then check the application's SWR estimate. The formula estimates a physical length; it does not replace the antenna solver.
Use MHz in the wire-length formulas, even though the transmitter frequency field uses Hz. For example, enter 4625000 Hz in the app but 4.625 in these formulas. Radio terms explains the units.
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 selects a nominal geometry template, which can still need tuning (and retains 32.5 m for the EFHW); 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.