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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):
{| class="wikitable"
! 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
{| class="wikitable"
! 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]].

[[Category:Antennas]] [[Category:SimTX]]

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