Antenna & RF
Convert between gain (dBi/dBd), power (W/dBm/dBW), VSWR / return loss and reflection coefficient, and compute EIRP and approximate beamwidth. A pocket RF tool.
Tx power in every unit
| Unit | Value | Definition |
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Impedance match
| Metric | Value | Definition |
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Mismatch loss is the power that bounces back from a poor
match; with SWR ≤ 1.5 it is negligible (< 0.18 dB).
How it is computed · gain, power, VSWR and EIRP
1. Gain. dBd = dBi − 2.15, because the reference dipole already has
2.15 dBi over the isotropic radiator. Ideal beam:
G(dBi) = 10·log₁₀(41253/(θaz·θel)), with the −3 dB widths in
degrees. Solving: θ = √(41253/10^(G/10)) for a symmetric beam.
2. Power. mW = 10^(dBm/10), dBm = 10·log₁₀(mW),
W = mW/1000 and dBW = dBm − 30.
So 1 W = 30 dBm = 0 dBW.
3. VSWR and return loss. Γ = (SWR−1)/(SWR+1), SWR = (1+|Γ|)/(1−|Γ|),
RL(dB) = −20·log₁₀|Γ|, |Γ| = 10^(−RL/20) and
mismatch loss = −10·log₁₀(1−|Γ|²).
4. EIRP. EIRP(dBm) = Ptx(dBm) + Gain(dBi) − cable loss(dB).
It is the power radiated relative to an isotropic antenna; in many
countries it is capped by regulation.
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How it works
It is a pocket RF tool that bundles the everyday conversions: antenna gain between dBi and dBd (dBd = dBi − 2.15, referenced to the half-wave dipole), power between W, mW, dBm and dBW (dBm = 10·log₁₀(mW), dBW = dBm − 30), and impedance matching between VSWR, return loss and reflection coefficient (Γ = (SWR−1)/(SWR+1), RL = −20·log₁₀|Γ|), including mismatch loss and the percentage of reflected power.
From the transmit power, antenna gain and cable loss it computes the EIRP: EIRP(dBm) = Ptx(dBm) + G(dBi) − cable loss(dB), which is the value regulators limit. It also relates gain and beamwidth using the ideal-antenna approximation G(dBi) ≈ 10·log₁₀(41253/(θaz·θel)): if you enter the −3 dB beamwidths it estimates the gain, and if you only provide the gain it estimates a symmetric beam.
Example: EIRP of a 16 dBi sector with a 23 dBm radio
- Tx power:
23 dBm ≈ 200 mW(10^(23/10) = 199.5 mW). - EIRP:
23 + 16 − 2 dB of cable = 37 dBm, about 5 W equivalent radiated power. - If the analyzer reads VSWR 2:1, the reflection coefficient is
Γ = (2−1)/(2+1) = 0.333: 9.5 dB return loss and 11 % of the power reflected.