Radiation Resistance⚠ unverified
Physics / Electromagnetics · Compute the radiation resistance of an antenna
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| P | P | W | 1.0 | Radiated power |
| I | I | A | 1.0 | Antenna current |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | R | — | Radiation resistance, in ohms (Ohm). Returns 0.0 when ``I`` is zero |
The science & history
Understanding the Parameters
- $P$ — power actually radiated (not conductor loss).
- $I$ — antenna feed current definition must match the $1/2$ vs RMS convention.
- $R$ — fictitious resistance that would dissipate $P$ at that current; part of antenna input resistance $R_{\mathrm{in}} = R_{\mathrm{rad}} + R_{\mathrm{loss}}$.
Derivation (Approaching a Proof)
Time-average power into a radiation resistance with peak current $I_0$ is $P = \tfrac12 I_0^{2} R_{\mathrm{rad}}$, hence $R_{\mathrm{rad}} = 2P/I_0^{2}$. For RMS current, $P = I_{\mathrm{rms}}^{2} R$ and $R = P/I_{\mathrm{rms}}^{2}$.
History
Radiation resistance is a standard antenna-theory parameter (Hertzian dipole $R_{\mathrm{rad}}\propto (L/\lambda)^{2}$, etc.).
Related Concepts: Poynting Vector, Wave Impedance, Watt's Law
Notes: Registry calculator radiation-resistance (unverified). Unit bug: result labelled
dimensionless — should be ohm. Confirm peak vs RMS current convention in the app.