Calculate radiation resistance of a short antenna from antenna length, wavelength, and free-space impedance, with results in Ω, kΩ, or MΩ.
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Radiation Resistance Formula
This calculator uses the very short dipole, or Hertzian dipole, radiation resistance approximation. It assumes the antenna is much shorter than the wavelength and is in free space.
When the impedance of free space is taken as approximately 377 Ω, the same formula is commonly written as:
- Rr = radiation resistance, in ohms
- Z0 = impedance of free space, usually about 377 Ω
- L = antenna length
- lambda = wavelength
- pi = 3.14159…
The calculator converts antenna length and wavelength to meters before applying the formula. It also converts the impedance of free space to ohms if you enter it in kΩ or MΩ. The final radiation resistance is then converted to the output unit you select, such as Ω, kΩ, or MΩ.
Typical Short-Dipole Radiation Resistance Values
The values below use Z0 = 377 Ω. They show how quickly radiation resistance changes as the antenna length becomes a larger fraction of the wavelength.
| Antenna length ratio, L/lambda | Approx. radiation resistance | Use of short-dipole approximation |
|---|---|---|
| 0.001 | 0.0008 Ω | Very good |
| 0.005 | 0.0197 Ω | Very good |
| 0.01 | 0.0790 Ω | Good |
| 0.02 | 0.3158 Ω | Good |
| 0.05 | 1.974 Ω | Approximate |
| 0.10 | 7.896 Ω | Use with caution |
Unit Conversions Used
| Input unit | Base conversion |
|---|---|
| 1 ft | 0.3048 m |
| 1 cm | 0.01 m |
| 1 in | 0.0254 m |
| 1 kΩ | 1,000 Ω |
| 1 MΩ | 1,000,000 Ω |
Example Problems
Example 1: Antenna length and wavelength in meters
Find the radiation resistance for a short dipole with an antenna length of 0.5 m, a wavelength of 10 m, and free-space impedance of 377 Ω.
The radiation resistance is approximately 1.974 Ω.
Example 2: Mixed length units
Find the radiation resistance for an antenna length of 12 in, a wavelength of 30 ft, and free-space impedance of 377 Ω.
First convert the length values:
- 12 in = 0.3048 m
- 30 ft = 9.144 m
The radiation resistance is approximately 0.8773 Ω.
FAQ
What is radiation resistance?
Radiation resistance is the part of an antenna’s resistance that represents power being radiated as electromagnetic waves. It is not the same as wire loss or ground loss. A higher radiation resistance usually means the antenna can radiate power more effectively relative to its loss resistance.
Why is the impedance of free space usually 377 Ω?
The impedance of free space is approximately 376.73 Ω, commonly rounded to 377 Ω. It is also equal to 120π Ω. When you enter 377 Ω, the formula is effectively the same as the common short-dipole equation Rr = 80π²(L/lambda)².
When is this radiation resistance formula valid?
This formula is for a very short dipole where the antenna length is much smaller than the wavelength. It is most reliable when L/lambda is small, such as 0.01 or 0.02. For antennas that are a significant fraction of a wavelength, such as quarter-wave or half-wave antennas, use an antenna model or a formula intended for that antenna type.