Enter the antenna length, wavelength, and impedance of free space into the calculator to determine the radiation resistance for a very short (Hertzian) dipole (where L ≪ λ).
Radiation Resistance Formula
The following formula is used to calculate the radiation resistance for a very short (Hertzian) dipole in free space (a short-dipole approximation that assumes L ≪ λ and an approximately uniform current distribution).
R_r = \frac{2}{3}\pi \, Z_0\left(\frac{L}{\lambda}\right)^2Variables:
- Rr is the radiation resistance
- L is the (very short) dipole/antenna length (must be much smaller than the wavelength)
- λ is the wavelength
- Z0 is the intrinsic impedance of free space (often approximated as 377 Ω; more precisely ≈ 376.73 Ω)
To calculate the radiation resistance, multiply (2/3)π by the impedance of free space, then multiply by the square of the ratio of the antenna length to the wavelength.
What is Radiation Resistance?
Radiation resistance is the equivalent resistance that represents the power radiated by an antenna as electromagnetic waves. It is an important parameter in antenna design as it affects the efficiency and performance of the antenna. The radiation resistance is determined by the physical dimensions and shape of the antenna, as well as the frequency of operation. It is typically expressed in ohms (Ω) and represents the portion of the antenna’s input impedance that is due to radiation of energy into space.
How to Calculate Radiation Resistance?
The following steps outline how to calculate the Radiation Resistance (very short/Hertzian dipole approximation).
- First, determine the antenna length (L) (ensure L ≪ λ).
- Next, determine the wavelength (λ).
- Next, determine the impedance of free space (Z0) (often approximated as 377 Ω).
- Finally, calculate the radiation resistance using the formula Rr = (2/3)π Z0 (L / λ)².
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge (note: this example uses a short dipole where L ≪ λ).
Antenna Length (L) = 0.5 m
Wavelength (λ) = 10 m
Impedance of Free Space (Z0) = 377 Ω