Half-Wave Dipole Antenna Calculator
Calculate the physical length, wavelength, gain, radiation resistance, and 50Ω VSWR for a half-wave dipole antenna at any frequency. Supports velocity factor for insulated wire.
Formula
L_{\lambda/2} = \frac{v_f \cdot c}{2f}, \quad Z_{in} \approx 73.1\,\Omega, \quad G = 2.15\,\text{dBi}
Reference: Balanis, "Antenna Theory: Analysis and Design", 4th ed., Chapter 4
How It Works
A half-wave dipole antenna is a fundamental RF radiating element consisting of a conductive wire or rod precisely half a wavelength long. The antenna operates most efficiently when its physical length matches exactly half the wavelength of the target frequency. Dipole antennas exhibit omnidirectional radiation patterns in the perpendicular plane, with maximum radiation at right angles to the antenna's axis. The fundamental physics relies on the interaction between electromagnetic waves and the antenna's resonant length, creating standing wave patterns that enable efficient energy radiation. At resonance, the antenna presents a near-ideal impedance of 73.1Ω, which is slightly mismatched to standard 50Ω transmission lines, causing a modest voltage standing wave ratio (VSWR).
Worked Example
Consider a half-wave dipole for 2.4 GHz Wi-Fi applications. Using the speed of light (c=3×10^8 m/s) and a velocity factor of 0.96, we calculate the antenna length as follows: λ = 3×10^8 / (2.4×10^9) = 0.125 m. The half-wavelength antenna length becomes 0.0625 m or 62.5 mm. At this frequency, the antenna will have a gain of approximately 2.15 dBi and a radiation resistance of 73.1Ω. When connected to a 50Ω transmission line, the reflection coefficient (Γ) will be approximately 0.188, resulting in a VSWR of 1.46.
Practical Tips
- ✓Use high-quality, precision-cut conductors for accurate resonant length
- ✓Consider environmental factors like dielectric constant when determining antenna length
- ✓Implement proper ground plane or counterpoise for optimal performance
Common Mistakes
- ✗Neglecting velocity factor when calculating antenna length
- ✗Failing to account for end effects that slightly alter actual resonant length
- ✗Assuming perfect 1:1 impedance match without considering transmission line characteristics
Frequently Asked Questions
How does antenna length change with frequency?
Antenna length is inversely proportional to frequency. Higher frequencies result in shorter wavelengths and correspondingly shorter antenna elements.
Why is 73.1Ω the typical radiation resistance?
This is a fundamental characteristic of center-fed half-wave dipoles, representing the theoretical impedance where maximum power radiation occurs.
Can I use a half-wave dipole for multiple frequencies?
A half-wave dipole is narrowband and works optimally at its design frequency. Significant frequency shifts will compromise performance.
What does 2.15 dBi gain mean?
2.15 dBi represents the antenna's gain relative to an isotropic radiator, which is the theoretical perfect omnidirectional antenna.
How important is precise length?
Antenna length accuracy is critical. Even small deviations can significantly impact resonance, VSWR, and overall radiation efficiency.
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