What is the input impedance of a half-wave dipole?

A half-wave dipole in free space (no ground plane) has an input impedance of 73.1 plus j42.5 ohms at exactly one half-wavelength. The reactive component (j42.5 ohms inductive) can be eliminated by shortening the dipole slightly (to about 0.48 times lambda), which brings the impedance to approximately 70 ohms resistive, a reasonable match to 75-ohm transmission line. The 73 ohm radiation resistance is a theoretical value for an infinitesimally thin conductor; real dipoles with finite diameter have slightly different impedance. A folded dipole (two parallel half-wave elements connected at the ends) has approximately 4 times the impedance of a simple dipole: 292 ohms, which is a good match to 300-ohm twin-lead transmission line. The impedance also changes dramatically when the dipole is near a ground plane: at a height of lambda/4 above a perfect ground, the impedance drops to about 50 ohms, conveniently matching standard coaxial cable.

How does dipole gain compare to other antennas?

The half-wave dipole has a gain of 2.15 dBi (relative to an isotropic radiator) or 0 dBd (since it is the reference for dBd). This gain comes from the doughnut-shaped radiation pattern: instead of radiating equally in all directions (isotropic), the dipole concentrates energy in the plane perpendicular to its axis, with nulls along the axis. A quarter-wave monopole over a ground plane has 5.15 dBi (3 dBd) because the ground plane doubles the gain by reflecting energy upward. A 3-element Yagi-Uda (dipole plus reflector plus director) achieves 7 to 8 dBi. A 5-element Yagi reaches 10 to 11 dBi. A collinear array of stacked dipoles achieves approximately 3 dB additional gain per doubling of elements: 2 dipoles = 5.15 dBi, 4 dipoles = 8.15 dBi, 8 dipoles = 11.15 dBi. Base station antennas use 8 to 16 collinear dipole elements to achieve 15 to 18 dBi sector gain.

What is the bandwidth of a dipole antenna?

A thin half-wave dipole has a bandwidth of approximately 5 to 10 percent (VSWR less than 2:1), limited by the rapid change in reactance with frequency. The bandwidth increases with the dipole's thickness-to-length ratio: a fat dipole (large diameter relative to length) has lower Q and wider bandwidth because the larger conductor surface stores less energy per cycle. A cylindrical dipole with length-to-diameter ratio of 50 has about 5 percent bandwidth, while a ratio of 10 achieves about 15 percent. Biconical and bowtie dipoles use flared conductors to achieve even wider bandwidth: a biconical dipole with 60-degree cone angle achieves approximately 30 to 40 percent bandwidth. For very wide bandwidth (multiple octaves), the log-periodic dipole array (LPDA) uses multiple dipoles of different lengths to achieve 3:1 to 10:1 frequency ratios with consistent gain and impedance, at the cost of lower gain (6 to 8 dBi) compared to a resonant Yagi at a single frequency.

Antenna Fundamentals

Dipole Antenna

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Two collinear conductors of total length ≈λ/2, center-fed. Z_in = 73.1 + j42.5 Ω (at λ/2), gain = 2.15 dBi (0 dBd by definition). Omnidirectional in H-plane, 78° HPBW in E-plane, nulls along axis. Folded dipole: 4× impedance (292 Ω). Shortening to 0.48λ eliminates reactance. Over λ/4 ground plane: Z_in ≈ 50 Ω. Building block for log-periodic, Yagi-Uda, and collinear arrays.

Z_in: 73 Ω

Gain: 2.15 dBi

BW: 5-10%

Understanding the Dipole

The dipole is the most fundamental radiating element in antenna engineering. It serves as the reference antenna for the dBd gain unit, the building block for complex array antennas, and the starting point for understanding electromagnetic radiation. Heinrich Hertz used a dipole to first demonstrate radio waves in 1887, and the basic design has remained unchanged because the physics is elegant and the performance is reliable.

The half-wave dipole resonates when its total length equals approximately one half-wavelength. At resonance, the current distribution is sinusoidal: maximum at the center feed point and zero at the tips. This current distribution creates a radiation pattern shaped like a doughnut around the antenna axis, with maximum radiation broadside (perpendicular) and nulls along the axis. The directivity of 2.15 dBi (1.64 linear) means the dipole concentrates 64% more power in the broadside direction compared to an isotropic source.

Dipole Design Equations

Half-wave dipole:
L = λ/2 = c/(2f)

Input impedance:
Z_in = 73 + j42.5 Ω (half-wave)
Z_in ≈ 73 Ω (shortened to resonance)

Radiation resistance:
R_rad = 20π²(L/λ)² Ω (short dipole)
R_rad = 73 Ω (half-wave)

Dipole Variant Comparison

Type	Length	Z_in	Gain	BW
Short (<λ/10)	<λ/10	<5 Ω	1.76 dBi	<1%
Half-wave	λ/2	73 Ω	2.15 dBi	8–15%
Full-wave	λ	∼5k Ω	3.8 dBi	10–20%
Folded	λ/2	292 Ω	2.15 dBi	15–30%
Sleeve	λ/2	50 Ω	2.15 dBi	20–40%

Common Questions

Frequently Asked Questions

What is the dipole input impedance?

Free space at λ/2: 73.1+j42.5 Ω. Shorten to 0.48λ: ~70 Ω resistive (reactance eliminated). Folded dipole: 4x = 292 Ω (matches 300 Ω twin-lead). Over λ/4 ground: ~50 Ω (matches coax). Impedance varies dramatically near ground plane and with element diameter.

Dipole gain vs. other antennas?

Dipole: 2.15 dBi (0 dBd by definition). λ/4 monopole: 5.15 dBi (ground plane doubles gain). 3-element Yagi: 7-8 dBi. 5-element Yagi: 10-11 dBi. Collinear stacking: +3 dB per doubling (2 dipoles: 5.15 dBi, 8 dipoles: 11+ dBi). BTS panels: 8-16 elements for 15-18 dBi.

What determines dipole bandwidth?

Thin dipole: 5-10% (VSWR <2:1). Bandwidth ∝ diameter/length ratio. L/D=50: ~5%. L/D=10: ~15%. Biconical (60°): 30-40%. Log-periodic dipole array: 3:1-10:1 frequency ratio using multiple resonant lengths. Wider BW = lower Q = more radiation resistance relative to stored energy.

Related Terms

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