Single wire radiation and travelling wave long wire

An antenna is a device that converts guided EM energy from a transmission line into radiated free-space waves, and vice versa.

Radiation mechanism in a single wire

Radiation comes from accelerated charges, i.e. time-varying current:

l · dI/dt = l · q · dv/dt

• No charge motion, or uniform motion along a straight infinite wire → no radiation.
• Uniform motion along a bent, curved, discontinuous or terminated wire → radiation at those points.
• Oscillating (AC) current → radiation along the whole wire.

So an antenna is fed with RF alternating current; the oscillating charges radiate. The field lines formed between the charges detach every half cycle and travel outward as free-space waves.

Travelling wave long wire antenna

A long wire (L of several wavelengths) a height h above ground, fed at one end and terminated at the far end in a resistor equal to its characteristic impedance (about 400–600 Ω). Because the end is matched, there is no reflection and only a forward travelling wave exists: I(z) = I0 e^(−jkz).

 feed                         R = Z0 (matched)
  |  ------> travelling wave     |
 (~)===========================[R]
  |                               |
 ////////////// ground //////////////
         |<-------- L -------->|

Pattern (θ from the wire axis):

E(θ) ∝ sinθ · sin[(kL/2)(1 − cosθ)] / (1 − cosθ)
Main lobe angle θm ≈ cos⁻¹(1 − 0.371 λ/L)

Example: L = 5λ → θm ≈ cos⁻¹(1 − 0.0742) ≈ 22.2° from the wire.

         main lobes (cone about wire)
           \       /
            \     /   ---> towards load end
 feed o------\---/-------[R]
            /     \
           /       \

Characteristics:

• Unidirectional: radiation is in a cone towards the terminated end; no backward lobe.
• Non-resonant and broadband, since no standing wave; input impedance ≈ Z0 (resistive).
• Gain increases and the main lobe moves closer to the wire as L increases.
• Efficiency is reduced because part of the power is lost in the terminating resistor (about 30–50 %).
• Example: Beverage antenna for LF/MF reception; two such wires form V and rhombic antennas.

Compared with a resonant (standing-wave) long wire, which has lobes in both directions, the travelling-wave antenna has a single-direction pattern and wider bandwidth.