16.1 Antenna Theory, Types & Patterns

16.1 Antenna Theory, Types & Patterns

Quick Answer: Antennas launch and collect RF fields. Radiation resistance is the fictitious resistance that would dissipate the same power the antenna radiates—critical for impedance matching. Half-wave (Hertz) dipoles and λ/4 verticals are the workhorse resonators; gain is relative to isotropic (dBi) or dipole (dBd); beamwidth and polarization set coverage. Yagis add gain/directivity; traps enable multiband use; an isolator passes RF one way and absorbs reverse power.

Topic 3-J (Antennas) is where Element 3 turns circuit theory into free space. GROL holders in aviation, maritime, and fixed public service install, tune, and diagnose antenna systems every day—wrong pattern or polarization can fail a distress path as surely as a dead PA stage.

What an antenna does

A transmitter delivers RF power into a transmission line. The antenna is the intentional discontinuity that converts that guided wave into a radiating electromagnetic field (transmit) or collects free-space fields into a guided voltage/current (receive). Faraday and Maxwell: time-varying currents on conductors produce magnetic (H) and electric (E) fields that detach and propagate at the speed of light in the medium.

An excited half-wave antenna produces both electromagnetic and electrostatic fields (pool wording for the full EM wave). You never radiate “magnetic only” or “electrostatic only” at radio frequencies in free space—the two fields travel together perpendicular to the direction of propagation.

Radiation resistance

Radiation resistance (Rr) is an equivalent resistance that would dissipate the same amount of power as that radiated from an antenna. It is not a physical resistor soldered into the element; it is the real part of the feedpoint impedance associated with useful radiation.

If an antenna radiates power Pr with RMS feed current I:

[ P_r = I^2 R_r \quad \Rightarrow \quad R_r = \frac{P_r}{I^2} ]

Why radiation resistance matters on Element 3: knowing Rr makes it possible to match impedances for maximum power transfer. Maximum power transfer requires the source/line impedance to conjugate-match the antenna feedpoint impedance. If Rr (plus loss resistance) is 50 Ω and the coax is 50 Ω at resonance, nearly all available RF becomes radiated power rather than reflected or heat.

Do not confuse Rr with front-to-back ratio, SWR alone, or “the trap coil resistance to received signals”—those are distractors on the pool.

Half-wave dipole (Hertz antenna)

A half-wave dipole is a center-fed conductor approximately λ/2 long. In free space its theoretical feedpoint resistance is about 73 Ω resistive at resonance (often treated as near 50–75 Ω in practical installations with height and ground effects).

Length formulas

Free-space wavelength:

[ \lambda_{\mathrm{m}} \approx \frac{300}{f_{\mathrm{MHz}}} \qquad \lambda_{\mathrm{ft}} \approx \frac{984}{f_{\mathrm{MHz}}} ]

Practical half-wave wire dipole (end effects / velocity in wire):

[ L_{\mathrm{ft}} \approx \frac{468}{f_{\mathrm{MHz}}} \qquad L_{\mathrm{m}} \approx \frac{143}{f_{\mathrm{MHz}}} ]

Worked example — 150 MHz half-wave:

[ \lambda \approx 300/150 = 2,\mathrm{m} \quad \Rightarrow \quad \lambda/2 \approx \mathbf{1\ m} ]

(Using 468/f in feet: 468/150 ≈ 3.12 ft ≈ 0.95 m—close enough for the “about 1 meter” exam framing.)

Pattern and polarization

A horizontal half-wave dipole radiates broadside (maximum perpendicular to the wire) with nulls off the ends in free space. Polarization is horizontal when the wire is horizontal. A vertical dipole (or vertical half-wave) is vertically polarized.

Quarter-wave vertical

A λ/4 vertical over a conducting ground plane (or radials) behaves like the upper half of a dipole with the ground plane as the image. Feedpoint resistance over perfect ground is about 36 Ω (half of a dipole’s ~73 Ω)—often near enough to 50 Ω coax with modest matching.

Horizontal-plane pattern: a vertical λ/4 receives and radiates equally from all horizontal directions—omnidirectional in azimuth. That is why marine VHF, aviation COM, and many base stations use vertical whips: every bearing around the horizon is served without rotating the antenna.

Worked example — 156.8 MHz marine VHF λ/4 whip:

[ L_{\mathrm{ft}} \approx 234 / 156.8 \approx 1.5,\mathrm{ft} \ (\approx 0.45,\mathrm{m}) ]

Physical whips are often slightly shorter than free-space formulas because of base loading and dielectric jackets.

Isotropic reference, gain, and beamwidth

An isotropic radiator is a theoretical point source that radiates equally in all directions. No real antenna is isotropic, but it is the 0 dBi reference for gain.

Gain is how much stronger the field is in the preferred direction compared with the reference, for the same input power:

[ G_{\mathrm{dBi}} = 10\log_{10}\left(\frac{P_{\mathrm{dir}}}{P_{\mathrm{iso}}}\right) ]

A half-wave dipole’s maximum gain is about 2.15 dBi, so:

[ G_{\mathrm{dBd}} = G_{\mathrm{dBi}} - 2.15 \qquad G_{\mathrm{dBi}} = G_{\mathrm{dBd}} + 2.15 ]

Beamwidth is the angular width of the main lobe between the half-power (−3 dB) points. High-gain antennas have narrow beamwidth—more “punch” on boresight, less fill-in off-axis. That is why microwave parabolic dishes (satellite links) and radar arrays are steerable or carefully aimed: their energy is concentrated in a thin pencil beam.

Directivity is gain assuming no ohmic loss; real gain includes efficiency. Marketing “gain” without a reference unit is incomplete—always ask dBi or dBd.

Polarization matching

Polarization is the orientation of the E-field as the wave propagates.

A vertically polarized wave into a horizontal dipole suffers deep polarization mismatch loss (ideally approaching total rejection for pure cross-pol). Element 1 already required vertical polarization for marine VHF telephony; Element 3 supplies the field theory: match polarization between stations for best received voltage (receive antenna open-circuit voltage is proportional to the component of E aligned with the element).

Beam antennas, traps, and one-way devices

Yagi-Uda (Yagi)

A Yagi places a driven element (often a dipole) near a slightly longer reflector and one or more slightly shorter directors. Mutual coupling reshapes the pattern into a forward lobe with useful front-to-back discrimination. Gain rises and beamwidth shrinks as well-designed elements are added—classic VHF/UHF point-to-point and weak-signal antennas.

Trap antennas

A trap is a parallel LC circuit inserted in an element that is resonant (high impedance) on one band, electrically “opening” the outer section so the inner section resonates alone, while on a lower band the trap acts more like a loading inductor. Advantage of a trap antenna: multiband operation on one physical structure without swapping antennas. Traps are not magic high-gain devices—pool distractors claiming “high gain” or “high directivity” miss the real benefit.

Isolator (and related hardware)

An isolator is an RF device that allows RF energy to pass in one direction with very little loss but absorbs RF power in the opposite direction. Ferrite isolators protect transmitter finals from reflected energy. A circulator is the multi-port relative that routes ports in a ring (common in duplexers/repeaters). Do not confuse either with a wave trap (frequency-selective rejecter) or a multiplexer (combines/splits bands).

What raises SWR at the antenna system

Even before feed-line math (Section 16.3), antenna theory explains a classic high-SWR cause: a detuned antenna coupler (antenna tuner/matching network not adjusted for the frequency in use). The antenna + coupler no longer present a matched load to the line, so energy reflects. Excessive modulation, mere power increase, or “low power” do not by themselves create a high SWR the way a detuned coupler or wrong-length radiator does.

Exam-day antenna theory checklist (3-J-063 + patterns)

1. Radiation resistance = equivalent R for radiated power; used to match for maximum transfer.
2. λ/2 dipole ≈ 468/f MHz feet; at 150 MHz ≈ 1 m half-wave.
3. λ/4 vertical = omnidirectional in the horizontal plane; vertically polarized.
4. Gain: dBi vs isotropic; dBd vs dipole; higher gain → narrower beamwidth.
5. Polarization match preserves signal; marine VHF = vertical.
6. Trap antenna → multiband; isolator → one-way pass, reverse absorb.
7. High SWR can come from a detuned antenna coupler.
8. Excited λ/2 radiates both E and H (EM) fields.

With types and patterns fixed, the next section maps voltage and current along the radiator and the power arithmetic that sits on the feed line.