16.2 Voltage, Current & Impedance on Antennas

16.2 Voltage, Current & Impedance on Antennas

Quick Answer: On a half-wave dipole, ends = max voltage / min current; center feed = max current / min voltage. Resonance ≈ 468/f MHz feet (half-wave). Matched line: (I = \sqrt{P/R}) (1,872 W / 52 Ω → 6 A). Best SWR = 1:1. Accepted power ≈ forward − reflected. Harmonic attenuation: 10 log(P1/P2) (500 W / 0.5 W → 30 dB).

Key topic 3-J-064 (Voltage, Current and Power Relationships) is pure distribution math. If you can sketch voltage and current along a half-wave and compute line current and reflected-power budgets, most of this group is mechanical.

Standing waves of V and I on a half-wave dipole

A resonant center-fed half-wave antenna supports a standing wave of RF voltage and current along its length (one half-cycle of the spatial distribution).

Pool wording: at the ends of a half-wave antenna you have maximum voltage and minimum current compared with the remainder of the antenna. That is why end insulators, corona balls, and clearance matter on HF wire antennas—RF voltage peaks can arc to nearby metal.

Why the center is a natural feedpoint

High current and moderate voltage at the center produce a convenient low impedance that matches common coax. Feeding a half-wave at an end would present a very high impedance and need a different matching network (as in some end-fed designs).

Receive side note

The voltage produced in a receiving antenna is always proportional to the received field strength (for a given antenna effective height/length and polarization alignment). Stronger E-field → larger open-circuit induced voltage. Phase quirks from wrong length or SWR are not the pool’s primary receive-voltage rule—field strength proportionality is.

Resonance length and feedpoint impedance

Half-wave (Hertz) length

[ L_{\lambda/2,(\mathrm{ft})} \approx \frac{468}{f_{\mathrm{MHz}}} ]

Worked examples:

Slightly longer or shorter than resonance introduces inductive or capacitive reactance at the feedpoint. A matching network (coupler) or physical trim restores a near-resistive match.

Quarter-wave vertical + ground plane

[ L_{\lambda/4,(\mathrm{ft})} \approx \frac{234}{f_{\mathrm{MHz}}} ]

The ground plane or radials provide the RF return image. Poor ground (few radials, rusty bonds, small aircraft skin discontinuities) raises loss resistance, lowers efficiency, and can shift feedpoint Z and pattern. Ship and tower grounds must be low RF impedance, not merely “a green wire somewhere.”

Feedpoint impedance summary

At resonance, feedpoint impedance ≈ Rr + RL (resistive). Off resonance, ±jX appears. The transmission line wants to see a load equal to its characteristic impedance Z0 (commonly 50 Ω for radio coax). Mismatch → reflections → SWR > 1.

Current on a matched transmission line

For a line delivering real power P into a resistive load R equal to Z0:

[ P = I^2 R \quad \Rightarrow \quad I = \sqrt{\frac{P}{R}} ]

Worked example (pool): current on a 52 Ω line with 1,872 W input:

[ I = \sqrt{\frac{1872}{52}} = \sqrt{36} = \mathbf{6\ A} ]

Also (V = \sqrt{P R} = \sqrt{1872 \times 52} = \sqrt{97344} = 312,\mathrm{V}) RMS, and (P = V I = 312 \times 6 = 1872,\mathrm{W})—useful cross-check.

Use RMS RF current for heating and ammeter comparisons; peak is √2 higher for sine waves.

Standing wave ratio (SWR) quality

SWR (or VSWR) compares the maximum and minimum RF voltage (or current) magnitudes along a line caused by reflections. Perfect match:

[ \mathrm{SWR} = 1:1 ]

Best standing wave ratio on the pool: 1:1. Larger ratios (1:1.5, 1:3, 1:4) mean more reflected power, hotter line, possible PA stress, and less power accepted by the antenna. Many solid-state transmitters fold back as SWR rises.

Forward, reflected, and “actually radiated” power

A directional wattmeter separates forward (incident) and reflected power. Power accepted by the load (antenna + losses) is approximately:

[ P_{\mathrm{accepted}} = P_{\mathrm{forward}} - P_{\mathrm{reflected}} ]

Worked example (pool): 30 W transmitter into a mismatched antenna with 5 W reflected:

[ P \approx 30 - 5 = \mathbf{25\ W} ]

(The pool phrases this as power “actually radiated” in the simplified model—real systems also convert some accepted power to heat in conductors and ground. For exam arithmetic, forward − reflected is the move.)

Harmonic attenuation in dB

If the antenna (or system) radiates 500 W at the fundamental and 0.5 W at the second harmonic:

[ A_{\mathrm{dB}} = 10\log_{10}\left(\frac{500}{0.5}\right) = 10\log_{10}(1000) = \mathbf{30\ dB} ]

That is a power ratio of 1,000:1. Filters, PA design, and antenna resonance all contribute to harmonic cleanliness—Element 3 ties the number to the log definition from Chapter 7.

Connecting impedance pictures to the coupler

An antenna coupler (tuner) transforms a non-50 Ω or reactive antenna impedance into a value the transmitter and line can accept. When the coupler is detuned, the match collapses, SWR rises, reflected power climbs, and accepted power falls—even if the PA meter still shows high forward power into a bad load. Always re-tune after frequency changes on multi-band HF marine and aeronautical installations.

Ground-plane effects on impedance

Raising a dipole higher above ground, adding radials under a vertical, or bonding a ship whip to a larger metal mass all change the reactive environment and slightly shift resonant frequency and feed Z. After mechanical changes (new mount, longer lead-in, damaged radial), re-measure SWR and retune; do not assume the old coupler settings remain valid.

Exam-day V/I/power checklist (3-J-064)

1. Half-wave ends: V max, I min; center: I max, V min.
2. Length ≈ 468/f MHz feet (λ/2); λ/4 ≈ 234/f.
3. Receive antenna voltage ∝ field strength.
4. (I = \sqrt{P/R}) → 6 A for 1,872 W / 52 Ω.
5. Best SWR = 1:1.
6. Accepted ≈ forward − reflected (30 − 5 = 25 W).
7. Harmonic attenuation 10 log(P1/P2) → 30 dB for 500 W / 0.5 W.
8. Ground plane/radials complete the vertical’s RF circuit and affect Z and efficiency.

Next: transmission lines—Z0, velocity factor, stubs, nitrogen, and loss/SWR behavior that connect the PA to this feedpoint.