3.4 Resonant Antennas: Dipoles, Verticals, and End-Fed Antennas

3.4 Resonant Antennas: Dipoles, Verticals, and End-Fed Antennas

ACMA Exam Focus: Resonant antennas are fundamental components of amateur radio stations. This section presents key formulas, physical dimensions, feedpoint impedances, polarisation, and radiation patterns for half-wave dipoles, quarter-wave ground-plane verticals, End-Fed Half-Wave (EFHW) antennas, folded dipoles, and off-centre fed dipoles.

---

1. Radiation Mechanisms and Antenna Resonance

An antenna is a specialised transducer that converts alternating RF electric currents into propagating electromagnetic waves (and vice versa).

When RF current ($I$) oscillates along a conductive element:

1. Accelerated electrical charges produce coupled Electric ($E$) and Magnetic ($H$) fields.
2. In the far field ($> 2\lambda$ away), these fields decouple from the conductor and propagate into space as an electromagnetic wave at light speed ($c$).
3. The $E$ field, $H$ field, and direction of propagation are mutually perpendicular ($90^\circ$).

Antenna Resonance

An antenna is resonant when its physical length matches a natural electrical fraction of the operating wavelength (such as $\frac{1}{2}\lambda$ or $\frac{1}{4}\lambda$). At resonance:

• Inductive reactance ($+jX_L$) equals capacitive reactance ($-jX_C$), cancelling completely ($X_{\text{net}} = 0$).
• The feedpoint impedance ($Z_{\text{feed}}$) becomes purely resistive:

$$Z_{\text{feed}} = R_{\text{radiation}} + R_{\text{loss}}$$

• Radiation Resistance ($R_{\text{rad}}$): The equivalent resistance that accounts for power radiated into space.
• Loss Resistance ($R_{\text{loss}}$): Ohmic heating resistance in conductors and surrounding ground.
• Radiation Efficiency ($\eta$): $\eta = \frac{R_{\text{rad}}}{R_{\text{rad}} + R_{\text{loss}}} \times 100\%$.

---

2. Half-Wave Dipole Antenna ($\frac{1}{2}\lambda$ Dipole)

The half-wave dipole is the reference element for almost all wire and directional antennas.

                       <- Leg 1: L/2 ->       <- Leg 2: L/2 ->
                       =======================|=======================
                                              |
                                          Feedpoint (~73 ohms)
                                              |
                                          Coaxial Feedline

Dimensions and Length Formula

Due to the end effect (capacitive loading at wire ends caused by boundary air insulation), electrical length in wire is approximately $5\%$ shorter than free-space wavelength ($K \approx 0.95$).

$$\text{Total Physical Length (metres)} = \frac{142.5}{f_{\text{MHz}}}$$ $$\text{Each Leg Length (metres)} = \frac{71.25}{f_{\text{MHz}}}$$

Electrical Characteristics

• Feedpoint Impedance: $\approx 73\,\Omega$ resistive at free-space resonance. Height above ground affects impedance (varying between $30\,\Omega$ and $90\,\Omega$).
• Radiation Pattern: Bidirectional figure-8 pattern perpendicular (broadside) to the wire, with deep signal nulls off the wire ends.
• Polarisation: Horizontal when mounted parallel to earth.

---

3. Quarter-Wave Ground-Plane Vertical Antenna ($\frac{1}{4}\lambda$ Vertical)

A quarter-wave vertical consists of a vertical radiating element mounted over a conductive ground plane (radials).

                                    | Radiator (L = 71.25 / f_MHz)
                                    |
                                    |
                         ===========+========== Drooping Radials (45 deg)
                                   / \
                                  /   \
                                 Feedpoint (~50 ohms)

Dimensions and Length Formula

$$\text{Radiator Length (metres)} = \frac{71.25}{f_{\text{MHz}}}$$

Electrical Characteristics

• Feedpoint Impedance: $\approx 36\,\Omega$ over an ideal flat ground plane. Angling ground radials downward at $45^\circ$ increases feedpoint impedance to $\approx 50\,\Omega$, matching $50\,\Omega$ coax directly.
• Radiation Pattern: Omnidirectional ($360^\circ$) in the horizontal plane, with a low elevation angle of radiation ($15^\circ - 25^\circ$), making it ideal for DX (long-distance) contacts.
• Polarisation: Vertical.

Ground Radial Systems

• Elevated Radials: 3 or 4 resonant $\frac{1}{4}\lambda$ wires elevated above ground.
• Buried Radials: 16 to 120 radial wires buried just below soil surface to reduce ground resistance losses ($R_{\text{loss}}$).

---

4. End-Fed Half-Wave (EFHW) Antennas

An EFHW antenna uses a half-wave radiator driven at one end rather than the centre.

• High Feedpoint Impedance: Because current is at a minimum and voltage is at a peak at the wire end, $Z_{\text{feed}} \approx 2000 - 3000\,\Omega$.
• 49:1 Broadband Transformer: A $7:1$ turns ratio broadband impedance transformer ($7^2 = 49$) steps down $2450\,\Omega$ to $50\,\Omega$.
• Multi-Band Operation: Resonates on its fundamental frequency and all higher harmonics (e.g. an 80 m EFHW operates on 80m, 40m, 20m, 15m, and 10m).

---

5. Folded Dipole Antenna

A folded dipole consists of two parallel half-wave conductors connected at both ends and fed at the centre of one conductor.

• Feedpoint Impedance: $\approx 300\,\Omega$ ($4 \times 73\,\Omega$).
• Matching: Fed via $300\,\Omega$ twin-lead or $50\,\Omega$ coax using a 4:1 balun.
• Bandwidth: Offers significantly wider operating frequency bandwidth than a standard single-wire dipole.

---

6. Off-Centre Fed Dipole (OCFD / Windom)

An OCFD is a half-wave dipole fed at a point 33% from one end (or 20% / 80%).

• Feedpoint Impedance: $\approx 200\,\Omega$.
• Matching: Matched to $50\,\Omega$ coax using a 4:1 current balun.
• Multi-Band Performance: Operates on multiple HF bands without requiring an ATU.

---

7. Dimension Table for Resonant HF/VHF Antennas