10.2 Directional Antennas: Yagi-Uda, Cubical Quad & Phased Arrays

10.2 Directional Antennas: Yagi-Uda, Cubical Quad & Phased Arrays

While omnidirectional verticals and bidirectional dipoles radiate energy across wide geographical sectors, directional gain antennas (commonly called "beams") concentrate transmitted RF power into a focused main lobe in a specific azimuthal direction. By focusing energy in the desired direction, directional antennas simultaneously amplify transmitted signal strength toward the target station and reject unwanted interfering signals arriving from the sides and rear during reception.

Understanding the operating principles of parasitic arrays, including the Yagi-Uda, the Cubical Quad, Delta Loops, and their specialized impedance matching networks, is a vital component of the FCC General Class examination. This section explores the electromagnetic coupling, phase relationships, gain metrics, and matching systems that make directional antennas the cornerstone of high-performance HF stations.

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1. Principles of Directional Parasitic Arrays

Unlike phased arrays where every antenna element is directly connected to the transmitter feedline, a parasitic array feeds RF power directly to only one element—designated the driven element. All other elements are unpowered conductors called parasitic elements, mounted parallel to the driven element along a central mechanical boom.

+-----------------------------------------------------------------------------------------+
|                         3-ELEMENT YAGI-UDA ARRAY TOPOLOGY                               |
|                                                                                         |
|             <================ MAIN FORWARD LOBE RADIATION ===============               |
|                                                                                         |
|       +-------------------------------------------------------------------------+       |
|       |                              CENTRAL BOOM                               |       |
|       +-------------------------------------------------------------------------+       |
|             |                                    |                        |             |
|             |                                    |                        |             |
|       +-----------+                        +-----------+            +-----------+       |
|       |           |                        |           |            |           |       |
|       | REFLECTOR |                        |  DRIVEN   |            | DIRECTOR  |       |
|       |  ELEMENT  |                        |  ELEMENT  |            |  ELEMENT  |       |
|       | (+5% Long)|                        | (Resonant)|            | (-5% Short)       |
|       | Inductive |                        | Center-Fed|            | Capacitive|       |
|       |           |                        |           |            |           |       |
|       +-----------+                        +-----------+            +-----------+       |
|             |<------- Spacing 0.15-0.25λ ------->|<--- Spacing 0.1-0.2λ -->|            |
|             |                                    |                        |             |
|          [REAR]                                [FEED]                 [FORWARD]         |
+-----------------------------------------------------------------------------------------+

How Parasitic Coupling Works

1. The driven element radiates an initial electromagnetic field.
2. This field induces RF currents in the adjacent parasitic elements through mutual electromagnetic coupling.
3. The induced currents cause each parasitic element to re-radiate electromagnetic waves.
4. By precisely engineering the length (which determines element reactance) and spacing (which introduces spatial transit phase delay) of each element, the re-radiated waves reinforce constructively in the forward direction and cancel destructively to the rear and sides.

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2. Anatomy & Tuning of the Yagi-Uda Array

A standard Yagi-Uda beam (invented by Japanese researchers Hidetsugu Yagi and Shintaro Uda in 1926) utilizes three distinct classes of elements:

1. The Driven Element

• A resonant half-wave dipole ($L \approx 468 / f_{\text{MHz}}$) connected directly to the transmission feedline.
• Operates at zero net reactance ($X = 0$) at the design frequency.

2. The Reflector Element

• Positioned behind the driven element at a spacing of $0.15\lambda$ to $0.25\lambda$.
• Physically cut approximately 5% longer than the driven element ($L_{\text{ref}} \approx 492 / f_{\text{MHz}}$).
• Phase & Reactance: Because it is longer than resonant half-wave length, the reflector exhibits inductive reactance ($+jX_L$). The induced current lags the inducing field in phase, causing the re-radiated wave to cancel energy traveling toward the rear while reflecting energy forward toward the driven element.

3. The Director Elements

• Positioned ahead of the driven element in the desired direction of transmission at spacings of $0.10\lambda$ to $0.20\lambda$.
• Physically cut approximately 5% shorter than the driven element ($L_{\text{dir}} \approx 445 / f_{\text{MHz}}$).
• Phase & Reactance: Because they are shorter than resonant length, directors exhibit capacitive reactance ($-jX_C$). The induced current leads the inducing field, pulling and focusing the electromagnetic wavefront forward like an optical lens.
• Multiple Directors: Adding more directors increases forward gain and sharpens directivity. A beam can have only one reflector behind the driven element, but can incorporate multiple directors (3, 4, 5, or more) ahead of it along an extended boom.

Boom Length vs. Gain

In Yagi design, forward gain is primarily determined by overall boom length, rather than merely the total number of elements. Adding elements to a fixed-length boom yields diminishing gain returns, though it sharpens the Front-to-Back ratio and widens operational bandwidth.

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3. Directional Gain Metrics: dBi, dBd & Rejection Ratios

Gain References: dBi vs. dBd

Antenna forward gain quantifies the increase in effective radiated field strength in the main lobe compared to a reference antenna receiving the same input power:

+-----------------------------------------------------------------------------------------+
|                            ANTENNA GAIN CONVERSION (dBi vs dBd)                         |
|                                                                                         |
|   ISOTROPIC RADIATOR (dBi):                   HALF-WAVE DIPOLE (dBd):                   |
|   - Theoretical point source                  - Real physical half-wave wire            |
|   - Radiates equally in a 360° sphere         - Exhibits 2.15 dBi intrinsic gain        |
|                                                                                         |
|               dBi = dBd + 2.15 dB             |            dBd = dBi - 2.15 dB          |
+-----------------------------------------------------------------------------------------+

Practical Conversion Examples:

• An antenna with a gain of $7.0\text{ dBd}$ has a gain of $7.0 + 2.15 = 9.15\text{ dBi}$.
• An antenna with a gain of $12.15\text{ dBi}$ has a gain of $12.15 - 2.15 = 10.0\text{ dBd}$.

Front-to-Back (F/B) Ratio & Front-to-Side Rejection

• Front-to-Back (F/B) Ratio: The ratio (expressed in decibels) of signal strength radiated in the maximum forward direction to the signal strength radiated in the exact opposite direction ($180^\circ$ rearward). High-performance Yagis achieve F/B ratios between $20\text{ dB}$ and $30\text{ dB}$, effectively silencing rear co-channel interference.
• Front-to-Side Rejection: The ratio of forward gain to radiation at $90^\circ$ and $270^\circ$. Directional beams feature deep nulls off their sides, allowing operators to rotate the antenna to null out adjacent interference.

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4. Driven Element Feedpoint Impedance & Matching Networks

When parasitic elements are brought into close proximity to the driven element, intense mutual impedance loading dramatically reduces the radiation resistance of the driven element from $73\ \Omega$ down to $15\ \Omega\text{ to }25\ \Omega$ (or even lower on tightly spaced, high-gain arrays).

Connecting a $50\ \Omega$ coaxial cable directly to a $20\ \Omega$ driven element would result in an unacceptable SWR of $50 / 20 = 2.5:1$. To achieve a perfect $1:1$ SWR match, specialized RF matching networks are integrated at the antenna feedpoint:

+-----------------------------------------------------------------------------------------+
|                        GAMMA MATCH & HAIRPIN (BETA) MATCH                               |
|                                                                                         |
|   GAMMA MATCH (UNBALANCED COAX MATCH):                                                  |
|   - Driven element is a continuous unbroken metal rod (grounded to boom at center)      |
|   - Coax braid connects directly to boom/element center                                 |
|   - Coax center pin connects through a variable series capacitor into a parallel rod    |
|   - Sliding shorting strap adjusts resistance; series capacitor tunes out inductance     |
|                                                                                         |
|   HAIRPIN / BETA MATCH (BALANCED MATCH):                                                |
|   - Driven element is cut slightly short (presents capacitive reactance R - jX)         |
|   - A U-shaped metal conductor (shunt inductor) is wired across the split center feed   |
|   - Forms an L-network that steps up 15-25 Ω to 50 Ω pure resistance                    |
+-----------------------------------------------------------------------------------------+

1. The Gamma Match

• Mechanical Advantage: The driven element does not need to be split or insulated from the conductive metal boom; the entire aluminum tube can be directly clamped and grounded to the boom, providing superior lightning protection and structural strength.
• Electrical Operation: A smaller parallel rod runs alongside one half of the driven element. The coaxial cable shield connects to the center of the boom, while the center conductor connects through a series variable capacitor into the gamma rod. An adjustable sliding shorting bar bridges the gamma rod to the driven element.
• Tuning: The sliding bar sets the stepped-up resistance to $50\ \Omega$, while the series capacitor cancels the inductive reactance introduced by the parallel gamma rod loop.

2. The Hairpin (Beta) Match

• Electrical Operation: The driven element is intentionally cut slightly shorter than resonance so that its feedpoint impedance exhibits a capacitive reactive component ($Z_{\text{feed}} = R - jX$, typically $20 - j40\ \Omega$).
• A U-shaped rigid conductor (hairpin) or coil is placed across the split feedpoint, acting as a shunt inductor ($+jX_L$). The shunt inductor and series capacitance form a classic L-network that transforms the $20\ \Omega$ resistance up to a pure $50\ \Omega$ resistive match.

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5. Full-Wave Loop Beams: Cubical Quads & Delta Loops

A Cubical Quad antenna uses full-wave perimeter closed wire loops mounted on non-conductive spreaders (such as fiberglass cross-arms) rather than linear half-wave tubing elements.

+-----------------------------------------------------------------------------------------+
|                              2-ELEMENT CUBICAL QUAD ARRAY                               |
|                                                                                         |
|                 <========= FORWARD DIRECTION OF PROPAGATION ========                    |
|                                                                                         |
|                     +---------------+             +---------------+                     |
|                    /|              /|            /|              /|                     |
|                   / |             / |           / |             / |                     |
|                  +--+------------+  |          +--+------------+  |                     |
|                  |  |  REFLECTOR |  |          |  |   DRIVEN   |  |                     |
|                  |  |    LOOP    |  |  BOOM    |  |    LOOP    |  |                     |
|                  |  |  (1030/f)  |  | =========|==|== (1005/f) |==|====                 |
|                  |  +------------+--+          |  +------------+--+                     |
|                  | /             | /           | /             | /                      |
|                  |/              |/            |/              |/                       |
|                  +---------------+             +---------------+                        |
|                                                    [Feedpoint]                          |
+-----------------------------------------------------------------------------------------+

Calculating Full-Wave Loop Dimensions

The total perimeter length ($L$) in feet of a resonant full-wave closed loop is given by:

$L_{\text{driven (feet)}} = \frac{1005}{f_{\text{MHz}}}$

• Reflector Loop: Cut approximately 3% to 5% larger ($L_{\text{ref}} \approx 1030 / f_{\text{MHz}}$) or tuned with a closed stub.
• Director Loop: Cut approximately 3% to 5% smaller ($L_{\text{dir}} \approx 975 / f_{\text{MHz}}$).

Operational Advantages of Cubical Quads & Delta Loops over Yagis:

1. Higher Forward Gain: A 2-element Quad provides approximately $1.5\text{ to }2.0\text{ dB}$ higher gain than a comparable 2-element Yagi of the same boom length.
2. Lower Precipitation Static Noise: The continuous closed-loop electrical geometry allows high-voltage electrostatic charges from windblown rain, snow, and dust to drain off naturally to ground, resulting in a substantially lower noise floor during stormy weather.
3. Flexible Polarization: Feeding the quad loop at the center of the bottom or top horizontal wire produces horizontal polarization; feeding the loop at the center of either vertical side wire produces vertical polarization.
4. Wider SWR Bandwidth: Closed full-wave loops generally exhibit a broader 2:1 SWR operating bandwidth across the amateur band.

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6. Directional Antenna Specifications Matrix