The Engineering Genius of the Moxon Rectangle: Compact Directional Beam Physics
Explore the mathematical regression models, 50-ohm direct feedpoint matching, and front-to-back null optimization developed by L.B. Cebik and Les Moxon.
For amateur radio operators seeking high directional performance without the mechanical overhead and turning radius of full-sized Yagi-Uda arrays, the Moxon rectangle is in a class of its own. Originating from British amateur Les Moxon (G6XN) and later perfected analytically by the late antenna educator L.B. Cebik (W4RNL), this 2-element directional beam antenna provides nearly 6 dBi of forward gain paired with staggering 25 to 35+ dB front-to-back (F/B) rejection ratios. With our specialized Moxon antenna calculator, you can compute all five critical geometric coordinates with millimeter precision for wire or aluminum tubing builds.
Cebik Moxon Dimensions and NEC Regression Algorithms
A standard 2-element beam with linear parallel elements produces a feedpoint impedance near 25 to 30 ohms when tuned for maximum front-to-back ratio, requiring gamma matches, hairpin loops, or matching transformers to couple to 50-ohm coaxial cable. The Moxon rectangle solves this challenge by folding the tips of both the driven element and the parasitic reflector toward each other at 90-degree right angles.
L.B. Cebik performed thousands of Numerical Electromagnetics Code (NEC-4) computer modeling runs to derive high-order polynomial regression equations that yield a pure 50-ohm resistive input impedance without any matching network. These equations define the five fundamental Cebik Moxon dimensions:
The Five Canonical Moxon Coordinates
Conductor Scaling and Selecting the AWG Wire Diameter
In NEC electromagnetic theory, the ratio of element conductor diameter to free-space wavelength (d / λ) dictates both self-resonance and radiation resistance. Thicker conductors exhibit reduced self-inductance and higher end capacitance, which shortens the required physical length of the elements and broadens the 2:1 SWR bandwidth significantly.
When designing a lightweight wire Moxon for 20m, 17m, 15m, or 10m portable work, builders typically select an AWG wire diameter between #14 AWG (0.064 inches / 1.63 mm) and #12 AWG (0.081 inches / 2.05 mm). For VHF/UHF bands like 6m or 2m, aluminum tubing measuring 0.375 to 0.75 inches (9.5 to 19 mm) is commonly used. Because the regression formulas rely directly on this diameter-to-wavelength ratio, inputting your exact conductor gauge into the calculator ensures the feedpoint impedance lands squarely at 50 ohms at your design frequency.
The Critical Tip Gap and High Front-to-Back Nulls
The hallmark feature that gives the Moxon rectangle its exceptional rear null is Dimension C, known as the critical tip gap. The space separating the driven element tips from the reflector tails acts as an open capacitive coupling junction. This mutual capacitance forces RF displacement currents into the reflector with a precise phase offset and amplitude distribution that cannot be achieved with conventional parasitic coupling in a flat Yagi.
This uniform current distribution creates near-total destructive interference in the rear hemisphere, producing a cardioid radiation pattern with deep 30 dB nulls directly behind the antenna. To preserve these nulls in outdoor installations, the critical tip gap must remain mechanically stable. Builders should utilize rigid, non-conductive insulators—such as UV-stabilized fiberglass rods, Delrin rods, or low-stretch Dacron line—to anchor the gap against buffeting wind, thermal expansion, and ice loading.