Fixed-Phase Hybrids or Delay Lines? Receive-Array Geometry

ON4UN's practical low-band work made delay-line and hybrid-fed receive arrays familiar to generations of radio amateurs. Joeri's useful inversion is this: instead of always asking which delay fits an established spacing, ask which spacing fits a chosen phase relationship. The algebra allows both questions. The installation still decides whether either answer works.

The Array Sees Spatial Delay First

For a far-field plane wave, two elements at different positions receive the same wave at different times. With the ej2πft convention, the spatial phase difference can be written:

f is frequency, s a unit vector for the declared propagation direction, Δr the element-position vector and c wave speed. A different sign convention is equally valid if it is used consistently. The combiner must add the network phase with the correct sign and amplitude weight for the wanted maximum or unwanted cancellation.

The important term is fΔr/c. Physical spacing measured in wavelengths changes with frequency, so the same site geometry creates a different spatial phase on every band.

Delay and Fixed Phase Are Not Interchangeable

An ideal time delay τ produces:

Its phase slope follows frequency. That is why true time delay can preserve a chosen directional relationship over a wider fractional bandwidth than one fixed phase value.

An ideal fixed phase network instead contributes a chosen angle φ0. It can cancel or reinforce the spatial phase exactly at a design frequency and direction. Move in frequency and the spatial term continues to change while the nominal fixed angle does not. The beam or null can move, broaden or weaken—often called beam squint in larger arrays.

Real hardware is less tidy. A hybrid's amplitude balance, phase difference, return loss, isolation and insertion loss all vary with frequency and termination. A physical delay line also has loss, velocity-factor tolerance, dispersion, connector error and temperature dependence. “Fixed phase” and “true delay” are design models whose completed networks must be measured.

Choosing Spacing Around a Hybrid Is a Valid Inversion

Suppose a practical network supplies a measured phase difference near a chosen value over its working region. The designer can solve the array equation for element spacing at a target frequency and arrival direction rather than solving for a cable delay after the positions are fixed.

That is the real insight behind “fix the phase; let spacing do the work.” Spacing is a design variable before the array is installed. It does not become a universal tuning knob afterward, and one solution does not automatically optimize several bands.

A Nominal Hybrid Angle Is Not a Pattern Specification

Angles such as 22.5°, 45°, 90° and 180° describe useful nominal network relationships. They do not state the phase tolerance, amplitude imbalance, isolation, load sensitivity or usable bandwidth. Nor do they include the element channels before the hybrid.

For branch n, record the complete complex transfer:

That transfer includes the receiving element, matching or active interface, feedline, filter, switch, connector and combiner port at declared reference planes. Equal cable length does not guarantee equal Hn, and a hybrid data-sheet value does not include the outdoor elements.

Null Depth Exposes Small Errors

A deep null requires the unwanted signals to arrive at the summing point with nearly equal amplitude and opposite phase. If one normalized branch has a small fractional amplitude error ε and a small phase error δ in radians, the first-order residual relative to one branch is approximately:

This approximation explains why a pattern that looks plausible can still have a disappointing null. Element mismatch, soil and terrain, mutual coupling, unequal feed loss, common-mode current and receiver-channel drift all appear as amplitude or phase error. A claimed null needs frequency, angle, bandwidth, measurement floor and uncertainty—not only a simulation colour scale.

Cardioid and RDF Are Results, Not Component Features

A cardioid-like pattern can be produced when geometry, element pattern and complex weights meet the required relationship. A fixed hybrid does not create that pattern by itself. Likewise, RDF—receiving directivity factor—is calculated from the complete receive pattern. It cannot be assigned from the nominal hybrid angle or element count.

Two-, three- and four-element layouts each offer useful possibilities. An equilateral three-element drawing does not automatically produce three clean broadband directions, and a four-square or Beverage array does not inherit a pattern merely because familiar labels are used. The array factor, embedded element patterns, ground and complete feed network must agree.

Passive Simplicity Still Has a Cost

A passive fixed network can avoid control software, moving contacts or a separate continuously variable phase control. That may improve operational repeatability. It does not mean “no switching,” zero loss or unlimited bandwidth. Selecting ports, directions or bands can still require switches, and unused or isolated ports need their specified terminations.

An ideal equal divider shows the expected division ratio; excess insertion loss is the additional dissipation or reflection in the real network. On receive, absolute loss may be tolerable while external noise dominates receiver noise, but channel-to-channel loss error still fills nulls. Evaluate both complete-path noise performance and balance.

Common Mode Can Bypass the Array Mathematics

The array equations assume that each branch represents its intended element. Exterior current on coax, power or control cables adds uncontrolled sensing conductors. It can reduce directivity, move a null or make a network adjustment appear to fix what is actually a cable-current problem.

Measure common-mode current on every branch, keep cable routes repeatable and verify that the combining network does not create a bypass path through grounds, shields or power supplies. Choke position follows the measured current boundary; it is not defined by the word “hybrid.”

Prove the Fixed-Phase Design Across Its Real Band

• State the target: bands, headings, elevation region, polarization, null width, RDF or wanted-signal SNR.
• Measure each element channel: record complex transfer, noise, overload and common-mode response at declared planes.
• Measure the network: capture all relevant S-parameters, phase difference, group delay, amplitude balance, isolation and terminated-port conditions.
• Model the installation: include embedded element patterns, mutual coupling, ground, cable routes and nearby conductors.
• Sweep frequency and direction: check the whole pattern for beam squint, lobe growth and spatial ambiguity rather than one target phase.
• Calibrate over the air: use known source directions or signals and keep an independent verification case outside the fitted data.
• Restore the baseline: repeat A/B/B/A measurements after reconnecting or swapping branches so drift is visible.

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