Fixed 45°/90° Hybrids in a Receive 4-Square
Fixed 45°/90° Hybrids in a Receive 4-Square
A phase label does not choose the footprint. The useful pattern comes from the measured complex weights, the wavefront delay across the square and the installed response of all four elements.
The practical question is attractive: if the combiner provides nominal 45° and 90° relationships, should the square be 60, 70 or 80 ft per side? The engineering answer is that the meaning of those angles must be established first. A frequency-independent phase shift and a physical time delay can have the same phase at one frequency and behave very differently one octave later.
Do not select spacing from the phase labels alone. State the phase convention, whether the network is fixed phase or true delay, the complete four-channel amplitude/phase weights, the operating frequencies and the pattern objective.
Start with the Square’s Actual Geometry
All dimensions here are side lengths measured centre-to-centre between adjacent elements. A square of side s has a corner-to-corner diagonal of s√2. When the array receives through a corner, the two middle elements occupy the same projected wavefront row; the projected separation from the front row to the middle row, and from the middle row to the rear row, is s/√2.
For a plane wave arriving at elevation angle e along that diagonal, the spatial phase between adjacent projected rows is:
ψspace = 360° · s cos(e)/(λ√2)
The cosine term matters: a network adjusted from a horizon-arrival model is not automatically optimum for a different elevation-angle distribution. The two middle elements also remain physically separated, so their mutual coupling and individual embedded patterns can differ even though their ideal plane-wave arrival phase is equal in the selected diagonal direction.
What 60, 70 and 80 ft Mean Electrically
The table uses 1.84, 3.60 and 7.10 MHz and a horizon-arriving wave. Each entry gives the physical side in wavelengths followed by the phase between adjacent diagonal rows. It is geometry—not a promised pattern.
| Side length | 160 m: 1.84 MHz | 80 m: 3.60 MHz | 40 m: 7.10 MHz |
|---|---|---|---|
| 60 ft / 18.3 m | 0.112 λ / 28.6° | 0.220 λ / 55.9° | 0.433 λ / 110.3° |
| 70 ft / 21.3 m | 0.131 λ / 33.3° | 0.256 λ / 65.2° | 0.505 λ / 128.6° |
| 80 ft / 24.4 m | 0.150 λ / 38.1° | 0.293 λ / 74.5° | 0.577 λ / 147.0° |
The tradeoff is visible without declaring a winner. At 160 m, a 60 ft aperture is compact and deep nulls become more sensitive to amplitude, phase and element-response errors. At 40 m, 70 and 80 ft are electrically large enough that sidelobes, heading overlap and other spatial responses need explicit inspection. A 60 ft square reduces that upper-band aperture, but it does not automatically preserve 160 m RDF.
A published Hi-Z Antennas active-element design study illustrates the design-specific trend: it places a 160 m emphasis in the 80–100 ft range and moves the emphasis toward 80 m while improving 40 m characteristics in the 50–70 ft range. Those figures belong to its element model, combining method, ground assumptions and chosen RDF/front-to-back criteria. They are useful starting points, not universal dimensions for every receive 4-square.
Why 45°/90° Does Not Automatically Mean 80 ft
For an 80 ft square at 1.84 MHz, pure horizon geometry produces about 38.1° between adjacent diagonal rows—not exactly 45°. A real design may deliberately use a different phase to trade forward response, RDF, front-to-back ratio, sidelobes and tolerance to error.
The Hi-Z study makes that distinction concrete. For its 80 ft model at 1.84 MHz, the stated delay-cable choices are approximately 30°/60° for maximum RDF and 47°/94° for its best-front-to-back mode, used with a fixed 180° inversion in the middle channels. A nominal 45°/90° pair is therefore near one published design result; it is not a geometric identity and is not the only defensible pair.
Quote the complete current or voltage convention. “45°/90°” is ambiguous if it omits which element is the reference, the sign of phase, any 180° inversion, the relative amplitudes and whether the figures describe cable delay, network S-parameters or desired element currents.
Fixed Phase and True Delay Are Different Networks
A fixed phase shifter aims to hold a stated angle over its usable passband. A true time delay τ produces phase proportional to frequency:
φ(f) = −360°fτ
A 67.9 ns delay is 45° at 1.84 MHz; a 135.9 ns delay is 90°. At 3.60 MHz the same delays are about 88° and 176°, and at 7.10 MHz they are about 174° and 347°. That scaling is exactly what a time-delay system is expected to do. Calling the cables “fixed 45°/90°” hides their broadband behaviour.
A lumped or hybrid network that remains near 45°/90° across 160, 80 and 40 m does something else: its phase no longer scales with the wavefront transit time across the fixed physical aperture. The resulting beam and nulls change with frequency. Practical networks add their own phase slope, amplitude ripple, impedance mismatch and temperature variation, so classification comes from measured complex transfer functions—not the schematic label.
A fixed 180° polarity inversion also deserves separate treatment. It is a sign reversal, not twice the delay of a 90° path. A broadband four-square may combine polarity inversions with true delays, but the entire channel transfer must be applied to the model.
The Array Factor Is Only the First Model
For four ideal identical elements, the received response can be written as a weighted spatial sum. A practical expression makes the missing terms visible:
V(û,f) = Σ wn(f) En(û,f) e−jk rn·û
The complex weights wn include cable, phase network, gain and combiner response. En is the installed embedded-element transfer response. Replacing every En with the same ideal pattern creates a useful array-factor study, but it does not prove the installed currents or voltages.
Real departures include:
- mutual coupling and source/loading interaction between elements;
- unequal active-probe gain, phase, noise and overload behaviour;
- different soil, vegetation, supports, feedlines and nearby conductors;
- amplitude and phase error in splitters, delay lines, hybrids and relays; and
- common-mode pickup that bypasses the intended four-channel weights.
ITU-R direction-finding guidance explicitly treats element patterns, spatial phase, mutual coupling and nearby-object interference as parts of the array response. That is the right boundary here: ideal weights are a target, while embedded element transfer is what the combiner actually receives.
Pattern, Combiner Loss and Receiver Noise Are Separate
An ideal lossless 3 dB hybrid divides power between ports without dissipating 3 dB as heat. In combining service, the coherent component appears at the intended port while an orthogonal or error component can be directed to the isolated port and its termination. Practical insertion loss is the excess beyond ideal division, and amplitude imbalance, phase imbalance, return loss and isolation all affect the realized weights.
That hardware loss is not the same as array-pattern rejection. A rear null is created by vector cancellation of signals arriving from a direction; energy routed to an isolated load is a network outcome; conductor and dielectric loss are dissipation. Keep those quantities separate in both simulation and measurements.
Location in the receive chain matters too. Passive loss before the first low-noise gain stage directly increases receiver noise factor by the loss at the same physical temperature. If each element has sufficient low-noise gain before the central network, downstream combiner loss is reduced by that preceding gain in a Friis analysis, although it still consumes output level and headroom. On HF, external atmospheric and man-made noise often dominates, so the installed array should be checked for external-noise margin rather than described simply as “quieter.”
A Defensible Use of Each Footprint
| Candidate | Useful reason to model it | Main qualification |
|---|---|---|
| 60 ft | Smaller 40 m electrical aperture and reduced land requirement | At 160 m, null depth and repeatability can be more sensitive to channel and site errors |
| 70 ft | Reasonable multiband candidate between the compact and 160-focused cases | Already about 0.5 λ per side at 7.10 MHz; inspect all lobes and headings |
| 80 ft | Published active-array studies use it as a strong 160/80 m starting point | Not implied by 45°/90° alone; at 40 m it is 0.577 λ per side and needs full-pattern verification |
For a 160 m priority, 80 ft is a credible candidate. For a genuine 160/80/40 compromise, 60 or 70 ft deserves equal modelling attention. None can be selected from physical size alone: define minimum RDF, front-to-back and sidelobe limits at each band and elevation angle, then choose the smallest site-compatible design that meets them with realistic errors.
Qualification Before Committing the Ground Plan
- Model the complete array: element geometry, ground, loads, mutual coupling, feedline and channel weights at band edges—not only band centres.
- State the objective: maximum RDF, deepest rear null, lowest sidelobes and best heading overlap are different optimizations.
- Measure every channel: VNA magnitude, phase or group delay, return loss and isolation across 1.8–7.3 MHz and the expected temperature range.
- Characterize the elements: inject a common field or test source, cross-swap elements and cables, and solve residual gain/phase offsets.
- Check common mode: verify feedline and control-cable current so an unintended fifth antenna does not bypass the combiner.
- Map the field pattern: use repeated bearings or a controlled distant source, record signal and noise separately, and compare every switch heading.
- Verify receive-chain margin: confirm external noise remains above receiver noise without sacrificing overload performance near local transmitters.
Bottom line: 80 ft with approximately 45°/90° can be a sensible 1.84 MHz design point for one active-element topology and one pattern objective. It is not a universal prescription. A three-band array needs either characterized true-delay behaviour or band-specific weights, plus full installed-pattern verification.
Primary technical references
- Hi-Z Antennas — Building a Low-Band Receiving 4-Square Antenna
- Chavdar Levkov, LZ1AQ — Receiving Phased Array with Small Electric or Magnetic Active Wideband Elements
- ITU-R M.1851-2 — Mathematical Models for Phased-Array Antenna Patterns
- ITU-R SM.2354 — Array-Response Modelling with Element Patterns and Mutual Coupling
- Analog Devices — Phased-Array Patterns: Grating Lobes, Phase Shift and True Delay
- Mini-Circuits — Quadrature-Coupler Insertion Loss, Balance and Isolation
- ITU-R P.372-17 — Radio Noise
Mini-FAQ
- Does a 45°/90° network require an 80 ft square? No. An 80 ft design is one credible low-band case, but spacing follows the complete topology, frequency range, element response and pattern objective.
- Is a 45° phase shifter the same as a cable cut for 45°? Only at the reference frequency. A true cable delay produces phase proportional to frequency; a fixed phase shifter aims to hold its angle across its passband.
- Which spacing is best for 160, 80 and 40 m? There is no universal best value. Model 60, 70 and 80 ft with realistic channel and element errors, then select against stated RDF, rear-null and sidelobe limits.
- Why can 80 ft become difficult on 40 m? At 7.10 MHz it is about 0.577 λ per side, so sidelobes and heading overlap can differ sharply from the 160 m pattern and must be checked.
- Does the ideal array factor include mutual coupling? No. A complete prediction needs the installed embedded-element responses, loading, ground and nearby structures as well as the combiner weights.
- Are hybrids inherently quieter than delay lines? No. Compare measured loss, amplitude/phase error, isolation and their location relative to the first gain stage; then verify the complete external-noise margin.