Front, Back, and 0°: Why Phasing Still Needs a Convention

A discussion between me, Joeri Van Dooren, ON6URE, and Hugo Cnudde, ON7FU, began with an apparently simple question: in a crossfire-fed four-square, what do front, back and 0° mean? We were not looking at two different kinds of physics. We were looking at one array through different reference systems.

The Question That Started It

Hugo was reading a familiar no-delay-front presentation. I was reading a network description whose reference branch was at the back. Both presentations can be internally consistent, yet the tables look as if one has turned the array around. That is the trap: the words front and back describe pattern directions, while 0° may describe any of several unrelated reference choices.

The safest physical labels are fixed ones—north, east, south and west, or E1 through E4—with a measured position for every element. “Front element” is then a temporary role belonging to one steering state. Rotate the selected main lobe and a different physical element may acquire that role.

Front and Back Belong to the Pattern

For one declared azimuth cut, front should mean the selected main-lobe direction and back the direction 180° opposite it. A directional array may have more than one lobe or more than one switch state, so the forward azimuth must be stated rather than assumed. A front-to-back value is meaningful only after that direction, frequency, polarization and pattern cut are fixed.

Receive drawings create an extra visual trap. We say that a signal arrives from the front, but its propagation vector points inward toward the array. A transmit pattern is normally drawn with an outward observation direction. Reciprocity lets the same linear reciprocal array pattern describe both cases, but the two arrows point in opposite senses. A diagram should say whether its arrow is the array’s look direction, an outward observation direction or the incident wave vector.

ITU-R BS.1195-1 makes the coordinate system and array-factor construction explicit. IEEE Std 145-2025 is the current terminology standard for antenna quantities. Neither a pattern direction nor an azimuth origin automatically chooses an electrical phase reference.

Zero Degrees Can Name Four Different Things

A table headed only “front 0°, centres −111°, back −218°” is incomplete. It needs a geometry drawing, the physical element labels, the chosen reference, the phasor time convention, the frequency and a statement of whether those angles describe element currents, terminal voltages or internal network signals.

Relative Current Phasors Make the Pattern

Using the time convention e^+jωt, write the current at element n as I_n = |I_n|e^jφ_n. For an outward observation unit vector u, one common far-field form is:

Here, r_n is the measured element position and F_n is that element’s embedded response in the installed array. A text using e^−jωt will reverse the phase signs. The sign is not a matter of taste halfway through a calculation: choose one convention and keep it through excitation phase, propagation phase and measurement.

Multiplying every current by the same phase factor e^jφ₀ rotates the phase of the total field but leaves |E| and the power pattern unchanged. That is why any one current may be called 0° without changing the physical pattern—provided every other current is shifted by the same amount and the element mapping is preserved.

NTIA’s Antenna Engineering Handbook similarly keeps element position, array orientation and the electrical phase angle of each element current as separate inputs. That separation is exactly what a readable amateur-array diagram needs.

Feed Voltage Is Not Automatically Element Current

Mutual coupling makes the distinction important. In matrix form, terminal voltages and currents are related by V = ZI, where the impedance matrix contains both self and mutual terms. Equal feed voltages do not guarantee equal current magnitudes or phases, and an internal network sample does not become an element-current measurement merely because a cable connects the two.

The installed current phasors depend on the element impedances, coupling, feedline transformations, terminations, switching network, ground and nearby structures. When the design target is a current set, verify current at a declared element feed plane or use a proxy whose amplitude and phase transfer function has been calibrated.

Lead, Lag and Modulo 360

Angles repeat every full turn. Under one unchanged reference and sign convention, +240° is identical to −120° modulo 360°. In plain language, a 240° lead can be written as a 120° lag. The equivalence is mathematical; the words lead and lag still require a declared time convention.

Do not compare a +120° entry from one table with a −120° entry from another until both tables have been normalized to the same element order, reference current and phasor convention. Subtract the reference phase from every entry, wrap the results consistently, and then compare the full complex current ratios—not the headings alone.

Phase Shift Is Not Automatically Time Delay

For a matched, approximately nondispersive path with delay τ = l/v_p, the e^+jωt convention gives:

A true delay therefore has a phase slope with frequency. A fixed phase shifter can equal that delay at one frequency but not across an unlimited band. Real cables and networks add dispersion, mismatch, parasitic coupling and load-dependent transformations, so physical line length alone does not establish the element-current phase.

Tom Rauch, W8JI, describes crossfire phasing as progressively transposing phase by 180°, making its behaviour with frequency more like time delay than a conventional fixed phase offset. That is the useful engineering idea. It is not a licence to call every internal angle a measured element delay. Its bandwidth and directionality still depend on topology, loads, line velocity factor, frequency and achieved currents. W8JI’s phasing-system discussion also shows why spatial phase and feed phase must track if an end-fire array is to retain its pattern across frequency.

Why a Table Can Start at the Back

W8JI’s transmitting four-square account places the phasing common point in the selected direction of maximum radiation. ON4UN’s 2005 Dayton four-square feeding presentation instead shows the back-element signal as its 0° reference, with the centre and front signals expressed relative to it. Other array sketches start from a no-delay branch at the front.

Those starting points are not contradictions by themselves. If two tables preserve the same physical element mapping, current magnitudes and relative current phases after normalization, they describe the same current state. If any of those conditions differ, “it is only a reference change” is no longer enough.

This is where Hugo’s reading and mine crossed. The disagreement was useful because it exposed the unstated convention. My rule now is simple: before debating an arrow or a phase number, make the author point to the physical element, the reference plane and the sign convention.

A Convention That Survives Hand-Off

Use fixed element names in switch tables. Reserve front and back for directions in the selected pattern. A compact table can then be unambiguous: “E1 current is the 0° reference at 3.600 MHz; phases use e^+jωt; positive angles lead; forward azimuth is 090° true; values are calibrated at the four element feed planes.”

Verify the Array, Not Just the Labels

1. Freeze the geometry. Record element coordinates, heights, orientation, feedline routes and the selected forward azimuth.
2. Declare the phasor convention. Name the reference element, reference plane, time sign and lead/lag usage.
3. Characterize the network. Measure amplitude and phase through every path at the calibrated planes across the intended band; include switch states, terminations and cable temperature where relevant.
4. Verify element currents. Measure current magnitude and phase at the feed planes, or validate the transfer function of the samples used as proxies.
5. Verify the pattern. Compare prediction with a controlled azimuth sweep, reciprocal remote-source test or suitable field measurement. Report main-lobe direction, front-to-back ratio and null depth across frequency.
6. Repeat after installation changes. Soil, structures, cable routing, coupling and component drift can move current balance and the resulting pattern.

NIST’s array-measurement work illustrates the broader principle: characterize the complete RF chain, remove known channel effects at declared reference planes, retain element locations and verify the array result. The frequency and hardware are different; the measurement discipline is the same.

Joeri’s Rule for Reading Any Phase Table

I no longer ask whether “front is zero” as if the sentence had one universal answer. I ask five smaller questions: Which way is front? Which physical element is this? What quantity is zero? Which sign convention is in use? Where was it verified?

If the table answers those questions, +240° and −120° stop looking like rival antennas. If it does not, even a correct network can become an argument waiting to happen.

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