KJ6ER Primer 2: More EIRP Is Not More Radiated Power

Greg Mihran, KJ6ER, invited my thoughts on his Antennas Primer 2: Antenna System Efficiency after our exchange about his first primer. My first response dealt with power accounting, ALC and tuners. Here I want to take his antenna tables seriously: what improvement do they actually describe, and what should another amateur take from them?

There is useful engineering in changing a radial arrangement or adding a parasitic reflector. My objection is not that directing energy is somehow a lesser achievement. Directing energy towards the station you want is precisely the point. The problem starts when directional gain becomes extra total radiated watts, a model percentage becomes a property of every installation, or a reference antenna is given a different comparison basis.

The Radial Comparison Already Tells a Better Story

Pages 23–24 and 27 compare the PERformer with two elevated radials separated by 180° and by 90°. These are two different arrangements of two radials, not a comparison between two radials and a large radial field.

The peak-gain increase is 0.95 dB. With the same accepted input power, that is about 24% more power density at the respective peaks. But the efficiency ratio in the table is only 90.29/89.51, or about 0.04 dB. If those efficiency values have the same physical meaning, almost all the reported gain change is therefore associated with redistribution over direction, not extra total radiation.

That last calculation checks the relationship between the published numbers; it does not independently validate their efficiency definition. The peaks also occur at slightly different elevations. To claim 0.95 dB more signal on one particular path, compare both patterns at that same elevation, bearing and polarization.

Notice something else: the elevation beam becomes wider, not narrower. That does not contradict a gain increase. The pattern is three-dimensional; concentrating the response in azimuth can accompany a broader elevation lobe. One beamwidth is not a complete measure of directivity.

The practical advantage is directional coverage. If the useful part of that pattern faces the wanted path, the change can help. If the path lies elsewhere, the peak number is not the answer. For a portable station, that is a reason to think about orientation, not to dismiss the radial arrangement.

A Reflector Is a Different Improvement

Page 21 compares the single-element PERformer with a two-element parasitic array. Greg specifies 21.225 MHz, a 52-inch feedpoint height, radials at 36 inches, and ground parameters of conductivity 0.008 S/m and relative permittivity 10. The reflector is a quarter wavelength away and labelled 2% longer.

The displayed gain changes from −0.71 to +2.40 dBi: 3.11 dB, with 7.8 dB front-to-back. The subtraction is correct, and a suitably coupled parasitic element can produce a genuine directional improvement. But this is the added-reflector comparison, not 3.11 dB supplied by merely turning the same two radials.

A useful lesson survives intact: extra conductor and controlled current phase can exchange coverage in unwanted directions for stronger coverage where it matters. The cost is space, orientation and sensitivity to the actual geometry. The result is an antenna pattern, not an amplifier hidden in the wire.

EIRP Is an Equivalent Directional Power

Page 26 correctly distinguishes the isotropic and half-wave-dipole references. The trouble is the page 27 summary, which describes EIRP as how much power radiates. That wording loses the essential word: equivalent.

Equivalent isotropically radiated power, or EIRP, describes how much power a lossless isotropic radiator would need to produce the same radiation intensity in the specified direction. It is not a sum of all the watts leaving the real antenna. The ITU's explanation of the radio-regulation definitions explicitly includes both antenna gain and direction.

Consider a deliberately simple illustration—not another measurement of Greg's antennas. Two antennas each accept 100 W and radiate 90 W. One has peak directivity 2; the other has peak directivity 3. Their peak EIRPs are 180 W and 270 W. Both still radiate 90 W in total. The second produces a stronger peak by distributing those watts differently.

Here θ and φ identify direction; G is gain and D is directivity in linear ratios. The equations require compatible power boundaries. Gain already includes radiation efficiency: multiplying by efficiency again would charge the same loss twice. Conversely, using incident rather than accepted antenna-port power requires a compatible realized-gain definition that includes the port mismatch.

ERP uses the ideal half-wave-dipole reference instead. For the same directional result, EIRP in dBW is ERP in dBW plus 2.15 dB, or EIRP in watts is approximately 1.64 times ERP in watts. We do not add “2.15 dBi” to a number of watts.

The station benefit is still real: more gain towards the other station increases the signal there for the same accepted power. It does not increase total radiation by the same factor, nor predict which ionospheric path is available.

The Efficiency Number Must Describe the Same Power Boundary

Greg's relationship G = ηD, or addition of efficiency in decibels, is sound when the quantities describe the same system. The difficulty over real ground is deciding exactly what a program's efficiency result includes.

The NEC output documentation describes a printed power budget in which radiated power is input power minus structure and network loss. Its structure-loss term is wire resistance; its network term accounts for network and transmission-line ports. That bookkeeping is not automatically the same calculation as integrating the power escaping into the distant sky above lossy earth.

That does not mean 4NEC2 offers only the raw power budget. Its own help documentation also describes a separate radiation-efficiency calculation from the full three-dimensional far field, accounting for ground, wire and other resistive losses. The distinction is between outputs and power boundaries, not between software that can and cannot consider ground loss.

Rudy Severns, N6LF, makes the latter boundary explicit in his elevated-ground-system study, printed page 37. He integrates power through a distant hemisphere, includes earth losses, and treats ground-wave power as outside that skywave account. That is a defined engineering question—not merely a percentage labelled “efficiency.”

This distinction matters when comparing an elevated system with a surface-radial system. A high percentage is not evidence that the same percentage escapes towards the ionosphere unless its denominator and loss boundary establish that. I cannot identify which output or derivation produced Greg's percentages from the tables alone. I can identify why mixing different definitions would invalidate the comparison.

A Negative Gain Is Fine; a Negative Maximum Directivity Needs Explaining

Page 24 subtracts the stated efficiency loss from gain and calls the result directivity. It gives −0.23 dBi for PERformer 180° and −0.03 dBi for Challenger; page 27 also gives −0.30 dBi for the reference vertical.

Negative gain is entirely possible. An inefficient antenna can have a peak gain below an isotropic reference. But conventional maximum total directivity has a different constraint: the strongest direction cannot be weaker than the average of all directions.

The standard definition, also used in Ansys's peak-directivity documentation, is radiation intensity divided by its full-pattern average. With U the total radiation intensity and dΩ a small solid angle:

If the table's figures are meant as that maximum, they cannot all retain the meanings assigned to them. This is a consistency check on the explanation, not proof of an impossible antenna or a defective solver. A nonpeak direction, a limited pattern cut, a single polarization component or a different ground/power normalization can produce a negative value without violating that rule.

The remedy is to reconcile the definitions before deriving one column from another. The NEC radiation-pattern controls distinguish power gain, directive gain, polarization components and angular averaging. A label alone does not establish which of those quantities was exported.

A Dipole Over Ground Is Not the Free-Space Reference

Page 39 describes a half-wave dipole half a wavelength above ground, but assigns it the familiar 2.15 dBi directivity of the ideal thin half-wave dipole in free space. Page 27 carries that reference into the comparison table.

The 2.15 dB conversion between dBi and dBd remains valid as a reference convention. It does not make every installed dipole a 2.15 dBi antenna. Ground reflection, height, direction and polarization determine the installed pattern; even a lossless dipole over ground is not the free-space pattern.

Comparing ground-dependent vertical patterns with a dipole assigned its free-space reference value is therefore not a like-for-like installed comparison. I would use the actual dipole pattern under the same environmental assumptions. There is no need to invent a replacement gain figure to recognise that requirement.

The 241-Watt Comparison Is Conditional, Not a Radial-Count Rule

Page 28 calculates that a ground-mounted quarter-wave with eight surface radials needs about 241 W to equal a 100 W PERformer with the 90° radial arrangement. Its displayed EIRPs are 39.4 W and 95.0 W:

That ratio is valid arithmetic. It shows what follows if the selected system gains, losses and power references hold. It does not establish a universal amplifier requirement for every eight-radial vertical. Radial length, height, soil, current distribution and the rest of the geometry are not encoded by the number eight.

Peak-to-peak EIRP also compares each antenna where it is strongest, not necessarily where the wanted station is. For a useful link comparison, use both antennas' gain in the same bearing, elevation and polarization, with the same feed-system power boundary. A 3 dB improvement there really is equivalent to roughly doubling transmitter power for that directional transmit comparison; it says nothing by itself about receive noise.

This is why I would retain the calculation as a worked conditional example, not use it as a buying or deployment rule. Improving a genuinely lossy ground system can be worth more than adding power. A good existing ground system has less loss left to recover.

RDF Is Useful, but It Is Not a Replacement Name for Gain

For reception, a useful pattern can improve readability by admitting less noise from unwanted directions. The receiving directivity factor, RDF, compares gain towards the wanted signal with an angularly averaged gain. L. B. Cebik's discussion of receiving directivity explains why a front-to-back reading from one cut cannot describe the whole receiving pattern.

The average must specify its angular region and polarization convention and use linear power values with solid-angle weighting. A uniform loss applied to the whole pattern cancels from this ratio. It does not cancel receiver-added noise or guarantee rejection of a particular nearby interferer.

I would therefore not replace “the radial arrangement adds gain” with “it only adds RDF.” Pattern redistribution can increase actual directional gain. Whether it also improves RDF requires the relevant three-dimensional pattern average; the listed front-to-back figure and elevation cut do not supply that number. Primer 2 does not give an RDF result for this comparison.

For a station troubled by interference from one direction, orienting a useful rejection region towards that interference can matter more than a small increase in peak transmit gain. For noise arriving with the wanted signal, that same pattern advantage may not help. Choose the pattern for the job.

Two Radials Can Be a Sensible Compromise

A portable operator has legitimate reasons to choose a small elevated radial system: less wire to deploy, a manageable footprint and the possibility of useful directional coverage. None of that requires an absolute efficiency promise.

Severns's work on asymmetry and radial currents shows the accompanying sensitivity: the radial fan, nearby conductors and unequal surroundings can change current division, loss and pattern. More radials can improve robustness against such asymmetries. That is an argument about engineering tolerance, not proof that two radials cannot work well.

Greg's own arrays offer another useful reminder. Page 27 assigns both the Dominator parasitic array and the Marauder parasitic array 3.53 dBi peak gain, yet gives them different peak elevations, beamwidths and front-to-back ratios. Equal peak EIRP is not equal coverage. The best choice depends on the direction and noise environment we actually want to serve.

Keep the Advantage; Describe It Correctly

My conclusion is not that modelling is useless or that comparisons are impossible. The published results already illustrate something worthwhile: geometry can redistribute radiation, improve a useful direction and change receive rejection. Those are proper antenna-engineering advantages.

What I would not carry into a station plan is a universal 90% efficiency attached to a radial count, total radiated watts inferred from peak EIRP, or an amplifier requirement detached from its model conditions. Definitions and arithmetic can be checked directly. Reproducing the exact geometry, loss allocation and convergence—and establishing the result at a real site—are separate jobs.

Choose the useful pattern, keep the power reference honest, and put the claimed advantage in the direction where you need it. That is a stronger practical lesson than reading a table of peak values as though one antenna wins everywhere.

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