- The free-space antenna factor is a property of the antenna alone. CISPR 16-1-6 and ANSI C63.5 define it in the same words: a plane wave arriving from boresight, in a free-space environment. The standard site method obtains it on a ground-plane site by calculating the ground out, then removing a small residual of up to 0.49 dB.
- Emission testing uses it, and only it. CISPR 16-1-4 requires the free-space factor from 30 MHz to 1 GHz, and CISPR 16-1-6 explains why: it is the best compromise against a separate factor for every height, polarisation and distance. What the ground does to the antenna during the 1 m to 4 m height scan is carried as an uncertainty in CISPR 16-4-2, not corrected: ±1.0 dB horizontal and ±0.3 dB vertical for a biconical below 200 MHz. ANSI C63.5 says the same from its first clause: a single antenna factor at each frequency, free-space or near-free-space, to be used for both polarisations and at any distance from 3 m.
- Calibrating at the test geometry adds error; it does not remove it. For C63.5's reference biconical, a factor calibrated at 3 m carries up to 0.9 dB in horizontal polarisation and 1.2 dB in vertical, against uncertainty allowances of ±1.0 dB and ±0.3 dB. The result is harder for another laboratory to reproduce, and three of the four calibrations were paid for without need.
- The GSCF belongs to site validation, and stays there. The theoretical NSA assumes two Hertzian dipoles, which is wrong by up to 2.39 dB for a pair of biconicals, and C63.5 corrects that comparison with a geometry-specific correction factor (GSCF). It states that GSCF results shall not be used to adjust emission antenna factors; a factor calibrated at the test geometry carries half of one inside it all the same.
What an antenna factor is
An antenna factor converts the voltage at the antenna's 50 Ω port into the field strength that produced it. In decibels it is simply the difference between the two, and an emission measurement adds it back:
AF = E − V → E = Vr + Lc + AF
where Vr is the receiver reading in dB(µV), Lc the cable loss and AF in dB(1/m). The antenna factor is the receiving-side view of the antenna's gain. For a matched 50 Ω load, AF = 9.73 / (λ·√G), where 9.73 = √(4π·η0/50) and η0 = 376.7 Ω. With the frequency in MHz this becomes the working form:
AF (dB/m) = 20·log FMHz − GdBi − 29.79
A half-wave dipole at 100 MHz, with its 2.15 dBi of gain, has AF = 40.00 − 2.15 − 29.79 = 8.06 dB(1/m). If the receiver reads 32.0 dB(µV) through a cable with 1.5 dB of loss, the field is 32.0 + 1.5 + 8.06 = 41.6 dB(µV/m). Every decibel of error in the antenna factor is a decibel of error in the reported emission, with nothing in between to dilute it.
Why “free space”
An antenna does not keep the same factor wherever it is put. Close to a conducting ground plane, its mirror image in the ground couples back into it, changing its input impedance and therefore the voltage it delivers for a given field. The change depends on the height, the polarisation, the frequency and the antenna's own construction. Near another antenna, the two couple to each other as well.
So a single antenna factor needs a definition of the setting it applies to, and the one setting that belongs to no particular site is free space. CISPR 16-1-6 and ANSI C63.5-2017 define the free-space antenna factor in the same terms: the ratio of field strength to voltage for a plane wave arriving from the direction of the antenna's mechanical boresight, measured in a free-space environment. CISPR writes it Fa, and gives the other quantity its own name and symbol: the height-dependent antenna factor, Fa(h,p), for an antenna at height h and polarisation p above the ground plane of an ideal open-area site. The free-space factor is a property of the antenna and nothing else, which is what makes it transferable: the same number is correct in any laboratory and on any site, because it describes none of them.
How it is measured: the standard site method
Nobody calibrates a biconical in actual free space. The standard site method (SSM) of ANSI C63.5 and CISPR 16-1-6 uses a ground-plane site and three antennas, measured in pairs. For each pair, the site attenuation A is the insertion loss between the two antennas, taken at the maximum of a receive-antenna height scan. C63.5 relates it to the two antenna factors through a term that is calculated rather than measured:
AF1 + AF2 = A12 + 20·log FMHz − 48.92 + EDmax
EDmax is the theoretical maximum field over the height scan for that geometry, from the direct and ground-reflected rays. That term is where the ground plane goes: its reflection is calculated out, not measured into the antennas. Three pairs give three equations, and solving them gives each antenna on its own:
AF1 = ½(A12 + A13 − A23) + 10·log FMHz − 24.46 + ½EDmax
C63.5 specifies the geometry that keeps the calculation honest, which it calls the near-free-space geometry: horizontal polarisation, R = 10 m, transmit antenna at 2 m, receive antenna scanned from 1 m to 4 m. None of those numbers is arbitrary. C63.5 prefers horizontal polarisation for four stated reasons: coupling between the antenna and its cable, which runs at right angles to it, is negligible; so is scattering from the cable; the horizontally polarised ground reflection depends less on the ground plane's conductivity and permittivity than the vertical one does; and reflections from the edge of the ground screen are smaller. CISPR 16-1-6 adds that a dipole-like antenna has a uniform pattern in the plane of the reflection, which is what makes the ground-reflected ray calculable at all. The distance and the height are there to starve the two couplings the calculation ignores: the separation has to be large enough to minimise near-field effects and coupling between the two antennas, and the heights great enough to minimise each antenna's coupling to the ground, which for a horizontal antenna matters below about 2.5 wavelengths. CISPR 16-1-6 notes that 10 m is enough for a biconical because at 30 MHz it is only 0.14 wavelengths long, at a cost of about 0.1 dB against 20 m. In that geometry what remains is small enough to tabulate. For a biconical, C63.5 Table G.1 gives the residual, and it is subtracted to reach the free-space factor:
AFFS = AFNFS − ΔAF
ΔAF is at most 0.49 dB for the 50 Ω biconical of C63.5 Figure G.1, and 0.25 dB for the 200 Ω version. Keep the ½ in the equation above in mind; it returns later.
CISPR 16-1-6 describes the same method in clause 8.4, with the same geometry: horizontal polarisation, 10 m or more, one antenna at 2 m and the other scanned from 1 m to 4 m, and three antennas of the same type and balun impedance. It is more guarded about the result. The SSM assumes an ideal site and infinitesimal dipoles, so the factor it gives can differ from the true free-space factor by up to ±1.2 dB until correction factors for the antenna type are applied, which for a biconical brings it typically to within ±0.3 dB. CISPR's preferred routes to Fa are the three-antenna method and the standard antenna method, at fixed heights or in a free-space environment; the SSM is permitted, with its correction. Both standards arrive at the same place: a ground-plane measurement is acceptable only once the ground has been taken back out.
Where the free-space factor is applied, and why nothing else is
For the antenna used in emission measurements, CISPR 16-1-4 leaves no room for choice between 30 MHz and 1 GHz: clause 4.5.1, in the clause on antennas for measuring radiated disturbance, says the antenna shall be a dipole-like antenna, and the free-space antenna factor shall be used. ANSI C63.5 makes the same requirement for measurements to the ASC C63 standards in clause 5.1.1. The reason is the measurement itself. In an emission test the transmitter is the product, whose pattern nobody knows in advance; the receive antenna is scanned from 1 m to 4 m in both polarisations; the distance may be 3 m or 10 m. There is no single geometry to correct for, because the geometry changes all the way up the mast.
The sketch below makes that concrete for typical tabletop equipment, placed on the usual 0.8 m table. Move the antenna up the mast and change the frequency: the angles at which the two rays arrive, the way they combine, and the antenna's electrical height above the ground plane all shift together.
The model is for typical tabletop equipment: a small source at the 0.8 m table height over an ideal ground plane, with the standard two-ray expressions behind the NSA tables. Floor-standing equipment sits lower and changes every number. It illustrates the geometry and does not predict any real product.
One test passes through all of these conditions, and which of them matters is decided by the product and the frequency, not by the laboratory. At 30 MHz and 1 m the antenna is a tenth of a wavelength above the ground plane; at 1 GHz and 4 m it is more than thirteen wavelengths up, looking down at the product at 47° on a 3 m site. A factor calibrated at any one geometry matches one point in that space and is off by an unknown amount everywhere else. The free-space factor carries nothing of the site at all, and what the site adds is bounded and put into the uncertainty budget.
CISPR 16-1-6 sets out the choice in clause 4.2 and Annex A.4.1: rather than a separate factor for every height, polarisation and distance, it chooses the free-space antenna factor, which it writes Fa, as the “best compromise” and puts the rest in the uncertainty budget. CISPR 16-4-2 carries that decision through by treating the effect as an uncertainty, not a correction. Its comment D2 explains that the antenna factor varies through coupling with its image in the ground plane, and that over a height scan the average is close to the free-space factor. The remaining deviation, δFah, goes into the uncertainty budget as a rectangular distribution: ±1.0 dB for horizontal polarisation and ±0.3 dB for vertical, for a biconical from 30 MHz to 200 MHz, and negligible above 300 MHz. That is the pattern the whole emission uncertainty budget follows: correct for what is known, which is the free-space factor, and carry what varies as uncertainty.
The free-space factor is itself usually measured over a ground plane, which may look like the same thing. It is not. It is measured in the one geometry where the ground can be calculated out cleanly, 10 m in horizontal polarisation with the transmit antenna at 2 m, and the small residual that remains is tabulated and subtracted. At 3 m, or in vertical polarisation, the simple model no longer holds, the residual is larger, two to four times at 3 m, and no standard provides a way to remove it. It stays inside the factor.
Calibrating at the test geometry: why it looks right, and is not
Some laboratories go the other way. They have the antenna calibrated at the distances and polarisations they actually test in, typically a 3 m factor and a 10 m factor, sometimes one for each polarisation, and apply whichever matches the test. It looks like the more careful approach: the calibration resembles the test, so the factor ought to be closer to the truth.
It is the opposite, for the reason just given. A factor calibrated at 3 m, or in vertical polarisation, still has that larger, unremoved residual inside it, and from there it goes into every emission result. It is not a more accurate antenna factor. It is the free-space factor plus an uncorrected error from the calibration site.
ANSI C63.5 rules the practice out in as many words. Its scope clause obtains harmonisation with the international standards by requiring a single measured antenna factor at each frequency, free-space or near-free-space. Clause 4.1 then says where that one factor applies: these antenna factors “shall be used for either vertically polarized or horizontally polarized measurements”, at distances of 3 m or more from the product. One factor, both polarisations, every distance from 3 m up. For a biconical it is the free-space factor, reached with the Annex G correction; for LPDAs and hybrids C63.5 uses the near-free-space factor as it stands.
How large is that error? From the figures C63.5-2017 computes for its reference biconical, the error a calibration at each of the four geometries leaves in the antenna factor can be worked out; the next section shows how. The reference is the geometry the free-space factor comes from: 10 m, horizontal, the other antenna at 2 m. The other three are taken with the other antenna at 2 m in horizontal polarisation and at 1.5 m in vertical, and a calibration made with it at a different height gives yet another factor. Because E = V + AF, whatever the factor carries goes into every emission result. Choose the geometry your factor was calibrated at:
Two things stand out. The four factors really are different, by more than 1 dB at some frequencies, which is what makes the practice look like diligence: the laboratory sees the numbers disagree and concludes that the matching one must be the right one. But only one of them is the free-space factor the measurement is defined with, and what separates the other three from it is not a property of the antenna. It is the second biconical a few metres away, the near-field terms and the ground coupling of a calibration set-up that no emission test reproduces, since the source is now a product with an unknown pattern and the antenna is scanned over 1 m to 4 m. At 3 m in horizontal polarisation the added error takes up nearly all of the height allowance the emission uncertainty budget carries; at 3 m in vertical polarisation it is four times the ±0.3 dB allowed. No uncertainty statement mentions either.
The practice has an honest pedigree, which is why it persists, and the editions of C63.5 tell the story. The first, in 1988, included antenna calibration at 3 m and information on vertical polarisation; when the standard site method was put forward to CISPR from 1993, both were judged unacceptable. The 1998 edition dropped vertical polarisation and made 10 m with the transmit antenna at 2 m the preferred, international geometry, but it kept three more horizontal geometries as a US national deviation: 3 m and 10 m, each with the transmit antenna at 1 m or at 2 m. It treated all four results as near-free-space factors, on the grounds that the variation between them stayed within ±1 dB. By the 2006 edition only the single geometry remained, 10 m and 2 m, with a table to take a biconical the rest of the way to free space. A laboratory that asks for a 3 m antenna factor for its 3 m testing today is following a convention that the standard which created it had withdrawn by 2006.
There is a reading of that history which explains why the convention felt right for so long, though it is our inference and not something the standard says. The four geometries of 1998 are the horizontal geometries of the NSA measurement. A pair of antennas calibrated in the same geometry as the NSA they are about to perform carries that geometry's error inside their two factors, where it cancels the matching error in the theory: a geometry-matched factor is, in effect, the site-validation correction of the next section, the GSCF, applied before the term existed. For site validation it was the right tool. The mistake was to carry the habit across to product testing, where there is no matching geometry for it to cancel against.
Any antenna factor that was not calibrated as a free-space antenna factor adds an error of its own to every emission measurement made with it. How large that error is depends on the geometry the calibration laboratory happened to use.
The curves above are for a biconical, the antenna the standards have numbers for. For a hybrid, CISPR 16-4-2 treats the antenna as a biconical up to about 100 MHz, as an LPDA above about 200 MHz, and as a linear transition in between, with the height dependence of the antenna factor shrinking through the transition; CISPR 16-1-6 puts the transition of typical models between 140 MHz and 240 MHz. So below about 100 MHz a hybrid calibrated at a specific geometry should be expected to behave like the curves above, and progressively less so towards 200 MHz. C63.5 provides no calculated GSCF for hybrids, so there is no table to draw their curves from; the numbers have to be measured for the pair.
For a hybrid the factor changes even more with the calibration geometry, mainly because of its length. CISPR 16-1-4 notes that with the marks of two typical hybrids 10 m apart, their phase centres are about 11.2 m apart; with the marks at 3 m the gap is proportionally far larger, and the log-periodic part is too directive for the two-ray model the SSM relies on. But not all of that change is error. The phase-centre part is a real distance effect, and CISPR 16-1-6 corrects it by calculation from the antenna's dimensions. A factor calibrated at 3 m mixes it inseparably with coupling and pattern effects that belong to the calibration set-up. The sound route for a hybrid is the free-space factor plus a calculated phase-centre correction for the test distance.
Why site validation is different, and why its correction stays there
Normalised site attenuation checks a site by comparing a measurement with a theory. Two antennas are set up at a defined geometry, the site attenuation between them is measured, their antenna factors are subtracted, and what remains should match the theoretical value for an ideal site within ±4 dB. C63.5 writes the equation for a pair of biconicals with one extra term:
AN = VDIRECT − VSITE − AFT,FS − AFR,FS − GSCF
The extra term exists because the theory is not the antennas. The theoretical NSA tables of CISPR 16-1-4 and ANSI C63.4 are calculated for two infinitesimally small Hertzian dipoles in each other's far field. C63.5 Annex H lists what that leaves out: the 1/r² and 1/r³ terms, the coupling between the two antennas, the coupling of each antenna to the ground plane, the real radiation patterns, and the non-uniform illumination of the receive antenna. CISPR 16-1-4 makes the same diagnosis in clause 6.5.2: using free-space factors in the NSA calculation causes errors, particularly for biconical and tuned dipole antennas below 300 MHz, because the model is a Hertzian dipole and not the antenna actually used.
The size of the difference is not small against a ±4 dB tolerance. C63.5 Table H.1 gives the error for a pair of biconicals from 30 MHz to 200 MHz:
| Polarisation | R | Transmit height | Error, dB |
|---|---|---|---|
| Horizontal | 3 m | 1.0 m | 2.00 |
| Horizontal | 3 m | 2.0 m | 1.76 |
| Vertical | 3 m | 1.0 m | 1.83 |
| Vertical | 3 m | 1.5 m | 2.39 |
| Horizontal | 10 m | 1.0 m | 1.24 |
| Horizontal | 10 m | 2.0 m | 0.98 |
| Vertical | 10 m | 1.0 m | 1.47 |
| Vertical | 10 m | 1.5 m | 1.17 |
Up to 2.4 dB of a 4 dB tolerance is systematic error from the model, before the site has had any say. A good chamber can fail on it, and a poor one can pass because it happens to lean the other way. Because the NSA geometry is fixed and both antennas are known, the error can be calculated: C63.5 Annex G tabulates NEC-computed GSCFs for its reference biconical, at 3 m and 10 m, for 50 Ω and 200 Ω baluns, and Annex I gives a measurement method for LPDAs, hybrids and biconicals outside the Figure G.1 dimensions. C63.5 also requires the two NSA antennas to have been calibrated together, as a pair, by the standard site method.
That correction stays where it was made. C63.5 Annex I says its GSCF method does not improve the antenna factors used for radiated emission measurements, and that GSCF results “shall not be used to adjust these AFs”. No laboratory would do that knowingly. A factor calibrated at the test geometry has done it already. The SSM and the NSA are the same equation read in opposite directions: the SSM assumes the theoretical site attenuation and solves for the antenna factors, while the true site attenuation at a geometry g is the theoretical one plus the two free-space factors plus GSCF(g). Whatever the theory leaves out at that geometry lands in the sum of the two antenna factors, and the ½ in the SSM solution gives each antenna half of it:
AFg − AFFS ≈ ½·GSCF(g)
C63.5's own tables confirm it. Table G.1, the ΔAF that takes the standard geometry to free space, is exactly half of the GSCF column of Table G.2 for that same geometry: at 65 MHz with a 50 Ω balun, 0.49 dB against 0.98 dB. Those halves are the curves in the visualiser above. Three things make the GSCF right for the NSA and wrong inside an emission antenna factor:
- It belongs to a pair, not an antenna. A GSCF describes two specific antennas at a specific geometry. In an emission test there is only one of them; the transmitter is the product, not a second biconical.
- It corrects a theory the emission test never uses. The GSCF is the gap between a Hertzian-dipole model and real antennas. An emission measurement is not compared with that model, so there is no gap to close.
- The site is already in the uncertainty budget. CISPR 16-4-2 carries the imperfect site as its own term, δAN, and the antenna's height behaviour as δFah. Carrying part of a GSCF inside the antenna factor counts the site a second time, invisibly.
What to check in your records
Accuracy aside: what a standard is for
There is a wider point here than a decibel of error. Set aside, for a moment, which antenna factor is closer to the truth. A radiated emission limit means something only because every laboratory measures against it in the same way: the same antenna factor, the same height scan, the same uncertainty budget. That shared method is what allows a result from one laboratory to be repeated in another, and it is what a standard everybody has agreed to is for. A laboratory that departs from it because its own approach seems more accurate has not made its result better. It has made it a result that no laboratory following the standard will reproduce.
It also pays more for that result than it needs to. Every additional geometry is another calibration to be paid for, so a laboratory that orders four antenna factors is paying for three it should not be using.
Testing to an agreed standard is about repeatability first. A deviation made in the name of accuracy works against it, however well meant.
Keeping the free-space factor and the site-validation correction apart is mostly a question of what goes on the certificate and what goes into the NSA report, and both are decided at the calibration. We calibrate antennas by the standard site method and report the free-space factor that emission measurements require; in site validation, the NSA calculation is the one place where a geometry-specific correction belongs, and the report should say which one was used. Our antenna calibration and site validation are carried out under LAB Support Ltd's A2LA accreditation.
One antenna factor per antenna, and it is the free-space one; one correction per NSA geometry, and it stays in the NSA. If a certificate or a test system mixes the two, we would rather point it out than calibrate around it. See antenna calibration and site validation for what we measure and how.
“Let there be one measure of wine throughout our whole realm…”
The case for one agreed measure is eight centuries old. A free-space antenna factor is the same idea, applied to an antenna.