Dear John, LF group
Some comments on John's queries about ERP and measuring antenna efficiency
- if of no interest, please delete now!
The first thing is to be clear about what is meant by ERP. There are
different ways of expressing it, but what they amount to is that ERP is the
amount of power fed into an ideal reference antenna, in an ideal
environment and at the same distance from the receiver as the actual
antenna, that would produce the same field strength as the actual antenna.
Thus ERP is not really a measurement of power at all, but a measurement of
field strength with the implicit assumption that the field strength is
proportional to the square root of the transmitted power and inversely
proportional to distance. Knowing ERP tells you how strong the received
signal should be at a given distance, which is usually the most important
thing, but is not directly connected with the radiated power, or the
antenna that is radiating.
The type of reference antenna is purely a matter of convenience - for
instance, an isotropic antenna does not exist, but it is easy to calculate
the field strength it would produce if it did, and therefore EIRP. A good
approximation to a dipole in free space is possible at UHF, and is a
convenient standard antenna, but of course at LF you can never get far
enough from the ground to get the same behaviour as in free space, even if
you could somehow put up the dipole. Nonetheless, you can still easily
calculate the power you would need to feed in to an orbiting LF dipole, to
get the same field strength in your fictional space ship 1 mile away, as
you are measuring while standing on the ground 1 mile from a real
transmitting antenna, and this would be the ERP (EDRP) of that particular
signal. This is relevant to us because the UK amateur radio regulations
define maximum power output on LF as ERP specifically with reference to a
dipole. A short, ideal monopole over a perfect ground plane is probably
the most practical LF reference antenna - it does not exist either, but at
least over a limited range of distances, a very efficient, well sited
vertical ant produces something close to the same field strength and
directional pattern as the theoretical monopole would. Once again, the
important thing is that it is easy to calculate what field strength would
be produced by the theoretical reference antenna.
For an isotropic antenna it is easy to work out the relation between
radiated power, distance, and field strength, since the power density is
uniform and independent of direction. The same amount of power applied to
an ideal dipole in free space would produce a greater field strength
because the dipole has directive gain; the ERP is defined in terms of field
strength produced in the direction of maximum radiation. It is quite
complicated to calculate the directivity of an antenna, but you can find
the details in any antenna theory text, and the directivity of a dipole is
about 1.67, whilst by definition directivity of an isotropic antenna is 1.
So for a given power, the dipole will give 1.67 times the power density, or
sqrt(1.67) times the E field strength. Or, for the same field strength, the
input power required is 1.67 times less than an isotropic antenna.
similarly, a short monopole with a perfect ground plane has a directivity
of 3. The formulas relating ERP, EIRP, and EMRP to field strength E and
distance r are:
EIRP = (E*r)^2 /30; E = sqrt(30*EIRP) /r
ERP = (E*r)^2 /50, =EIRP/1.67 E = 7*sqrt(ERP) /r
EMRP = (E*r)^2 /90, =EIRP/3; E = sqrt(90*EMRP) /r
EIRP, ERP, and EMRP therefore differ more or less by the factors John gave,
which are the directivities of the different reference antennas. Once
again, it does not matter whether you use ERP, EIRP, or EMRP provided you
are consistent - since they are just measures of the field strength;
exactly how the field is generated is not important. So the type of
transmitting antenna actually in use, or how efficient it is, is not an issue
The efficiency of an antenna is a bit harder to define. One definition
would be the ratio of power radiated to total power fed into the antenna.
This is the same as Rrad/(Rloss+Rrad), however while it is fairly easy to
measure Rloss+Rrad, the resistive part of the antenna impedance, it is not
possible to directly determine Rrad. One approach is to calculate Rrad,
using one of the formulas or numerical modelling techniques like NEC.
Calculating Rrad assumes a knowledge of the current distribution in the
antenna, and this depends on many unknowns for typical amateur antennas -
influence of trees, buildings, ground conductivity etc, etc. So in less
than ideal sites, the calculation is at best an approximation. If we assume
that the effective height of John's antenna is about 8m, we can calculate
Rrad = 160*pi^2*(h/lambda)^2, = 21milliohms.
Another approach is to infer a value of Prad or Rrad by measuring the
field strength and calculating the ERP. To get from this to the actual
power radiated by the antenna, you have to assume a value for the
directivity of the antenna, since the radiated power required to produce
this field strength depends on the directivity. The best assumption for a
tuned vertical antenna is that it has the same directivity as an ideal
monopole - practical experiments show this is fairly close to the truth. If
we then calculate the EMRP (not ERP or EIRP) from the field strength it is
the same as the radiated power from the antenna, Prad. Prad is the power
which we would need to feed into the antenna to get the measured field
strength if the antenna was 100% efficient.The radiation resistance can
then be calculated if the antenna current Iant is known; Rrad =
Prad/Iant^2. Or we could calculate the efficiency directly from the
transmitter power output, Ptx; Efficiency = Prad/Ptx. Then again, if we
know Ptx, Prad, and Rloss, Rrad is very nearly Rloss*Prad / Ptx. So in
John's case, 10uV/m at 63km gives an EMRP using the formula above of 4.4mW,
and the efficiency is 4.4mW / 200W = 0.0022%. Rloss is 93 ohms, so Rrad is
93ohms * 4.4mW/200W = 2milliohms.
There is usually a difference between Rrad and Prad determined from field
strength measurements, and calculations from antenna geometry.The
difference between the radiated power calculated from what is going in to
the antenna, and that calculated from field strength measurements has been
called "site loss"; the site loss in John's case is about 10dB - quite high
compared to mine of around 3dB, but similar to G3XDV's antenna. Quite what
happens to the missing power is not clear - The argument is clouded also by
the many uncertainties and unknown factors. For example, it is difficult to
find out just how much antenna current is going down a nearby tree, and so
find out what effect that has on radiation. The field strength measurements
I did showed apparently random, but consistent variations of a few decibels
in field strength from one place to another. In my case, with site loss of
only a few dB, so it is hard to know if it is a real effect or not -
although the fact that most people measure lower field strengths than they
expect suggests that it does exist. But the practical upshot is that it all
adds to the difficulty of obtaining high ERP.
Hope this is helpful and not too long - have now forgotten what I started
out to do!
Cheers, Jim Moritz
73 de M0BMU
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