Dear Steve and Jerry,
I think I might not have been clear in my original post about the 3 dB
gain "error" in NEC. The moment method codes like NEC, EZNEC, Mininec,
and all of their variants are calculating gain in dBi correctly. I
cannot access the "IEEE Standard Definitions of Terms for Antennas"
right now, but I am sure that it states or implies that gain measured
in dBi is always referenced to an isotropic radiator in free space
whether the antenna being modeled is over a ground plane or not. It
has to be this way; otherwise, it could create untold confusion. What
I was saying in my original post (and I think Jerry agrees) is that to
be "fair," one should compare an antenna mounted over ground to an
isotropic radiator radiating into a half-space (a "hemi-isotropic"
radiator?). However, there is no standard gain unit defined this way.
However one chooses to define the terms, NEC and its variants do
calculate the correct fields, and they corroborate with the standard
definition of the dBi unit. A concrete example might help:
Imagine a 1-kW transmitter feeding a 1/4-wave monopole over perfect
ground. The transmitter is perfectly matched to the antenna, so all of
the 1 kW of power is radiated. EZNEC predicts that the electric field
right at the horizon (0 degrees of elevation) at a distance of 1 km
from the antenna is 313 mV/m (rms). That translates to a maximum power
density (S_max) of 260 microwatts per square meter, using
S_max = E^2/eta,
where E is the rms value of the electric field, and eta is the
intrinsic impedance of free space (377 ohms).
The gain of the monopole reported by EZNEC is 5.14 dBi (a multiplying
factor of 3.27), which means that in the direction of maximum
radiation, the power density should be 3.27 times that of an isotropic
radiator for the same input power. For a 1-kW input power (Pin) and a
distance (r) of 1 km, using
S_iso = Pin/(4*pi*r^2) [for a full sphere],
the power density from an isotropic radiator would be 79.6 microwatts
per square meter. If we multiply S_iso by the 3.27 (5.14 dBi) gain of
the monopole reported by EZNEC, we get
(79.6 microwatts/m^2)*(3.27) = 260 microwatts/m^2,
which is exactly the maximum power density that EZNEC predicts for the
monopole as derived from the calculated electric field data.
It doesn't seem "fair" to compare the fields radiated by an antenna
over a ground plane to a free space isotropic radiator, but that is
the standard definition as adopted by the IEEE (with the guidance of
the Antennas and Propagation Society), and so that is what all of the
antenna analysis software uses. The advantage of the standard
definition is that one can predict the actual power density or
electric field at a given distance from an antenna knowing nothing
more than the antenna's gain and the input power.
73,
Dave ND3K
> Jerry,
>
> I can understand that the interpretation of dBi which appears in most
> engineering texts (and possibly the IEEE definition?) throws up
> conundrums with which you are uncomfortable. But what I think is unfair
> is to claim that EZNEC is in error, simply because it adopts the
> "industry standard" interpretation rather than an alternative that you
> might prefer.
>
> I make widespread use of EZNEC, and when I saw someone as authoritative
> as yourself state that it is 3dB in error I felt it needed further
> investigation!
>
> 73,
> Steve G3TXQ
>
> On 08/01/2011 00:20, Dr. Gerald N. Johnson wrote:
>> My conundrum is that I expect equal power intensity at the the measuring
>> point from the isotropic source whether a ground plane is involved or
>> not and that I also expect equal intensity from a vertical dipole in
>> free space and a quarter wave vertical on the ground plane (except for
>> the ground absorption at the real ground plane).
>>
>
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