7.July 2014 UPD: July 29th 14
Calculations and explanations to
Radiation Resistance / Efficiency
The radiation resistance is often wrongly
understood, with the opinion, that an
antenna with the higher radiation resistance means a higher
Many theory books and teachers say, that a higher radiation
resistance Rs = Rrad (serial)
leads to a better antenna.
Here the formula Rrad =radiation resistance
(depends of the type of dipole)
(vereinfacht = simplified)
And: Ps = Radiation power (Rs = Rrad)
Radiation power Ps: into the far-field radiated power
This fomula leads to the wong conclusion: higher Rs = higher
This would means, that you always would have the same current
therefore a construction is searched, where a higher Rs is
Thereby the efficiency can to decrease!
The the wrong conclusion made also ON4UN
(Low Band DX), and thereby some
super large antennas originated, who did not offer any
(Here the equivalent circuit, where Rrad (= Rs)
and Rloss (= Rv) are in serial.
X stays for the inductiv or capacitiv reactance)
The best antenna is found by seaching the highest efficiency eta(A).
Here the formula of the efficiency:
(Rs = radiation resistance, Rv = total
This most important:
greatest relation of Rs to Rv
Note: The amount of Rs alone says nothing about the quality of
Therefore the efficience of the Roomcap is high, as we have
a high relation Rs/Rv.
To obtain a high eta, look to
have a low Rv.
The loss-resistance Rv = addition of ground-loss-resistance
and loss of antenna.
Here you see the ground loss Rg:
Most at a classic antenna is gone lossed in the
ground, because the loss of the
antenna current is lost on the way back to the antenna in
Therefore, they recommend to lay many radials, in order to
lower the ground-
Rg = ground-resistance
Here you see, how the Rg depends from the number of the
radials, and from the length
of the radials.
The spatial progation of the ways of the return current
depends from the length
of the antenna. The most ground-current fields come back
within a distance
of 1.5 length of the antenna.
Therefore, as smaller the antenna, so shorter way goes the
Therefore, we need for the Roomcap a short length for the
Besides we do not use radials, instead of them we have a
"counter plane", in the length
of about 2.25m.
Thereby the Rg of a "classic antenna" is between 5 to 30 Ohms.
We obtain a ground resistance Rg below
1 Ohm for the Roomcap! <<<
Here to the Rs radiation resistance
Above indicated formulas, who result by derivation of Maxell's
equations for the
"current in wire".
The table from D.Jefferies (University of Surrey) here
there you see, that the Rrad is smaller than 0.5 Ohms for
L/lambda of 1/20 wave length,
(L = length of the antenna) in according with the "current
in wire" method.
With the method "current over planes" with an area of
1m x 1m size, I obtain a
radiation resistance Rs of abt. 5 Ohms at 7 MHz.
More than 10 times more !
And now you apply the formulas to obtain the efficiency
The result tells, why this good
signal reports results for Roomcap!
Now have a look at W8JI, the best known expert from ARRL for
He published articles about short antennas. See HERE (in
He obtaines a Rg (ground loss resistance) of 11 Ohms. Study
his report, and read
what efficiency is calculated with "current in wire" method.
This demonstrates, that today we need a progress after we are
using "current in
wire" over 110 years. Since Heinrich Hertz and Guglielmo
NEW: 10th July 2014
Here we see the precise calculation
of the efficient : Roomcap
This antenna is working as parallel circuit, therfore one has
to learn how
to calculate in parallel equivalent circuit diagram.
Here we work with parallel radiation resistance.
Below you see an extract of the analyse :
And note: The correct value of the SWR is 2.62
for bandwidth reading at F1 and F2!
I ask you to refresh your electric and math knowledge to
understand the calculation of
the diagram, and to understand the correlation of the
You have to study of the referenc above (VE2AZX-Q-factor.pdf).
PS: The complete analyse you find HERE
However, then you can learn a big amount.
I ask you to write me, if you have more questions.
ringing ? >>>