Roomcap -THEORY Remarks1                                                                             
7.July 2014 UPD: July 29th 14                                                                               
Felix Meyer HB9ABX                                                                                    

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 efficiency.

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 radiated:

This fomula leads to the wong conclusion: higher Rs = higher radiation power
This would means, that you always would have the same current I ... 
therefore a construction is searched, where a higher Rs is searched!
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 better solutions.

(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 loss-resistance)


This most important: greatest relation of  Rs to Rv !

Note: The amount of Rs alone says nothing about the quality of the antenna.

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 ground.
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 ground-current.

Therefore, we need for the Roomcap a short length for the "counter plane". 
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!  <<<

Next step:

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 eta(A).

The result tells, why this good signal reports results for Roomcap! 


Now have a look at W8JI, the best known expert from ARRL for antennas.
He published articles about short antennas. See  HERE 
(in PDF)
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 Marconi.


>>> 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 different parts.
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.

It's ringing ?   >>> I hope!