Why does Kraus include both A and r in his equation for a small-loop antenna?

[qnach]

I am reading Kraus' book on Antenna, Chapter 6.
I think Eq. (8) and (9) is his solution for the far field of a small-loop antenna.
However, why does he need A (the area) and r both in the equation (8)?
A= \pi r^2 and can be simplified?

 

[the_emi_guy]

It would be best if you attach the equation in question.

My guess is:
"A" is the area of the loop antenna
"r" is the distance from the center of the loop antenna to the point of far field measurement

 

[qnach]

It would be best if you attach the equation in question.

My guess is:
"A" is the area of the loop antenna
"r" is the distance from the center of the loop antenna to the point of far field measurement

o.k. I attached that page of Eq. (8) and (9)
But I think that is no use. I know the definition of A and r
But my question is why did he keep it without canceling out.

 

[Baluncore]

However, why does he need A (the area) and r both in the equation (8)?
A= \pi r^2 and can be simplified?

The loop radius was a. The distance from the dipole was r. The radius of the loop was NOT r.
Since a does not appear in the equation, what can you possibly cancel ?

The term A / λ² is a pure ratio. It is the aperture in wavelengths. It appears as a recognisable term with many antenna configurations. If it could be canceled now it would have to be extracted again later, when any shaped loop is considered.

 

[the_emi_guy]

...
But I think that is no use. I know the definition of A and r
But my question is why did he keep it without canceling out.

I think we are having a hard time figuring out why you think A and r can cancel. You are right, the definitions of A and r are clearly stated in the text that you attached:
"r is the distance from the dipole" , "...the area A of the loop..."

But A=πr² only applies if A and r are part of the same circle right?

Let A be the area of my yard, and r be the distance from the Earth to the Sun, can these cancel?

 

[qnach]

I think we are having a hard time figuring out why you think A and r can cancel. You are right, the definitions of A and r are clearly stated in the text that you attached:
"r is the distance from the dipole" , "...the area A of the loop..."

But A=πr² only applies if A and r are part of the same circle right?

Let A be the area of my yard, and r be the distance from the Earth to the Sun, can these cancel?

sorry, I mixed up the symbols, since I can only read the book from my screen...

 

[qnach]

The loop radius was a. The distance from the dipole was r. The radius of the loop was NOT r.
Since a does not appear in the equation, what can you possibly cancel ?

The term A / λ² is a pure ratio. It is the aperture in wavelengths. It appears as a recognisable term with many antenna configurations. If it could be canceled now it would have to be extracted again later, when any shaped loop is considered.

I have a further question about the r and the retarded current I.
Since I am considering the receiving antenna, the wave come from infinity.
So, how should the r be defined? Should it be infinity? And, the retarded I does not seems to be meaningful?

 

[Baluncore]

Consider a reference plane, perpendicular to the direction of r, in or near to the antenna. The retarded element currents are sinusoidal currents with phase shifts measured relative to that reference plane. All retarded element currents can then be summed as phasors in the direction of r. That gives both the receive and transmit antenna pattern.

The range, r, allows for the reduction in energy per square meter with range as the energy is radiated over a greater spherical surface. If you make r infinite the energy will be zero.

Now go back to chapter 5 in Kraus, on short dipoles. On page 203, fig 5-3b you will see a reference plane and the independent definition of r and the retarded currents.

Learning about loop antennas backwards is a very inefficient way of modelling photosynthesis.