Richard Fry wrote:
"K7ITM" wrote
Assuming the two "waves" existed independently at some points
in space, you'll have to first tell us _exactly_ what was done to
combine them into one wave.
__________

The physics of EM radiation.

As an example, consider an array comprised of two, identical radiators
on the same vertical axis, in the same physical orientation, with a
vertical separation of 1 wavelength, each driven with equal r-f power
and relative phase by the same r-f source.

The fields from the two radiators are generated and radiated separately,
but once well past the near-field boundary of the array, the EM field
existing at every point in free space will be the vector sum of those
separate fields.

When the net field at the radiation peak of the array is measured in the
far field, there will be no way to determine from that measurement
whether the field was generated using a single radiator with X power
input, or the described 2-element array having about 1/2 that power input.

RF

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate

Dave wrote:
Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate
0 Infinity
is interpreted as zero times infinity

Dave wrote:
Dave wrote:
Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate
0 Infinity
is interpreted as zero times infinity


That's the rule all right. Notice, however, that I said, "in the limit."
Does Mathematica teach you about taking limits and such?
73,
Tom Donaly, KA6RUH

Tom Donaly wrote
So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would go to
zero.
____________

As the number of radiators in a given array never can reach infinity,
neither will the input power for a given peak ERP from that array ever go to
zero. Obviously there are practical limits as well.

But this does not change the realities that...

1) other things equal, the greater the number of discrete radiators in an
array, the less input power is needed for that array to produce a given peak
ERP, and

2) the peak free-space, far field produced by a given ERP is the same for
all combinations of antenna gain and antenna input power producing that ERP.

This has been proven in commercial FM and TV broadcast systems for many
decades.

RF