[TowerTalk] P-P voltage on an antenna

[Jim Lux]

At 10:57 AM 2/3/2004 -0500, Eric Scace K3NA wrote:
>    W1MK and I wonder if anyone can point us to an authoritative reference 
> for an answer to these two questions:
>
>1.  An antenna model predicts a current of I amps at a particular segment 
>on an antenna.  What is the maximum (peak) RF voltage V
>that will be found at that location on the antenna?
>
>    The practical application is to understand what voltage must be 
> tolerated by any support (e.g., insulator and guy wire) attached
>to the antenna at that point.
>
>2.  Similarly, what is the maximum (peak) RF voltage V to be found at the 
>tip of an antenna element?
>
>    I'm sure there is a way to calculate this ... but I can't lay my hands 
> on it quickly.
>
>-- Eric K3NA


This is actually tougher to calculate than you think.  You might get a 
start by looking up or calculating what the feed point impedance of an "end 
fed" half wave is, for the dimensions of your antenna (typically a few 
thousand ohms).  Then, if you know the power, you can calculate the voltage 
from E = sqrt(P*magnitude(Z)).  This would probably give you an "upper bound".

In a real antenna, near other real objects, you need to consider that there 
are image charges in those neighboring objects, the fields of which tend to 
cancel the fields from the antenna, reducing the local E field.

One way to approach it is to generate the near field data (E field) then 
sum the values moving away from the antenna towards "free space".  The 
voltage is the sum of all the "distance * volts/meter" numbers.  The 
problem is that the field drops off quite quickly as you move away from the 
element, so the numerical integration approach may give you an under 
estimate.  The other sticky part of this can of worms is that the fields 
you're summing are also not all in phase (so it's not like calculating DC 
fields).

For a rough approximation, where the distance involved is very small 
compared to a wavelength, you can probably safely assume that the phase is 
constant, and just sum.

You can also calculate the voltage from the charge that is moving 
around.  If you know the charge distribution, you can calculate the voltage 
(again, by numerical integration) (which is essentially how the near fields 
are calculated in NEC, anyway).

I'm sure there's a detailed analytical treatment of a trivial case (i.e. a 
short dipole) in the usual electromagnetics texts (e.g. Balanis, Kraus) 
although I don't recall it in Kraus, at least in an explicit form.

The upshot, though, is that there isn't a nice equation for this.

Jim, W6RMK