[TowerTalk] Fwd: Peak Voltage at the tips of ants ?

[Lux, Jim]

On 10/4/22 9:14 AM, Larry Banks via TowerTalk wrote:
> Good point Jim!   I wonder what the "ideal" characteristics of an 
> antenna are that would radiate 100% of the energy near the earth?   Is 
> this true in free space?

yes.. The power radiated is related to the current, and since the 
current is highest at the feedpoint (for a half wave dipole) that's the 
part that radiates the most.

That's why shortened antennas with capacity hats and loading radiate 
pretty much as well as a full size antenna.  The inefficiencies are in 
the resistive losses (since they go as I^2).

As you get shorter, the current along the antenna becomes less like a 
cosine, and more like a triangle ("short" dipole) or constant current 
(with capacity hat)

The thing to watch for in any analytical approach is a statement along 
the lines of "Assuming a xyz current distribution", which may or may not 
be valid.


This is the cool thing about numerical models (and the full on 
analytical models) is that they break the wire up into many segments, 
compute the current (and current distribution) in each segment, taking 
into account the interaction of each segment with all the others.  They 
essentially solve a big matrix, and from that, they can calculate the 
impedance and radiated field.

For each segment in NEC, the current is approximated by a combination of 
a constant current + a cosine + a sine terms. (That's called the basis 
function, if you're reading the literature).   Older programs 
approximated the current as a constant over the whole segment (often 
called "pulses" in the papers)

The hard core analytical types did it with calculus, making the segments 
infinitely small.  There's some subtleties in those analyses for "not 
infinitely thin wires" - is the join a gap, or two cones meeting at a 
point, or what. Some analyses work with infinitely thin wires, others 
with cones, etc.

OK, I confess that revisiting all of this makes my head hurt... Much 
easier that someone has put it all into NEC and other tools, and there's 
no *need* for an analytical solution.  As my father's differential 
equations professor put it - any *useful* problem with have equations 
that are not solvable analytically, and you'll have to use numerical 
methods, so get through this class and learn the ideal, and all the 
places it breaks, then take the classes on numerical methods.   My 
differential equations professor said essentially the same thing - "you 
won't be able to directly use anything in this class, because all real 
problems have exceptions"

What *is* useful is that there are some analytically solved problems, 
and you can use them to test the numerical solutions (do you get the 
same answer?).   The NEC documentation is full of this.




>
> Larry / W1DYJ
>
>
> On 10/4/2022 12:06, Lux, Jim wrote:
>> On 10/4/22 9:04 AM, Larry Banks via TowerTalk wrote:
>>> Theoretically infinite.  I = 0, therefore V = infinite with any 
>>> power at the tip. 
>>
>> In theory (!) all the power would have been radiated by the time you 
>> get to the tip - so zero voltage.
>>
>>
>>> However the real case is very complex and depends on the environment 
>>> and therefore the actual impedance at the tip caused by capacitive 
>>> end effects, etc. I don't believe there is a simple solution.
>>>
>>> Larry / W1DYJ
>>> .
>>>
>>> On 10/4/2022 11:21, Pete Smith N4ZR wrote:
>>>> I'd be interested in this.  I think the answer is fairly 
>>>> straightforward, depending on how far the end is (electrically) 
>>>> from the feedpoint, but specifics escape me.
>>>>
>>>> 73, Pete N4ZR
>>>> Check out the new Reverse Beacon Network
>>>> web server at<https://reversebeacon.net>.
>>>> For spots, please use your favorite
>>>> "retail" DX cluster.
>>>>
>>>> On 10/4/2022 11:07 AM, jim.thom jim.thom at telus.net wrote:
>>>>> Ok, simple question.  With 1.5 kw (measured at feedpoint)  applied 
>>>>> to the
>>>>> 50 ohm input  of the (full sized) dipole / yagi... what is the 
>>>>> PEAK V at
>>>>> the tips ?   Assume 1:1 swr at the feedpoint.
>>>>>
>>>>> Same question, but ant is not full size, and may have various 
>>>>> forms of
>>>>> loading schemes used.  (Say 50-80%) of full size.
>>>>>
>>>>>
>>>>> Ok, what about  a single, full size  1/4 wave vertical ? Or a loaded
>>>>> vertical ?
>>>>>
>>>>>
>>>>> I can't find a straight answer anywhere.
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