# [TowerTalk] Feedpoint Impedance

Ward Silver hwardsil at gmail.com
Tue Jul 29 02:26:39 EDT 2008

```> Radiation resistance should be fixed..

Oh, right...duh.

The current equation will do - but the radiator (I may have confused things
by referring to it as a "dipole") may be anywhere between one-half and one
wavelength long, so the current won't be a simple cosine function.  It
*will* be zero at the ends :-)

Thanks.

73, Ward N0AX

----- Original Message -----
From: "Jim Lux" <jimlux at earthlink.net>
To: "Ward Silver" <hwardsil at gmail.com>; "Towertalk Reflector"
<towertalk at contesting.com>
Sent: Monday, July 28, 2008 4:16 PM
Subject: Re: [TowerTalk] Feedpoint Impedance

>
>
> -----Original Message-----
>>From: Ward Silver <hwardsil at gmail.com>
>>Sent: Jul 28, 2008 12:46 PM
>>To: Towertalk Reflector <towertalk at contesting.com>
>>Subject: [TowerTalk] Feedpoint Impedance
>>
>>While we're on the math subject, does anyone know of an equation that
>>gives
>>either feedpoint impedance or radiation resistance as a function of
>>position
>>along a linear radiator of known electrical length?  Free space would be
>>fine, I can work in the effects of ground later.
>
> Radiation resistance should be fixed.. it's a function of the size and
> shape of the radiator.  Feedpoint impedance will change with position, of
> course (essentially, it's some transformation of the combination of
> radiation resistance, loss resistance and the reactance of the antenna)
>
> I don't think there's a nice analytical expression for it.  One could
> start with the Schelkunoff formulation (the one using sine and cosine
> integrals, which are series expansions).  Do you need the reactive part?
> If not, you could assume that the current has a sinusoidal distribution,
> and once you know the radiation resistance, the feedpoint R at the center
> will be the Rrad+Rloss.. Moving away from the center, it would scale as
> 1/cos(distance), becoming infinite at the very end.
>
> Orfanidis's online book might be a good source.. he has equations for the
> current at various places along the element, and that's really what you're
> looking for. http://www.ece.rutgers.edu/~orfanidi/ewa/  Chapter 16 or 22,
> I suspect.
>
>
> Practically, I've done this kind of thing with NEC.. run a series of cases
> with systematic variation in the position, generate a table, and then do
> interpolation.
>
> Jim, W6RMK

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