[TowerTalk] Feedpoint Impedance

Jim Lux jimlux at earthlink.net
Mon Jul 28 19:16:10 EDT 2008

-----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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