# RE: [SI-LIST] : Antenna Problem on the Board

From: Chris Rokusek ([email protected])
Date: Tue May 29 2001 - 18:12:56 PDT

Doug,

The formula I used for E(f) can be found in both Clayton Paul and Henry
Ott's text. If is essentially the superposition of two electric (Hertzian)
dipoles carrying purely differential currents. Paul provides a derivation
while Ott references Weeks 1964, p.565, Eq 91. They would probably shoot me
if I did not mention that their are limitations to these models to which I
will refer you to their texts. Most notable are far field and constant
current segment. Beyond these (>200 MHz on a typical PCB) it is an
approximation for non-elemental structures (integration could be used).

The terms that account for field pattern were replaced with worst case
(sin(x) = 1) to simplify the expression.

I can't comment as to the applicability of the folded dipole structure
(non-elemental) but just wanted to provide some rebuttal for the concern
over use of the "Max-Electric-Magnitude-in-far-field" formula.

Chris Rokusek
Innoveda

> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of Doug McKean
> Sent: Tuesday, May 29, 2001 1:58 PM
> To: [email protected]
> Subject: Re: [SI-LIST] : Antenna Problem on the Board
>
>
> Chris,
>
> This E(f) relation being used looks like the magnetic
> dipole equation. My question is in terms of radiation,
> why is the magnetic dipole equation being used and
> any more valid than the electric dipole equation?
>
> Now, I understand the loop circuitry of a trace over a
> ground plane, but traces can also act very much like
> dipoles. Especially folded dipoles in some cases.
>
> Where you have
>
> H(f) = k(H) * [ I * f^2 * A / d ] (Amps/meter)
>
> where
>
> k(H) = 1.316*10^-14
> I = amps
> f = frequency in Hertz
> A = area in meters squared
> d = distance from antenna in meters.
>
> You also have for the electric field
>
> E(f) = k(E) * [ I*f*l/d ] (Volts/meter)
>
> k(H) = 6.3*10^-6
> I = amps
> f = frequency in Hertz
> A = area in sq. meters
> d = distance from antenna in meters.
>
> Two points:
>
> One - I've seen this loop equation used quite a lot and
> I have to disagree with it. There has to be some sine
> or cosine factor in there as well as to compensate for
> position from the loop.
>
> Second, even if the magnetic relation is accepted, the
> constant factors alone show that there are orders of
> magnitude differences in amplitude between the two.
>
> My bottom line here is that where people seem to
> assume a loop, I see quite clearly a folded dipole.
>
> - Doug McKean
>
>
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