one for the theorist

[jhaible]

Rules of thumb have their use, even though they can never be accurate.
The famous "one nH per mm of PCB trace" is useful to get a feeling for
the magnitude of inductance, but you can only know exactly when you also
know the return path (usually a ground plane).

But before we start to frown about the rules of thumb, let's keep in mind
that
this whole concept of "inductance" is an approximation, closed loop or not.
Only valid in a quasi static case.

I guess the only way to make a precise description of the "electronic word"
are Maxwell's equations - but gladly you can do without them in many
practical cases.
And when you cannot, sadly you always fight to get the right boundary
conditions ...

In your example, try to solve for a finite wire length, and use a second
parallel
wire for a return path, and vary the distance to the first wire. Have not
(recently)
done it, but I think it might give you a feeling of what's going on.
Alternatively, use
an infinite conductive plane as return path, and also vary the distance.

JH.



----- Original Message -----
From: Martin Czech <martin.czech at intermetall.de>
To: <synth-diy at mailhost.bpa.nl>
Sent: Tuesday, July 13, 1999 5:58 PM
Subject: one for the theorist


> I've recently read a book where the inductance of a single piece of wire
> was given. This is strange, I thought, because you can only speak of the
> inductance of a loop. And, after all what I know, the magnetic energy
> of a single wire without "back" current path goes towards infinity and
> so does L.
>
> Contrary a normal twisted pair arrangement makes sense.
>
>
> Example:
>
> If you have a cylindric shaped wire then H=i/(2*PI*r).  The magnetic
> flux will be phi=u*l* int{H(r)dr}
>
> = i*u*l/(2*pi)*ln(r/r0)
>
> (u=my, r0 radius, r distance)
>
> The total flux will need r->infinity and this is clearly also infinite,
> thus the inductance is also infinite.
>
> This makes sense, you simply need the back current path to have finite
flux.
>
> So, is this a stupid book, or is it me who is the stupid?
>
> m.c.
>
>
>
>
>