Steve, W3AHL wrote:
> Jim,
>
> A good approximation is to consider a right angle bend as a 1/4 turn
> coil with the same radius of the bend. But the typical coil inductance
> calculators make too many simplifying assumptions to handle this. AC
> power system engineering handbooks are a good source of info on this
> topic. I'll look for a reference next time I'm at the university
> library. Seems like something every savvy ham should know....?
Indeed.. and I've looked around a lot. The usual "inductance of a
single turn loop of an infinitely thin conductor" formula isn't valid
for partial turns (that is, 1/4 of a loop doesn't have 1/4 the
inductance of a single turn loop). Part of the problem is that the
mathematical representation of the shape isn't nice (it's not a circle
or line), so there's not any analytical solution.
It's not something which folks "make" so there's no real interest in an
approximation, like those from Wheeler or Nagaoka or Grover. I did turn
up a possible source, which I'll have to track down:
Analytical series expressions for the self- and mutual inductances of
two-dimensional coils in the form of partial sectors
Thiagarajan, V.
Magnetics, IEEE Transactions on
Volume 39, Issue 1, Jan 2003 Page(s): 158 - 163
>
> I did a quick measurement with a 4' piece of #6 copper wire. Adding a
> 1" radius 90 degree bend increased the impedance about 5 ohms at 10 MHz,
> which would equate to an inductance of about 0.08 uH for the bend.
> This was not a precision test, but gives an order-of-magnitude estimate
> at least.
But how did you do the measurement? Fixturing effects at 10MHz will be
significant. It's not like you can just hook up a inductance meter,
because the leads are there too.
>
> My experience with this relates to PCB trace layout modeling and the
> effect of sharp corners on trace inductance on fast edge rate signals.
> I'm retired now and don't have access to the EM modeling software we used.
>
> The mechanical stress is only high because of the interaction of the
> magnetic fields with surrounding objects. The interaction of magnetic
> fields in a right angle bend of the current-carrying conductor not only
> cause high stresses at the bend, but an increase in self-inductance at
> the bend also.
I agree, but I think the increase in L is small, if not negligible, over
the same length of wire in a straight line (that is, a 90 degree bend
with radius 10 cm will have pretty much the same inductance as a
straight piece of the same wire that is 17 cm (10*pi/2) long. I think
you have to start getting up to 180 degrees of bend before the field of
one piece of the turn starts really interacting with the field of
another piece.
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