[DSP-10] Winding Torroids

[William N. Carver]

Well Bob, that "rule of thumb" is only accurate for small changes in the
number of turns. The inductance is actually proportional to the square
of the number of turns so if you change turns to 0.9 times the previous
turns (-10%) the inductance actually comes out to 0.9 * 0.9 = 0.81 or
81% which is "only" -19% change.

If the coil whose "inductance is proportional to turns squared" is used
in a simple parallel or series tuned circuit, resonance formula is one
divided by 2*pi*square root of L*C and the "turns squared" and "square
root of L*C" cancel each other out perfectly. A 1% turns change would
give you a 1% frequency change! Because resonant frequency formula has
square root of L*C on the BOTTOM of the formula there's a minus sign:
+1% turns change gives -1% frequency change (which jibes with our gut
feeling that "more inductance = lower frequency).

It's fine to puzzle over the way the formulas interact, but don't get
too wound up: a pi-type lowpass filter with two C's and one L is rarely
critical. Most lowpass filters are built with 5% capacitors and they
"just work", hi. If Bob suggested you do something special, like
selecting capacitors to 2% accuracy or something like that, then you
might figure the inductor is similarly critical. Absent some specific
indication like that, just count your turns and plow onward!

73 - Bill