Assuming you have edges quite a bit shorter than the period, it's easy
to see what pulse widths you want to avoid to maximize the 5th: don't
let 5*pi*width/period be an integer multiple of pi. So avoid
width/period = 1/5, 2/5, 3/5 or 4/5. 2/5 and 3/5 (40% and 60%) are
not all that far from 50%. There are lots of ways to get 50% (or
close to it). One is to slow the edges a bit, and put the result into
a Schmitt trigger with adjustable DC level; the DC level will then
adjust the period. You can servo the DC level with an integrator tied
to the output and referenced to (v(high)+v(low))/2, for high accuracy.
Maybe that's too complicated, though, if you want things small. Note
that by not causing dissipation of the fundamental or other harmonics,
a multiplier can be considerably more efficient than indicated by the
percentage available power in the selected harmonic. In other words,
don't put a filter on a logic output that shorts out the fundamental,
but rather one that looks like an open circuit to the fundamental,
etc.

Cheers,
Tom


Paul Burridge wrote in message . ..
On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate
wrote:

I read in sci.electronics.design that Reg Edwards
wrote (in
et.com) about 'Extracting the 5th Harmonic', on Fri, 12 Mar 2004:
According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.


For a waveform like this (use Courier font):
_____
/ \ /
_____/ \____________/

with rise-time f, dwell time d, fall time r and period T, the harmonic
magnitudes are given by:

Cn = 2Aav{sinc(n[pi]f/T)}{sinc(n[pi][f+d]/T)}{sinc(n[pi][r-f]/T)},

where sinc(x)= {sin(x)}/x

There seems to be a number of opportunities for a harmonic to 'hide' in
a zero of that function.

Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug