>The question is numbering of harmonics.
>One side says that given a fundamental frequency of 200 MHz, the first
harmonic is 400 MHz, the second harmonic is 600 MHz and the third harmonic
is 800 MHz.
>The other side says that given a fundamental frequency of 200 MHz, the
first harmonic is 200 MHz (or same as fundamental), the second harmonic is
400 MHz and the third harmonic is 600 MHz.
Fundamental *is* the first harmonic, 2nd is 2 times, 3rd is 3 times, etc.
Don't get confused. One is not allowed to depart from convention simply
to duplicate the ways floors in a building are named.
>The other part of the discussion revolved around even and odd harmonics.
>One side says that even harmonics are lower amplitude than the odd
harmonics, the other side says odd harmonics are lower amplitude than even
harmonics.
>All discussions assumed non-sinusoidal sources, generally our sources are
square- or modified-square waves.
Can't make a general statement. A "perfect" square wave of 50% duty
cycle is missing all the even harmonics. A "perfect" 25% duty cycle is
missing every harmonic that's a multiple of 4 with even harmonics higher
than odd harmonics. As you "slide" between 25% and 50%, harmonics come
and go with some odd higher and some even higher, depends.
To see the effect draw a sinx/x waveform. Then every zero crossing call
that an odd harmonic and every maximum is an even harmonic for a 50%
square wave. Mark all the potential harmonics you have as dots along the
axis.
Assume you change to 25% duty cycle, that's like having higher frequency
content, but still with the basic sinx/x. Since you changed the width of
the pulse in half the frequency spectrum (which was sinx/x) moves out 2:1.
That just means the gentle slope of your sinx/x now crosses at the 4th
harmonic instead of the 2nd harmonic. As you draw the little spikes of
energy, you'll see you have 2nd, 3rd, no 4th, 5th, 6th, 7th, no 8th, etc.
As the square wave changes from 25% to 50% duty cycle that sinx/x curve
simply "contracts" along the frequency axis with that first zero crossing
moving from the 4th harmonic down through the 3rd harmonic until it
obliterates the 2nd harmonic at 50% duty cycle.
At 37.5% duty cycle, every multiple of 3 disappears, so you have a large
2nd, no 3rd, 4th & 5th the same, no 6th, 7th & 8th the same, no 9th, etc.
>Can someone shed some light on harmonic numbering and if possible, point
to a reference material that specifies this?
My 3 main references (Fourier Transforms by Ron Bracewell, ITT Ref, and
ARRL Handbook) show this naming convention without specifically stating
the origin of the custom.
- Robert -
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