Avery Fineman wrote:

In article , Peter John Lawton
writes:

The above will hold true at any fundamental frequency provided the
rise and fall times are equal and each equal to 0.02 times the
repetition period. Those numbers will change given faster or slower
rise/fall times. All db calculated as 20 x Log (voltage). Width is
determined at the baseline, not the 50% amplitude point.

Len Anderson
retired (from regular hours) electronic engineer person

I wonder what happens to these numbers as the rise/fall time tends to
zero?

The harmonic content will increase...but also show dips depending
on the percentage width relative to the period. I could present those
(takes only minutes to run the program and transcribe the results)
but that is academic only. The rise and fall times will NOT be zero
due to the repetition frequency being high (repetition time short).

Consider that a 3 MHz waveform has a period of 333 1/3 nSec and
that Paul is using a TTL family inverter to make the square wave.
Even with a Schmitt trigger inverter the t_r and t_f are going to be
finite, possibly 15 nSec with a fast device (and some capacitive
loading or semi-resonant whatever to mess with on- and off-times).

15 nSec is 4.5% of the repetition period, quite finite...more than I
showed on the small table given previously.

I'm sure someone out there wants to argue minutae on numbers but
what is being discussed is a squarish waveform with a repetition
frequency in the low HF range. Periods are valued in nanoSeconds
and the on/off times of squaring devices are ALSO in nanoSeconds.
There's just NOT going to be any sort of "zero" on/off times with
practical logic devices used by hobbyists.

I just wondered from a theoretical point of view what the program would
say about the harmonic content as you decreased the values you put into
it for t_r and t_f.

What is not intuitive to me (and to others) is that harmonic energy
of a rectangular waveform drops drastically by the 5th harmonic
and is certainly lower than "obvious" numbers bandied about.

This is connected with my question. I am pondering why the energy
available for higher harmonics is less than for the fundamental and also
how your program works out this energy.

But, also mentioned before by others is that shortening the rect-
angular waveshape DOES increase the 5th harmonic, as evident
by the approximate 12 db increase at 40 to 35 percent of the
repetition period.

Its like pushing the baby on the swing in the park, you only need to
give it the occasional push or pull in the right direction. A 5f
resonator gets has to go for 2.5 cycles in between refuelling from a
square-wave (1:1) of frequency f.
With a mark/space ratio of 2:3 it looks to me as though the 'pull' on
the 5f resonator as the rectangular wave drops will take out all the
energy that was put in on the preceding 'push' - so no 5th harmonic. On
the other hand, 1.5:3.5 (30%) should be just as good for 5th as 1:1 (but
no better).
All that's assuming a zero t_r and t_f. In practice it must be that the
energy transfer to a resonator depends on these times. It seems that the
energy transfer is not so great to a faster resonator. Pursuing the
swing analogy, your arm has to move faster than the swing if you're
going to add to the swings energy.

An equivalent shortening happens in vacuum tube multipliers
through biasing (self, fixed, or both) and that can be adjustable
along with the drive level. It's not quite the same with bipolars
since the overdrive effects are more saturation than in the self-
bias conditions of tubes. It's close, though.

From all indications of the Fourier series results, there's a definite
reason why so few multipliers went beyond tripling. The amount
of energy (relative to fundamental and taking into account the
finite rise and fall times) of 4th and higher harmonics just isn't as
much as intuition would have everyone believe!

What do you mean by intuition here?
My intuition suggests to me that as the rise and fall times get shorter,
the energy available for the harmonics approaches that for the
fundamental. In other words, as a square wave approaches perfection it
gains the ability to stimulate all odd harmonic resonators equally - but
surely that can't be right. Possibly the energy transfer to a f and
(say) 5f resonator approaches the same value but the 5f resonator loses
5 energy at five times the rate of the f one, assuming equal Q.

Peter

Len Anderson
retired (from regular hours) electronic engineer person