Copied for interest from another newsgroup.

The performance of a single-transistor pulse (harmonic)-generator is covered
in program HARM_GEN now available from website below in a few seconds. Easy
to run.

The manner in which the amplitude of the harmonics 1 to 30 vary with
frequency and with operating angle (pulse width) are shown.

In general, with a very short pulse width, as the harmonic number increases,
the harmonic output level falls fairly slowly and uniformly. But as pulse
width (operating angle) increases then some harmonics almost disappear from
the spectrum. The program displays harmonic levels in decibels.

Fourier, that great French mathematician/philosopher wuz right! I think he
missed the tumbril and Madame guillotine.

Download program HARM_GEN now. It might be useful one day.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Why would varying the pulse width without changing the characteristics of
the pulse transitions (rise/fall) affect the harmonic content of the pulse?
No bandwidth and no harmonics at all are produced by the constant DC level
of the pulse before and after each transition.

Wouldn't the harmonic structure and bandwidth needed to produce/reproduce a
pulse be related only to the rise and fall times of that pulse, and the
transition shapes (sin^2, etc), and be independent of the width (time)
between the transitions?

RF

Visit http://rfry.org for FM broadcast RF system papers.

"Richard Fry" wrote in message
...
Why would varying the pulse width without changing the characteristics of
the pulse transitions (rise/fall) affect the harmonic content of the
pulse?
No bandwidth and no harmonics at all are produced by the constant DC level
of the pulse before and after each transition.

Wouldn't the harmonic structure and bandwidth needed to produce/reproduce
a
pulse be related only to the rise and fall times of that pulse, and the
transition shapes (sin^2, etc), and be independent of the width (time)
between the transitions?
============================

The shape of the pulse, the width of the pulse, the time interval between
pulses, all affect the harmonic frequency spectrum. They act both
independently and in conjunction with each other.

The best way to grasp what happens is to calculate the amplitudes of the
series of harmonics which result from several different shaped pulses, of
different pulse widths, spaced at different intervals.

In particular, you will find that varying the ratio of pulse width to
spacing results in some of the harmonics virtually disappearing in
amplitude.

You can also graphically reconstruct pulses and waveshapes but excluding
harmonics beyond the N'th to see what happens.

You will need a good book which gives the amplitudes and phases of the
harmonic sinewave terms in the infinite series of a selection pulse shapes.

Or you can construct a harmonic generator and examine its output with a
spectrum analyser.

Fascinating if you have the time to spare.

Reg Edwards wrote
The shape of the pulse, the width of the pulse, the time interval
between pulses, all affect the harmonic frequency spectrum.
They act both independently and in conjunction with each other.
________________

Please explain the reason why the bandwidth characteristics needed to
generate a single transition from one DC level to another is different than
when repeating that same transition any number of times before or after.

RF

I'm sorry. I do not understand your question. Perhaps someone else could
have a go.

----------------------------------------


"Richard Fry" wrote in message
...
Reg Edwards wrote
The shape of the pulse, the width of the pulse, the time interval
between pulses, all affect the harmonic frequency spectrum.
They act both independently and in conjunction with each other.
________________

Please explain the reason why the bandwidth characteristics needed to
generate a single transition from one DC level to another is different
than
when repeating that same transition any number of times before or after.

RF

Please consider this:

A step at t=0 results in some spectrum. If you have an identical step
which occurs at some other time, the amplitude of the spectrum is the
same, but the phases are different, and the difference depends on the
time difference. In fact, a negative step will have the same spectral
amplitude as a positive step, but inverted phases when comparing two
steps at the same time. (Note this gives the right result when you
add a positive and negative step coincident in time.) When you add
the two steps (perhaps one positive at t=0 and one negative at t=tau,
producing a pulse of width tau, for example), you will get
cancellation at some frequencies and reinforcement at others. The
resulting spectrum, then, depends on the time difference between the
edges, because the relative phases depend on the time difference.
Having a repetitive waveform (that has always existed and always will)
results in full cancellation of all spectral components except at DC
and 1/repetition rate and all harmonics of 1/repetition rate. But the
amplitudes (and phases) of the harmonics still depend on the timings.

Another (equivalent) way to look at it is that an impulse has a flat
spectrum, independent of the position of the impulse, but the phase of
the spectral components depends on the position (time) of the impulse.
Any waveform may be decomposed into an infinite series of impulses.
Consideration of the phases will lead you to the same conclusion as
the comments in the paragraph above.

You can use the basic properties of the Fourier transform to
demonstrate all this numerically or analytically if you wish.

Cheers,
Tom

"Richard Fry" wrote in message ...
Why would varying the pulse width without changing the characteristics of
the pulse transitions (rise/fall) affect the harmonic content of the pulse?
No bandwidth and no harmonics at all are produced by the constant DC level
of the pulse before and after each transition.

Wouldn't the harmonic structure and bandwidth needed to produce/reproduce a
pulse be related only to the rise and fall times of that pulse, and the
transition shapes (sin^2, etc), and be independent of the width (time)
between the transitions?

RF

Visit http://rfry.org for FM broadcast RF system papers.

"Richard Fry" writes:

Reg Edwards wrote
The shape of the pulse, the width of the pulse, the time interval
between pulses, all affect the harmonic frequency spectrum.
They act both independently and in conjunction with each other.
________________

Please explain the reason why the bandwidth characteristics needed to
generate a single transition from one DC level to another is different than
when repeating that same transition any number of times before or after.

One way to look at it is to consider the harmonics produced by all the
rising edges, and spearately consider the harmonics produced by the
falling edges. Both contain all of the harmonics, but since they are
displaced in phase, some of them get cancelled.

Obvious example: a square wave contains only odd harmonics.

Regards,
Allen WA0OHE
--
Allen Windhorn (507) 345-2782 FAX (507) 345-2805
Kato Engineering (Though I do not speak for Kato)
P.O. Box 8447, N. Mankato, MN 56002

"Allen Windhorn" wrote:

One way to look at it is to consider the harmonics produced by all the
rising edges, and spearately consider the harmonics produced by the
falling edges. Both contain all of the harmonics, but since they are
displaced in phase, some of them get cancelled.

Obvious example: a square wave contains only odd harmonics.
________________

Would that not require the components of rising edges to be time-coincident
with a trailing edges? How could that occur when the these transitions
occur at different times?

RF

Visit http://rfry.org for FM broadcast RF system papers.

Richard,

I think I see the problem here. The Fourier transform considers its
input over all time, from the beginning of time until eons into the
future. Its output is a frequency-domain spectrum which is
time-independent. That spectrum exists for all time, unchanging, to
accurately represent the input waveform. So from a Fourier transform
standpoint, there is not a spectrum associated with an edge, and a
different spectrum associated with "flat" parts of the waveform. The
integral runs from minus infinity to plus infinity. And to the degree
you've done the math exactly, you can exactly reconstruct the whole
input over all time from that single spectrum.

Of course, our practical approximations to the Fourier transform have
to limit the time over which the input is considered. So with a
modern "FFT spectrum analyzer," for example, you would indeed get zero
output when the input is zero, an interesting spectrum when the input
takes a step, and a simple DC output when the input is the flat DC
level after the step has been taken. If you get into using such an
analyzer, please do take the time to learn about that approximation to
the Fourier transform, and also about "windowing" and why it's needed
and how to select the proper window for what you're doing.

Cheers,
Tom

"Richard Fry" wrote in message ...
"Allen Windhorn" wrote:

One way to look at it is to consider the harmonics produced by all the
rising edges, and spearately consider the harmonics produced by the
falling edges. Both contain all of the harmonics, but since they are
displaced in phase, some of them get cancelled.

Obvious example: a square wave contains only odd harmonics.
________________

Would that not require the components of rising edges to be time-coincident
with a trailing edges? How could that occur when the these transitions
occur at different times?

RF

Visit http://rfry.org for FM broadcast RF system papers.

Richard,

Lets look at a real case. A 7 MHz square wave contains no energy at 14 MHz.
Now change the duty cycle so that the signal is ON for 25% and OFF for 75%
of the time. Now you have energy at 14 MHz. One way to look at what we have
done is to think of the 25/75 signal as being a 1/2 cycle of 14 MHz every 2
cycles of 14 MHz. Obviously, the rise and fall times have to be short enough
to transmit these narrower pulses. The faster the rise and fall times, the
more higher frequencies you get.

Tam/WB2TT
"Richard Fry" wrote in message
...
Reg Edwards wrote
The shape of the pulse, the width of the pulse, the time interval
between pulses, all affect the harmonic frequency spectrum.
They act both independently and in conjunction with each other.
________________

Please explain the reason why the bandwidth characteristics needed to
generate a single transition from one DC level to another is different
than
when repeating that same transition any number of times before or after.

RF