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Michele Ancis
- Jan 1, 1970
- 0
John Larkin said:Hi, Michel,
What I'm making is a programmable arbitrary waveform generator to
modulate this laser. It works by summing a bunch of individually
programmable fast impulses, spaced 250 ps apart. The filter smooths
them into, ideally, a nice continuous waveshape, and we use waveform
feedback, from further up in the optical system, to tune the impulse
train to get the actual optical pulse shape we need. So what I need is
actually a filter with a Gaussian time-domain (impulse) response,
which is about what a Bessel does; but there's no hard
frequency-domain performance requirement, and the filter response is
convoluted with a lot of other elements in the chain anyhow. So I
figured I'd start with a Bessel, and tweak it (x-acto knife? crazy
glue dielectric blocks?) until the overall system response is nice.
Along the way, it ocurred to me that a series of Gaussian impulses is
a nice way to do curve fitting, as opposed to polynomials or Fouriers
or whatever. If the Gaussian impulses are spaced so as to overlap at
about their half-amplitude points, they can be tweaked nicely to
follow most any reasonably smooth function.
John
Hi John,
ok now I start to see what you intend to do with your filter...Just
keep in mind that the one proposed by Frank, at least to my
simulations, does NOT have a Bessel response. As you know, the
frequency response must be characterized through both amplitude and
phase. Or, in our case, amplitude and group delay. What I'm saying is
that, since the group delay is not constant, you can't expect to have
a simmetrical gaussian pulse response from Frank's filter (unless my
simulations are completely wrong :-( ). I've simulated my lumped
element - ultra-ideal-with-theoretical-values - filter, and the one
proposed by Frank (wich has ideal microstrips). The result is a nice
"gaussian" pulse response with mine, and something that resembles a
gaussian shape but is not simmetrical and has ripple with Frank's one.
I don't know what you're looking for, it is just to warn you about
what you're about to get, according to my understanding.
However, the ripple may well be generated by the time domain model of
the microstrips, therefore I wouldn't trust it that much.
On the other hand, I'd rather be sure that, without equal group delay,
you won't get simmetrical pulses, and your control over the waveform
will possibly get more difficult. As you'll have noticed, also the
"bandwidth" of the filter is related to the width of the pulses
(responses in TD), therefore to the capabilities of your waveform
generator to create "arbitrarily" fast functions...if you're slow
enough, maybe you can obtain nice simmetric pulses, but don't expect
too much if you want to drive your filter "harder". I mean, there's a
portion of the frequency spectrum where the response of Frank's filter
has nearly constant group delay (after all, this happens with all
kinds of LP, more or less): if the "relevant" frequency content of
your synthesized waveform is in that portion, everything should be
fine. But if you intend to change its amplitude too fast, you will see
distortion. This is, at least, what I can understand...
Please keep me informed as you go ahead,
Michele (not Michel, which is french!)