Re: [SI-LIST] : RE: Split Plane

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From: Doug (dmckean@gte.net)
Date: Thu Jun 01 2000 - 08:37:21 PDT


Dennis Tomlinson wrote:
>
> gkimball@indra.com wrote:
> >
> > Doug et al-
> > Has anyone extended the '0.35' rule beyond single-order systems?
> > Terman's
> > Radio Engineers Handbook talks about '0.45' for multi-order waveforms
> > with overshoots in the 10% range - but doesn't reference any derivation.
> > I'd be curious about high Q networks up to 50% for ex.
> > Anyone?
>
> I'll take a shot at a second order low pass with two infinite zeros. It
> may necessarily contain terms like Q or z[eta], and w0 in addition to
> BW (a function of z and w0). I expect the result to be mucked up a
> bit more that the first order case.
>
> One caveat, It'll have to wait for the weekend. Anyone else wishing to
> take a crack at it is welcome.

Sure.

The classical +/-3dB point at critical is based on a
circuit with real poles or zeros with the transfer
function of the form

  H(s) = 20*log(sqrt[(wT)^2 + 1])^(+/-N)

or

  H(s) = +/-10*N*log[(w^2)(T^2) + 1]

At the knee where w = 1/T, and N = 1, we have

  H(s) = +/-10*log[2] = +/-3dB

Specifying something out to the +/-6dB point implies

  (w^2)(T^2) + 1 = 4

where

  w = sqrt(3)/T = 1.7/T

We're talking circuit response here.
And lumped parameters no less.

Another circuit that has a transfer function of
complex conjugate poles and zeros of the form
will behave in an entirely different manner.

But this all implies a signal input of constant
amplitude from DC to daylight. Such is not the
case with the odd waveforms dealt with in the
real world where Fourier demonstrates something
different. And where with some waveforms, the
7th harmonic can become nearly insignificant.

Thus it becomes painfully apparent to me that
mucho stuff is being assumed. And who said
engineering is supposed to be an exact science?

- Doug McKean

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