Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <3D809F7A.email@example.com> <5Pgg9.firstname.lastname@example.org>
Subject: Re: LT SwitcherCAD Current Source Help
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Date: Fri, 13 Sep 2002 21:13:17 +0100
NNTP-Posting-Date: Fri, 13 Sep 2002 21:13:16 BST
"Mike Engelhardt" wrote in message
> Kevin wrote:
> > > > ...The spice SW voltage controlled switch is not discontinues.
> > > > It varies from its min value to its max value. You can not
> > > > make it infinite...
> > >
> > > Err, well, yes, that is discontinuous. You can make switches
> > > continuous and smoothly
> > Er... Nope...don't know what you mean at all.
> > If something various from a to b with no missing bits in-between its
> > continuous, and that is what the spice switch does. Maybe you are
> > confusing continuity with differentiability. For example, a triangle
> > wave is continuous, but it is not differentiable at its turning
> > its derivative depends on the direction of approach.
> I've always been of the persuasion that a triangular wave is
> continuous but has a discontinuous 1st derivative. A square
> wave has a continuous 1st derivative(always zero) but the
> function itself is discontinuous.
There is a subtlety here that makes the square wave derivative
technically discontinuous, but I can understand the rational for saying
that it might be continuous.
A definition of continuous is if and only if:
f(xo) = f(x)|x->xo
That is, the limit of a function as x->xo must equal that function at
xo, independant of .
In posh talk it would be:
|f(x)-f(a)| < epsilon for all x with |x-a|< delta,
A square wave function would have to be so defined as to be single
so that only on one side of the jump is it say -0 is 0 and at 0+ it is 1
Calculating the derivative on the positive side:
or (1 - 1)/dx
On the negative side:
(0 - 1)/dx
These cannot be equal, hence its derivative does not exist at x=0.
Or, in more simple terms, differentiating an ideal square gives infinite
spikes at the discontinuity, and it is positive or negative, depending
on the direction, hence it clearly has no derivative at that point.
However, there are other functions that are discontinuous at a point xo,
yet still have a derivative at that point.
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.