AW: fun with gnuplot prg (poles and zeros)

[Haible Juergen]

	[...]

Very nice description.

	>There is no sudden jump from -180deg to +180deg.  These artefacts
are only
	>confusion that comes up with stupid programs or measurement
equipment.
	>The only exeption is a zero pair on the jw axis, first you have 0
	>deg, then suddenly -180 deg. This is a very sharp and deep notch
filter,
	>so the magnitude is also 0 , or very small around the zero.  I
think,
	>phase angle has no real meaning for magnitudes -> 0.
	>So the discontinuity is not harmfull for group delay and such.

Exactly. So the recent question about an ideal series resonant circuit
from your signal to GND boils down to this:
"With what delay will a signal arrive at the other side, after passing
an ideal short circuit to GND ?", or "Which angle has a vector with zero
length?"
This is a general problem with teaching at school and univerity. You're
learning how the "ideal" case is working, the problems carefully set
up so that the limitations are not obvious, and when you think a little
further,
you're puzzled and stuck in contradictions. Starting with real, practical
examples is so much more rewarding.
It's the same thing if you're simulating in Spice. With a (Resonance)
feedback loop set to 1 (or very close to 1), the simulator will show
you a random result, but surely not the large peak you'd expect. Starting
with values of 0.9 and slightly increasing is the right method.

JH.