[SI-LIST] Re: Gaussian Pulse
- From: "Howard Johnson" <howie03@xxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Sun, 16 Aug 2009 13:05:11 -0700
Dear Ben,
For Gaussian time-domain simulation in SPICE, I like to use an analog filter
model. The advantage of that, compared to a PWL approximation, is that you
can put any signal into the front end of the filter, including steps, long
pulses, short pulses, whatever, and the filter approximates pretty well what
would come out of a driver with your stipulated rise time.
I get my analog filter designs from: Anatol I. Zverev, "Handbook of Fliter
Synthesis", 1967(573 pages). The field of filter design has not changed in
a long time, so don't bother looking for modern books about it.
Zverev lists circuits for implementing many types of filters, including
approximations to the Gaussian filter. It is an approximation, not exact,
because of course the actual, perfect, Gaussian response has an infinitely
long precursor.
Here is the formula for his 10-pole ladder-circuit approximation.
The source to the filter is a current source.
The current source is shunted by a 1.0-ohm resistor (Rfirst).
In shunt with that, place capacitor C1 (see list of values below)
In series with that, place inductor L2 (see list...)
In shunt with that, place capacitor C3...
In series with that, place inductor L4...
Continue adding shunt capacitors and series inductors.
The last reactive element will be series inductor L10.
In shunt with the last reactive element place a 1-ohm resistor (Rlast).
The values are:
Rfirst = 1 ohm
C1= .0512 F
L2= .1525 H
C3= .2509 F
L4= .3451 H
C5= .4353 F
L6= .5250 H
C7= .6244 F
L8= .7597 H
C9= 1.0147 F
L10= 2.2594 H
Rlast=1.0 ohm
The input/output impedance of this circuit is 1 ohm. To scale the impedance
level of the circuit to a new impedance Z0, multiply all the resistors by
Z0, multiply the inductors by Z0, and divide the capacitors by Z0.
If I read Zverev's notes correctly, the 3-dB freuqency of this circuit is 1
rad/sec (= 0.159154 Hz). Check that. To scale the filter to another cutoff
frequency W0, where the number W0 is given in units of RAD/SEC (=
two*pi*frequency), divide all the inductors by the number W0 and also divide
all the capacitors by W0. Leave the resistors unchanged.
For a perfect gaussian filter, in response to a perfect input step, the
product of the 10-90% rise/fall time T[10-90%] and the 3-dB cutoff frequency
F[3dB] in units of Hz should equal 0.33864. If you want, for example, to
make a filter with T[10-90%] equal to 1 ns, then set
F[3dB]=(0.33864)/T[10-90%], which equals 338.64 MHz. Converting that to
rad/sec produces W0 = 2*pi*338.64 MHz = 2127.73 rad/sec. Now divide all the
L and C values by W0 to create a 1-ohm filter with a 10-90% rise/fall time
of 1 ns.
Always check the final result before using it.
If you have read this message and are unsure how or why someone would want a
Gaussian response, here are a couple of reasons:
"Sharp Edges" www.sigcon.com/Pubs/edn/SharpEdges.htm
A PWL edge over-stimulates the resonant behavior. A smooth Gaussian edge
better represents a real digital signal, eliminating phantom ripples in your
simulation output.
"Rising Problem" www.sigcon.com/Pubs/news/9_05.htm
A Gaussian edge best represents actual digital logic. It displays virtually
no perceptible ringing in the time domain-just like the real circuit
Good luck,
Dr. Howard Johnson, Signal Consulting Inc.,
tel +1 509-997-0505, howie03@xxxxxxxxxx
www.sigcon.com -- High-Speed Digital Design seminars, publications and films
P.S. -- I'll be teaching public classes in Phoenix Nov. 2-5, 2009.
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Behzad
Sent: Saturday, August 15, 2009 3:08 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Gaussian Pulse
Hi folks;
Who knows how we can define a Gaussian pulse as voltage source in Hspice
netlist?
Regards;
Ben
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