Re: transient analysis of linear system
- From: The Phantom <phantom@xxxxxxx>
- Date: Fri, 18 Aug 2006 09:46:59 -0700
On Fri, 18 Aug 2006 14:05:07 GMT, Fred Bloggs <nospam@xxxxxxxxxx> wrote:
First of all this is not homework it's just that linear systems and
transient circuit analysis hasn't been in the job description for a
while, actually ever.
R1 A R2 B R3
+---/\/\/\/\----+-----/\/\/\/\-----+-----/\/\/\/\-------+
| | | |
x(t) | | C1 | C2 | y(t)
===== ----- ----- =====
=== ----- ----- ===
| | | |
| | | |
+---------------+------------------+--------------------+
GND
Anyway the circuit is shown above. Clearly in steady state it's just a
voltage divider of the difference of Vx and Vy. The problem is that Vx
and Vy vary with time (out of my control). I need to report VA and VB to
the user but it must be the steady state result. In other words I must
filter out the transient effects caused by x and y. Please note that I
can't modify the circuit in any way. I know all the values for caps and
I can also measure *all* voltages. I even know the nominal values for
the resistors. The point of all this is to 'see' if the resistors change
through the "fog" caused the time varying sources.
My idea was to somehow use the system response [h(t)] to work out the
steady state result for A and B. Perhaps divide VA(t) by h(t) ????
eg in the case of VA:
x(t) --->| |
| h(t) |---> VA(t)
y(t) --->| |
I guess the first thing is, am I on the right track?
Not even close.
Secondly I could do
with some tips on calculating h(t) at A and B.
I really appreciate any help.
Your system is undetermined. The problem statement is to predict a new
steady state for Va and Vb as a function of R1,2,3. These resistors are
on the order of 2e15 ohms
He said the resistors are on the order of 2000 G ohms, Fred. That's 2e12
ohms, giving a time constant of 4 seconds, not 4000 seconds.
and the capacitors are on the order of 2e-12
for a time constant of 4e3, or thousands of seconds, and this holds for
relatively minor +/-10% change in R. Then Vx and Vy exhibit a drift
characteristic on the order of hundreds of seconds. You can get an idea
of what happens by thinking of C1 and C2 as DC sources, batteries, of
magnitude steady state Va and Vb. As the resistor fluctuate at a rate
nearly instantaneous relative to the circuit time constants, all
voltages remain unchanged, and charge will be circulated through the
resistors to maintain those node voltages constant. Looks like you have
everything wrong, attempting to measuring a circuit parameter that
nature is forcing to be constant, meaning you have to measure *current*
to detect the resistor changes, the voltage measurements will barely
move by ppm and be undiscernible from drift. And what does this have to
do with your original ill-posed resistor network that was another failed
identification problem? You're a starting to look like a big waste of time.
.
- References:
- transient analysis of linear system
- From: wombat
- Re: transient analysis of linear system
- From: Fred Bloggs
- transient analysis of linear system
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