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transient analysis of linear system

J

John Woodgate

Jan 1, 1970
0
dated Fri said:
I can connect LPF's to A and B however I don't see the benefit. A and B
are already 'filtered' by the nature of the arrangement of R's and C's.
That's the problem!

When I wrote my post, you hadn't told us the R and C values. But that's
beside the point. If the voltages are varying, and you want to know the
average voltages, the RC time-constants in the circuit itself are not
long enough to smooth out the variations. So you need to add low-pass
filters, also known as averaging circuits, to smooth them out.

I get the strong impression that you are 'thinking complicated', and, as
happens too often in this NG, people who should know better are
encouraging that.
 
W

wombat

Jan 1, 1970
0
John said:
When I wrote my post, you hadn't told us the R and C values. But that's
beside the point. If the voltages are varying, and you want to know the
average voltages, the RC time-constants in the circuit itself are not
long enough to smooth out the variations. So you need to add low-pass
filters, also known as averaging circuits, to smooth them out.

I get the strong impression that you are 'thinking complicated', and, as
happens too often in this NG, people who should know better are
encouraging that.


I don't think LPF's will help. The reason being is that when the
resistors change (this was explained in a previous post 5560128 - not
sure if that number is of any use, found it in the header) they change
approx +/- 10% of their value for only 10 secs. I think the kind of
filtering you are suggesting would attenuate it too much and I would
miss the event.

However recent postings (cheers John O'Flaherty) have made me think of
the whole thing in a slightly different way... If I can calculate what A
and B should be by using the nominal values in a mathematical model
together with the measurements from the sources then I can just compare
the expected A or B with the measured A or B.

Ok I've just simulated it with SPICE. Two identical circuits driven by
the same sources except the 'real-world' circuit has an altered
resistor. Obviously the waveforms vary. The hard bit for me (being
mathematically challenged) is to run the model in real-time on a device.
Any suggestions? I guess I could use SPICE algorithms that use the
measured source voltages as a pseudo piece-wise source???

wombat
 
T

The Phantom

Jan 1, 1970
0
The said:
The Phantom wrote:

On Thu, 17 Aug 2006 21:50:18 +0200, wombat



Hi All,

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? Secondly I could do
with some tips on calculating h(t) at A and B.

I really appreciate any help.


You need to give as much detail as you can for problems like this. For
example, detail that you didn't give that would be helpful:

Tell us more about the nature of Vx and Vy. Are they sine waves (what
frequency) that vary only slowly? Or, do they vary quickly? What varies,
the frequency? The amplitude? If they aren't sine waves, what are they?
What are their nominal characteristics and how do they vary? Are they
steady most of the time with some variation only occasionally? Or, do they
vary constantly?

How much are the resistors likely to vary? One percent? Ten percent?
Quickly, or slowly? How quickly or slowly? What are the nominal values of
the resistors and capacitors?

To what accuracy do you need to determine the change in the resistors?
How quickly must you report the change in the resistors when they do
change?


Thanks for your interest. I'll try to answer your questions but as far
as I see it it's a mathematical issue so the nature of waveforms is
largely irrelevant (within reason).


You should understand that since the resistors are time-varying, this is
not a linear system in the traditional sense, and traditional methods of
solving linear systems are not applicable (except for short times while the
resistors are nearly constant).

x and y vary but there is no waveform that can be associated with them.
They are at the whim of nature. However they move relatively slowly,
perhaps 50% of their nominal value in one minute. Sometimes they are
essentially constant but I don't have the luxury of measuring only when
they are constant. I must monitor them all, all of the time for a
discrepancy event.


Are Vx and Vy low impedance so that you might load them with another
network without upsetting your existing circuit?

Are the voltages at points A and B converted (A-D, probably) so that they
are available as numbers for number crunching, and, if so, how much
computer power do you have available?

I need to pick up variance in resistance of +/-10% when the variance
occurs for more than 5 secs. The resistors are ~2000G ohms (that's right
giga) and the caps 2.2pF.

An accuracy of +/-2% of the nominal would be great. I can report the
change up to 1 minute after the event.

Now that I look at it I guess one could consider it analogous to a
series of strain gauges where the overall excitation voltage floats
around and the caps represent stray capacitance to ground.

Thanks again for the input Phantom. I appreciate the resistors are time
varying but given that is what I am trying to detect can't we just work
out how we _expect_ the circuit to behave (when R's aren't time varying)
and then compare that to what is measured (when R's might be time varying)?

That's why I asked you what the maximum expected change in the resistors
is. You said you needed to "...pick up variance in resistance of +/-10%
when the variance occurs for more than 5 secs.", but you haven't yet told
me what the max expected change is.

I'm thinking that if the change isn't too much and doesn't happen too
rapidly, you may be able to treat the system as though it *were* linear
without too much error.
Vx and Vy are low impedance and can be loaded with external circuitry.
In fact that was my first solution. I added a 'T' (R-C-R) circuits in
parallel with R1 and R3 and then tuned them to compensate for the
changes. This worked extremely well but I prefer the mathematical method
as it simplifies fabrication of the system.

In another post, I asked you:

" Are you saying that they (Vx and Vy) are essentially random noise? Are
they bipolar? That is, do they present both positive and negative
polarities, with an average of zero? What is the maximum voltage they
attain?"
 
J

John O'Flaherty

Jan 1, 1970
0
wombat said:
John said:
wombat said:
The Phantom wrote:

On Thu, 17 Aug 2006 21:50:18 +0200, wombat



Hi All,

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? Secondly I could do
with some tips on calculating h(t) at A and B.

I really appreciate any help.


You need to give as much detail as you can for problems like this. For
example, detail that you didn't give that would be helpful:

Tell us more about the nature of Vx and Vy. Are they sine waves (what
frequency) that vary only slowly? Or, do they vary quickly? What varies,
the frequency? The amplitude? If they aren't sine waves, what are they?
What are their nominal characteristics and how do they vary? Are they
steady most of the time with some variation only occasionally? Or, do they
vary constantly?

How much are the resistors likely to vary? One percent? Ten percent?
Quickly, or slowly? How quickly or slowly? What are the nominal values of
the resistors and capacitors?

To what accuracy do you need to determine the change in the resistors?
How quickly must you report the change in the resistors when they do
change?


Thanks for your interest. I'll try to answer your questions but as far
as I see it it's a mathematical issue so the nature of waveforms is
largely irrelevant (within reason).

x and y vary but there is no waveform that can be associated with them.
They are at the whim of nature. However they move relatively slowly,
perhaps 50% of their nominal value in one minute. Sometimes they are
essentially constant but I don't have the luxury of measuring only when
they are constant. I must monitor them all, all of the time for a
discrepancy event.

I need to pick up variance in resistance of +/-10% when the variance
occurs for more than 5 secs. The resistors are ~2000G ohms (that's right
giga) and the caps 2.2pF.

An accuracy of +/-2% of the nominal would be great. I can report the
change up to 1 minute after the event.

Now that I look at it I guess one could consider it analogous to a
series of strain gauges where the overall excitation voltage floats
around and the caps represent stray capacitance to ground.


What if you could take the measurements of the voltage sources, and
apply them either to a simulation program or to a circuit set up to
represent the nominal values of your subject circuit, but with handier
values- 2 Mohm and 2.2 nF, say, and then see at some interval how much
the subject circuit deviates from the simulation/test circuit?

That's a possibility (I can measure all voltages) but I want to avoid
requiring a full blown PC for the calcs if I can. DSPs, FPGAs and
microcontrollers are preferable for the computations due to size
limitations.

Try the physical component simulation. You can claim you are using a
RISC analog computer to generate a comparison standard.
 
W

wombat

Jan 1, 1970
0
That's why I asked you what the maximum expected change in the resistors
is. You said you needed to "...pick up variance in resistance of +/-10%
when the variance occurs for more than 5 secs.", but you haven't yet told
me what the max expected change is.

I'm thinking that if the change isn't too much and doesn't happen too
rapidly, you may be able to treat the system as though it *were* linear
without too much error.




In another post, I asked you:

" Are you saying that they (Vx and Vy) are essentially random noise? Are
they bipolar? That is, do they present both positive and negative
polarities, with an average of zero? What is the maximum voltage they
attain?"

Ok, the expected resistance change could be 100%. The resistance is
unlikely increase much (unless wire is cut) but could drop close to 0.
However as I said I need to detect when in drops by %10 of it's value.
Usually this 'event' where the it drops by 10% only occurs for 5-10secs.
I need to detect this event, that is the purpose of the gadget.

Vx and Vy are not random noise as such but I can't predict them, I can
only measure them. Vx should always be at least 20% greater than Vy to
ensure there is current flow through the system. For arguments sake
let's say that Vx is 100kV which ramps up to 150kV and back down again
over the course of 2 mins (not necessarily a nice linear ramp though).
Vy tries to keep itself around 20kV below Vx.

wombat
 
W

wombat

Jan 1, 1970
0
John said:
wombat said:
John O'Flaherty wrote:

wombat wrote:


The Phantom wrote:


On Thu, 17 Aug 2006 21:50:18 +0200, wombat




Hi All,

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? Secondly I could do
with some tips on calculating h(t) at A and B.

I really appreciate any help.


You need to give as much detail as you can for problems like this. For
example, detail that you didn't give that would be helpful:

Tell us more about the nature of Vx and Vy. Are they sine waves (what
frequency) that vary only slowly? Or, do they vary quickly? What varies,
the frequency? The amplitude? If they aren't sine waves, what are they?
What are their nominal characteristics and how do they vary? Are they
steady most of the time with some variation only occasionally? Or, do they
vary constantly?

How much are the resistors likely to vary? One percent? Ten percent?
Quickly, or slowly? How quickly or slowly? What are the nominal values of
the resistors and capacitors?

To what accuracy do you need to determine the change in the resistors?
How quickly must you report the change in the resistors when they do
change?


Thanks for your interest. I'll try to answer your questions but as far
as I see it it's a mathematical issue so the nature of waveforms is
largely irrelevant (within reason).

x and y vary but there is no waveform that can be associated with them.
They are at the whim of nature. However they move relatively slowly,
perhaps 50% of their nominal value in one minute. Sometimes they are
essentially constant but I don't have the luxury of measuring only when
they are constant. I must monitor them all, all of the time for a
discrepancy event.

I need to pick up variance in resistance of +/-10% when the variance
occurs for more than 5 secs. The resistors are ~2000G ohms (that's right
giga) and the caps 2.2pF.

An accuracy of +/-2% of the nominal would be great. I can report the
change up to 1 minute after the event.

Now that I look at it I guess one could consider it analogous to a
series of strain gauges where the overall excitation voltage floats
around and the caps represent stray capacitance to ground.


What if you could take the measurements of the voltage sources, and
apply them either to a simulation program or to a circuit set up to
represent the nominal values of your subject circuit, but with handier
values- 2 Mohm and 2.2 nF, say, and then see at some interval how much
the subject circuit deviates from the simulation/test circuit?

That's a possibility (I can measure all voltages) but I want to avoid
requiring a full blown PC for the calcs if I can. DSPs, FPGAs and
microcontrollers are preferable for the computations due to size
limitations.


Try the physical component simulation. You can claim you are using a
RISC analog computer to generate a comparison standard.

Out of interest has anyone ever done that? Calculated a SPICE model out
in real-time using real time-varying sources. I guess it's like having a
piecewise source with the 'pieces' coming from real world measurements.
Interesting.

RE: "Try the physical component simulation"

Very funny. I wish it was that easy. A few 0402 parts hidden under a
black plastic square and I make the claim... problem is that this isn't
even an electrical system, just one that can be modelled by one.

I think the solution will be something like: A numerical SPICE style
solver that digest the measurements of Vx and Vy and spits out the
expected voltage of VA and VB in real-time. That result is compared with
the measured values of VA and VB. I probably only need to calculate
every half a second to successfully catch the event so it's probably
doable with a decent micro. Thoughts?

wombat
 
J

John O'Flaherty

Jan 1, 1970
0
wombat said:
John said:
wombat said:
John O'Flaherty wrote:


wombat wrote:


The Phantom wrote:


On Thu, 17 Aug 2006 21:50:18 +0200, wombat




Hi All,

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? Secondly I could do
with some tips on calculating h(t) at A and B.

I really appreciate any help.


You need to give as much detail as you can for problems like this. For
example, detail that you didn't give that would be helpful:

Tell us more about the nature of Vx and Vy. Are they sine waves (what
frequency) that vary only slowly? Or, do they vary quickly? What varies,
the frequency? The amplitude? If they aren't sine waves, what are they?
What are their nominal characteristics and how do they vary? Are they
steady most of the time with some variation only occasionally? Or, do they
vary constantly?

How much are the resistors likely to vary? One percent? Ten percent?
Quickly, or slowly? How quickly or slowly? What are the nominal values of
the resistors and capacitors?

To what accuracy do you need to determine the change in the resistors?
How quickly must you report the change in the resistors when they do
change?


Thanks for your interest. I'll try to answer your questions but as far
as I see it it's a mathematical issue so the nature of waveforms is
largely irrelevant (within reason).

x and y vary but there is no waveform that can be associated with them.
They are at the whim of nature. However they move relatively slowly,
perhaps 50% of their nominal value in one minute. Sometimes they are
essentially constant but I don't have the luxury of measuring only when
they are constant. I must monitor them all, all of the time for a
discrepancy event.

I need to pick up variance in resistance of +/-10% when the variance
occurs for more than 5 secs. The resistors are ~2000G ohms (that's right
giga) and the caps 2.2pF.

An accuracy of +/-2% of the nominal would be great. I can report the
change up to 1 minute after the event.

Now that I look at it I guess one could consider it analogous to a
series of strain gauges where the overall excitation voltage floats
around and the caps represent stray capacitance to ground.


What if you could take the measurements of the voltage sources, and
apply them either to a simulation program or to a circuit set up to
represent the nominal values of your subject circuit, but with handier
values- 2 Mohm and 2.2 nF, say, and then see at some interval how much
the subject circuit deviates from the simulation/test circuit?
--
John


That's a possibility (I can measure all voltages) but I want to avoid
requiring a full blown PC for the calcs if I can. DSPs, FPGAs and
microcontrollers are preferable for the computations due to size
limitations.


Try the physical component simulation. You can claim you are using a
RISC analog computer to generate a comparison standard.

Out of interest has anyone ever done that? Calculated a SPICE model out
in real-time using real time-varying sources. I guess it's like having a
piecewise source with the 'pieces' coming from real world measurements.
Interesting.

RE: "Try the physical component simulation"

Very funny. I wish it was that easy. A few 0402 parts hidden under a
black plastic square and I make the claim... problem is that this isn't
even an electrical system, just one that can be modelled by one.

I think the solution will be something like: A numerical SPICE style
solver that digest the measurements of Vx and Vy and spits out the
expected voltage of VA and VB in real-time. That result is compared with
the measured values of VA and VB. I probably only need to calculate
every half a second to successfully catch the event so it's probably
doable with a decent micro. Thoughts?

You might set it up as a state variable system. The state variables are
the variables that represent the current state of the system, that is,
the capacitor voltages and inductor currents. Since the form of your
system is fixed, you only need to figure out the form of its
representation once. The current state of the system, the inputs, and
the system form are represented as matrices, and you can calculate the
next state of the system by fixed procedures. This is a time-domain
procedure. There is a chapter of a textbook available free on the net
that describes the procedure. I can't be of further help because I
haven't studied the chapter yet!

http://highered.mcgraw-hill.com/sites/0072283645/student_view0/chp_19_state_variable_analysis.html

Engineering Circuit Analysis | Chapter 19 State-Variable Analysis
 
F

Fred Bloggs

Jan 1, 1970
0
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 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.
 
J

Jim Thompson

Jan 1, 1970
0
On Fri, 18 Aug 2006 01:39:10 +0200, wombat

The Phantom wrote:
On Thu, 17 Aug 2006 21:50:18 +0200, wombat


Hi All,

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
[snip]

Change to Laplace notation such that Xc = 1/(C*S)

Calculate y(S)

How would you calculate y(S), since R1, R2 and R3 are unknown functions
of time?
Partial fraction expand y(S)

Convert y(S) expansion terms to y(t)

Trivial ;-)

...Jim Thompson

If R1, R2 and R3 are *unknown* functions of time, then how can you
solve it period?

Unless you're just asking for an generalized differential equation?

If R1, R2 and R3 are *known* functions of time then R1(S), R2(S) and
R3(S) exist.

...Jim Thompson
 
W

wombat

Jan 1, 1970
0
John said:
wombat said:
John O'Flaherty wrote:

wombat wrote:


John O'Flaherty wrote:



wombat wrote:



The Phantom wrote:



On Thu, 17 Aug 2006 21:50:18 +0200, wombat





Hi All,

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? Secondly I could do
with some tips on calculating h(t) at A and B.

I really appreciate any help.


You need to give as much detail as you can for problems like this. For
example, detail that you didn't give that would be helpful:

Tell us more about the nature of Vx and Vy. Are they sine waves (what
frequency) that vary only slowly? Or, do they vary quickly? What varies,
the frequency? The amplitude? If they aren't sine waves, what are they?
What are their nominal characteristics and how do they vary? Are they
steady most of the time with some variation only occasionally? Or, do they
vary constantly?

How much are the resistors likely to vary? One percent? Ten percent?
Quickly, or slowly? How quickly or slowly? What are the nominal values of
the resistors and capacitors?

To what accuracy do you need to determine the change in the resistors?
How quickly must you report the change in the resistors when they do
change?


Thanks for your interest. I'll try to answer your questions but as far
as I see it it's a mathematical issue so the nature of waveforms is
largely irrelevant (within reason).

x and y vary but there is no waveform that can be associated with them.
They are at the whim of nature. However they move relatively slowly,
perhaps 50% of their nominal value in one minute. Sometimes they are
essentially constant but I don't have the luxury of measuring only when
they are constant. I must monitor them all, all of the time for a
discrepancy event.

I need to pick up variance in resistance of +/-10% when the variance
occurs for more than 5 secs. The resistors are ~2000G ohms (that's right
giga) and the caps 2.2pF.

An accuracy of +/-2% of the nominal would be great. I can report the
change up to 1 minute after the event.

Now that I look at it I guess one could consider it analogous to a
series of strain gauges where the overall excitation voltage floats
around and the caps represent stray capacitance to ground.


What if you could take the measurements of the voltage sources, and
apply them either to a simulation program or to a circuit set up to
represent the nominal values of your subject circuit, but with handier
values- 2 Mohm and 2.2 nF, say, and then see at some interval how much
the subject circuit deviates from the simulation/test circuit?
--
John


That's a possibility (I can measure all voltages) but I want to avoid
requiring a full blown PC for the calcs if I can. DSPs, FPGAs and
microcontrollers are preferable for the computations due to size
limitations.


Try the physical component simulation. You can claim you are using a
RISC analog computer to generate a comparison standard.



Out of interest has anyone ever done that? Calculated a SPICE model out
in real-time using real time-varying sources. I guess it's like having a
piecewise source with the 'pieces' coming from real world measurements.
Interesting.

RE: "Try the physical component simulation"

Very funny. I wish it was that easy. A few 0402 parts hidden under a
black plastic square and I make the claim... problem is that this isn't
even an electrical system, just one that can be modelled by one.

I think the solution will be something like: A numerical SPICE style
solver that digest the measurements of Vx and Vy and spits out the
expected voltage of VA and VB in real-time. That result is compared with
the measured values of VA and VB. I probably only need to calculate
every half a second to successfully catch the event so it's probably
doable with a decent micro. Thoughts?


You might set it up as a state variable system. The state variables are
the variables that represent the current state of the system, that is,
the capacitor voltages and inductor currents. Since the form of your
system is fixed, you only need to figure out the form of its
representation once. The current state of the system, the inputs, and
the system form are represented as matrices, and you can calculate the
next state of the system by fixed procedures. This is a time-domain
procedure. There is a chapter of a textbook available free on the net
that describes the procedure. I can't be of further help because I
haven't studied the chapter yet!

http://highered.mcgraw-hill.com/sites/0072283645/student_view0/chp_19_state_variable_analysis.html

Engineering Circuit Analysis | Chapter 19 State-Variable Analysis

Thanks for that John. Ok I've had a read. Lets assume I could get my
head around all that and develop a state-space model for the system. The
problem as I see it that I can't describe the inputs with a mathematical
equation. They are measured values that change due to the influence of
the quasi-random environment. This is why I'm thinking that some sort of
iterative numerical method (like SPICE) might be the way to go.

You mention determining the next state of the system by a fixed
procedure. I didn't see anything on that. The inputs were all 'cos' this
or 'sin' that...
 
J

Jim Thompson

Jan 1, 1970
0
I don't think LPF's will help. The reason being is that when the
resistors change (this was explained in a previous post 5560128 - not
sure if that number is of any use, found it in the header) they change
approx +/- 10% of their value for only 10 secs. I think the kind of
filtering you are suggesting would attenuate it too much and I would
miss the event.
[snip]

Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson
 
F

Fred Bloggs

Jan 1, 1970
0
Jim said:
I don't think LPF's will help. The reason being is that when the
resistors change (this was explained in a previous post 5560128 - not
sure if that number is of any use, found it in the header) they change
approx +/- 10% of their value for only 10 secs. I think the kind of
filtering you are suggesting would attenuate it too much and I would
miss the event.

[snip]

Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson

At 1000G-ohm source impedance and pf shunt? I don't think so-do you
believe this clueless ME has a hint in hell of what he's trying to do or
knows what is even close to realizable? Bwahahaha- as you say.
 
W

wombat

Jan 1, 1970
0
Fred said:
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 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.

My original post was probably a little premature and therefore
misleading with regard to the problem statement so I'll clarify.

"I need to know if the resistors change by more than 10% while having to
contend with the sources of x and y moving up and down."

Regarding the time constant, I have modelled the circuit. As an example:
When R2 decreases it's resistance by 10% (to 1800G) point B changes to
it's maximum voltage (however only 0.4% change) in under 8 secs.

Unfortunately the current through the resistors can't be measured so I
have to rely on voltage measurement. It sounds pretty extreme, 0.4%
accuracy is hard to come by but if I measure differentially across the
resistor it equates to ~5% change - definitely achievable.

The previous problem is related but my methodology changed when I
realised I couldn't do it that way. It wasn't solvable.

wombat
 
W

wombat

Jan 1, 1970
0
Jim said:
I don't think LPF's will help. The reason being is that when the
resistors change (this was explained in a previous post 5560128 - not
sure if that number is of any use, found it in the header) they change
approx +/- 10% of their value for only 10 secs. I think the kind of
filtering you are suggesting would attenuate it too much and I would
miss the event.

[snip]

Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson

That's correct I am trying to determine the R's. My original post was
misleading because I was thinking that if I could somehow 'convert' the
measured voltages at A,B using some sort of inverse system I would
arrive at a steady state version of A,B. With that knowledge I could
calculate the R's. My mistake.
 
J

Jim Thompson

Jan 1, 1970
0
Jim said:
John Woodgate wrote:

In message <[email protected]>, dated Fri,


I can connect LPF's to A and B however I don't see the benefit. A and
B are already 'filtered' by the nature of the arrangement of R's and
C's. That's the problem!


When I wrote my post, you hadn't told us the R and C values. But that's
beside the point. If the voltages are varying, and you want to know the
average voltages, the RC time-constants in the circuit itself are not
long enough to smooth out the variations. So you need to add low-pass
filters, also known as averaging circuits, to smooth them out.

I get the strong impression that you are 'thinking complicated', and, as
happens too often in this NG, people who should know better are
encouraging that.


I don't think LPF's will help. The reason being is that when the
resistors change (this was explained in a previous post 5560128 - not
sure if that number is of any use, found it in the header) they change
approx +/- 10% of their value for only 10 secs. I think the kind of
filtering you are suggesting would attenuate it too much and I would
miss the event.

[snip]

Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson

At 1000G-ohm source impedance and pf shunt? I don't think so-do you
believe this clueless ME has a hint in hell of what he's trying to do or
knows what is even close to realizable? Bwahahaha- as you say.

I haven't been able to make much sense as to what he's trying to
accomplish, though I've re-read the whole thread :-(

...Jim Thompson
 
J

Jim Thompson

Jan 1, 1970
0
Jim Thompson wrote:
[snip]
Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson

That's correct I am trying to determine the R's. My original post was
misleading because I was thinking that if I could somehow 'convert' the
measured voltages at A,B using some sort of inverse system I would
arrive at a steady state version of A,B. With that knowledge I could
calculate the R's. My mistake.

Are the R values very high as Bloggs implied?

I haven't found where you stated the R and C ranges. Can you
re-state?

...Jim Thompson
 
T

The Phantom

Jan 1, 1970
0
On Fri, 18 Aug 2006 01:39:10 +0200, wombat

The Phantom wrote:
On Thu, 17 Aug 2006 21:50:18 +0200, wombat


Hi All,

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

[snip]

Change to Laplace notation such that Xc = 1/(C*S)

Calculate y(S)

How would you calculate y(S), since R1, R2 and R3 are unknown functions
of time?
Partial fraction expand y(S)

Convert y(S) expansion terms to y(t)

Trivial ;-)

...Jim Thompson

If R1, R2 and R3 are *unknown* functions of time, then how can you
solve it period?

That is exactly the question the OP would like to have answered.
Unless you're just asking for an generalized differential equation?

If R1, R2 and R3 are *known* functions of time then R1(S), R2(S) and
R3(S) exist.

The OP has clearly said that they vary with time and he would like to
detect when they vary and by how much. This means that transform methods
aren't applicable, or at best, only approximately applicable.
 
A

Abstract Dissonance

Jan 1, 1970
0
wombat said:
Fred said:
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 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.

My original post was probably a little premature and therefore misleading
with regard to the problem statement so I'll clarify.

"I need to know if the resistors change by more than 10% while having to
contend with the sources of x and y moving up and down."

Regarding the time constant, I have modelled the circuit. As an example:
When R2 decreases it's resistance by 10% (to 1800G) point B changes to
it's maximum voltage (however only 0.4% change) in under 8 secs.

Unfortunately the current through the resistors can't be measured so I
have to rely on voltage measurement. It sounds pretty extreme, 0.4%
accuracy is hard to come by but if I measure differentially across the
resistor it equates to ~5% change - definitely achievable.

The previous problem is related but my methodology changed when I realised
I couldn't do it that way. It wasn't solvable.


I'm still not sure what your after but if I interpret what you said above
correctly then all you want to do is determine the change in R?

This is quite easy if you can measure the sources and have some standard
value of R to compare to. All you have to do is measure the voltage across
R and the voltage sources and compare it to what would theoretically be
expected with the standard value that R is suppose to be.

i.e., You use the "theoretical" values of the resistanaces and capacitances
and the experimental voltages sources and then the experimental values for
all and then compare for differences.

If your circuit is fixed and you can solve it algebraically then all you
have to do is "plug in" the measured values and the theoretical values and
compare. If you can't solve the circuit algebraically then you will have to
do numerics on it to get the results.


You could do more advanced mathematics(stochastic DE's and such) but I think
for your problem it would be quite easy since you can measure the voltage of
the voltage source. (else it would be impossible for an arbitrary voltage
source because you can't tell if the extra voltage drop on the resistors are
coming from the change in resistance or from the voltage source)



for example,
R
+---/\/\/\/\----+
| |
If, say, you are trying to figure out the change in R then its quite easy.

Vx - I*R - Q/C = 0

==>

I = dQ/dt

so

Vx - dQ/dt*R - Q/C = 0



and Q(t) = exp(-t/RC)*(Q0 + int(Vx(s)*exp(s/RC)/R,s=0..t))

but VR(t) = dQ/dt*R =

so the voltage drop across the resistor is given by

VR(t) = Vx(t) - exp(-t/RC)/RC*int(Vx(s)*exp(s/RC),s=0..t) - VC0*exp(-t/RC)


But we can measure VR(t), Vx(t), and VC0 and hopefully we know the
theoretical value for C(else its more complicated and probably impossible to
measure) then we can calculate the value R for this(numerically).

i.e., say the theoretical value for R is 10ohms. Then we can measure and
plug into the equation above and test for different R's until we get a true
statement. This R then can be compared with 10 ohms to see how much it
varied to a "hidden" variable.

If, say, C = 1, VC0 = 0, and Vx(t) = t when we start measuring(So we will
have to sample the voltage sourc) and suppose that we measure the voltage
across the resistor at the end of 1 sec to be 1/2V

then

1/2 = 1 - exp(-1/R)*int(s*exp(s/R),s=0..1)

we get the equation

1/2 = 1 - R^2*exp(-1/R) - R^2 + R

We can solve this numerically to find out what R has to be to produce those
measurements: This equation has solutions at about 1.065 ohms.

So one would have a change in about 9 ohms.

Anyways, Thats just an example and the measurements are made up for the
purpose of demonstrating what you could do. It might not be the best way to
do this though depending on the circuit and such. If you could measure the
current then it would be hell of a lot easier as you would only need to
measure the voltage and current of the resistor you want to measure and then
compute its value using ohms law... and it would be correct regardless of
the circuit topology(for the most part).

The above method may not work well though since its possible to have
multiple solutions and there might be stability issues in trying to
implement it.

Ultimately it would probably be much easier to just measure the current
along with the voltage. You can also do the same to measure the capacitance
since V = Q/C and I = dQ/dt but you will need to sample the current enough
to build a history for the integration.

Ofcourse if this was some type of research then you would be using much more
complication mathematics and physics to get the answers but I doubt you want
to spend the next 10 years on that.

Hopefully I'm on the right track with what you want to do. If so then one
thing you have to realize is that there are probably thousands of factors
that can change the resistance and can complicate matters. Even the simple
RC circuit above is quite complicated in this aspect if both the resistance
and capacitance can change. If you don't know what is making them change and
cannot model that sufficiently then it can be very difficult to measure
there change by limiting yourself to measuring only one aspect of them(such
as there voltage). The reason is simple. What we measure as a change of
resistance my actually be from a change of capacitance and vice versa. So
you would have to be vary careful not to allow this type of situation to
occur in your method. Also, say, assuming the capacitance is constant when
it is not could contribute. So, in this problem is not only what you
measure but what you don't. This is not to say that there might be
simplifications and approximations that could make the problem much easier
to deal with. I'm just not completely clear on what you are trying to do.

Anyways,


Jon
 
T

The Phantom

Jan 1, 1970
0
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.
 
W

wombat

Jan 1, 1970
0
Jim said:
Jim Thompson wrote:

[snip]
Is it the value of the resistors that you are trying to determine,
since you said "I can also measure *all* voltages"?

...Jim Thompson

That's correct I am trying to determine the R's. My original post was
misleading because I was thinking that if I could somehow 'convert' the
measured voltages at A,B using some sort of inverse system I would
arrive at a steady state version of A,B. With that knowledge I could
calculate the R's. My mistake.


Are the R values very high as Bloggs implied?

I haven't found where you stated the R and C ranges. Can you
re-state?

...Jim Thompson

Yes they are. The R's are ~2000G and the C's are ~2pF. They're not
really electrical bits so I know I can't by them at Digikey.
 
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