Damped Sine Oscillator

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haklesup
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Damped Sine Oscillator

Post by haklesup » Wed Jan 02, 2008 1:23 pm

I want to make some noise. I need to design a simple oscillator that makes a single damped sine transient noise pulse when triggered (by a button or logic signal). I want to be able to control the Amplitude, Frequency and damping time and I want it to be an analog circuit (I already can do this with an ARB)

Amplitude and frequency not specified yet but it will be less than 30V and less than 2MhZ ringing. and last less than 100ms. Ideally, it would be variable via pots but I think a cap decade box is more likely.

Anybody got any specific Ideas. I think it can be done by putting a square pulse through an LC circuit but I am not clear on the details yet.

In case you're not sure what I want, see fig 1 of this reference
http://www.aetherwire.com/UWBWG_Archive ... WFinal.pdf

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Post by Robert Reed » Wed Jan 02, 2008 2:04 pm

Hackles
"Anybody got any specific Ideas. I think it can be done by putting a square pulse through an LC circuit but I am not clear on the details yet."
I think you may have answered your own question. Damping would be directly related to the Circuit "Q". Is this for one frequency or multiple frequencys (not the same time).If just a few, I suppose you could switch in a few LC circuits to accomodate any particular frequency. High "Q" circuit , shunted by a 10 K- 50K pot to contol damping or ringing time, however will probably also affect amplitude simultaneously. Sounds like an interesting project. What's it for?

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Post by jwax » Wed Jan 02, 2008 4:40 pm

Wow! I remember when I saw the first description of the TimeDomain method of UWB transmission/Reception. Impressive! It's a method that the FCC said "You can't build those", because they were un-snoopable. A RxTx pair would be impossible to intercept and interpret.
Your design will depend on how much power you're after, and your load impedance of course. Will you be transmitting this damped pulse, or wired directly to a load?
Interesting project! :)

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haklesup
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Post by haklesup » Wed Jan 02, 2008 6:17 pm

My project has nothing to do with transmission, the signal will stay in a wire for my purpose.

I'll probably drive a 50 ohm load to make it easier since the properties of such a circuit are often quite sensitive to load impedance.

I am going to add this "noise"signal to a DC offset and use it power an IC device. The idea is to see how the device reacts to such a disturbance of the supply voltage. I need it to be variable to explore what parameters cause device failure. This is but one of a number of noise signatures we are trying.

Why this pulse? Because it resembles the pulse used by ESD guns in the system level ESD tests. (IEC something or other) and the users of this test will be ESD and device test guys. I need some data from this pulse to correlate to another I use to show these guys they can use my simplified pulse not this one.

I've been playing about with MultiSim most of today and I can get it with a series L, parallel R, C. However if I drive that with a square wave, I get the transient with a DC offset. I next tried a series C at the input to give me an AC decouple but the induces an asymmitry in the pulse. Tomorrow I will try decoupling the output and some other ideas.

If I had a decent arbitrary waveform generator, I wouldn't bother but no $ in the budget for such a specialized piece of equipt right now.

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Post by MrAl » Wed Jan 02, 2008 10:07 pm

Hi there hackle,

I was going to ask what you are going to drive with this?

The reason is because the complexity of the circuit largely depends
on what you have to drive with it. You may end up needing an
output amplifier if the load can change because that will throw the
damping off every time if it changes too much.

Also, how critical is the way the wave damps out for this app?

Zapping a parallel LC circuit with a pulse might generate some offset
dc because there is dc in the pulse itself. Trying to cap couple will
result in a problem too because it becomes part of the circuit.
You would probably need a square wave that goes both plus and
minus. Maybe an amplifier with some dc offset built in to compensate
for the dc in the pulse.

One way to get a very controlled wave is to use an actual train
of square wave pulses, going both plus and minus, and an LC circuit
tuned to the same frequency as the square waves. The square
waves are then made to decrease in amplitude over the damping
time period (say 100ms) and the output (sine waves) follow the
amplitude shifting. The LC circuit has to be retuned if the square wave
pulses change in frequency or the output doesnt look like a sine
wave anymore.

Oh yeah, one more idea...
Use a relatively high pulse amplitude, say 10v peak, and 100ns pulse,
in series with the pulse generator connect five (5) 1N4148 diodes
(anode toward pulse generator), and the output of the last diode
(cathode) to a parallel RLC network. After the pulse a series of
waves appear that are pretty much centered about zero volts
and damp out. The damp out time depends on the parallel resistor
value.
For example, a 10v pulse for 100ns, five diodes, L=100uH and C=0.001uf
and R=10k, the waves appear for about 80us and then pretty much die
out to zero.

The diodes help to provide a dc offset as well as isolate the generator
from the RLC network after the pulse goes away.

You should probably try to get an inductor with a low series R.
The example above the L had 3 ohms series resistance and the
C had 1 ohm ESR.

Note that if you connect this directly to a 50 ohm resistor the damping
will increase meaning the waves will die out MUCH quicker, probably
not even 1us.
LEDs vs Bulbs, LEDs are winning.

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MrAl
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Post by MrAl » Wed Jan 02, 2008 11:32 pm

Here are some equations that can help to figure out the damping
time period as well as the oscillation frequency of the chirp waves...


The resonant frequency is
wo=1/sqrt(L*C) rad/sec
f=wo/(2*pi) Hertz

The neper frequency is
a=1/(2*R*C)

The voltage response is
V=(e^(-at))*(B1*cos(wd*t)+B2*sin(wd*t))

since both the cos and sin terms multiply by the
exponential, we can look at e^(-a*t) as a sort of
percentage of peak voltage. When the percentage
is low the waves are damped out almost completely.
This gives us some idea how the value of R affects
the damping as to the approximate time period.

Looking at a few values for e^(-a*t) for periods
of time of say 20us, 40us, 60us, 80us and 100us:

000us: V=1.000v (100%)
020us: V=0.368v
040us: V=0.135v
060us: V=0.050v
080us: V=0.018v
100us: V=0.007v (less than 1%)

Thus, after 100us the wave has died down to less than
one percent of it's initial peak value.
Note that if we change R or C the neper frequency changes
and that changes the damping and hence the time it takes
to damp out to less than 1 percent of the initial peak
value of the wave.

We could easily solve for the value of t for a given
percentage. Starting with the equ for voltage,
V=(e^(-at))*S
where S stands for the sin and cos terms,
setting V=0.01 we then solve for R:

V=e^(-a*t)*S
V=e^(-t/(1/a))*S
V=e^(-t/(2*R*C))*S
now solve for R:
V/S=e^(-t/(2*R*C))
ln(V/S)=-t/(2*R*C)
-2*C*ln(V/S)/t=1/R
so
R=-t/(2*C*ln(V/S))

Now set S=1 and plug in the other numbers:
R=-0.0001/(2*(0.001e-6)*ln(0.01))
and so R comes out to be 10857 ohms for
100us damping time.

Of course we need a certain frequency, so we would
have first solved for the value of L and C with:
wo=1/sqrt(L*C) rad/sec
f=wo/(2*pi) Hertz
where f is the frequency in Hertz we want as the
chirp waves. The number of waves before the 1%
damping point will depend on how long the damping
is divided by the time for one cycle of the frequency.

Note however that the output of the example network
had a 10k ohm resistor. Connecting a load with even
a high resistance like 10k would immediately cut the
damping time in half. A much lower load could cause
it to damp out so quickly it's not even noticable,
so an output amplifier would have to be used in most
cases.
LEDs vs Bulbs, LEDs are winning.

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Post by Robert Reed » Thu Jan 03, 2008 8:02 am

In lieu of a train of square waves, I think you would rather drive The LC circuit with just one short DC offset pulse that has a rise time sufficient to contain all the frequencies you want to spike the LC cicuits with. The LC circuit could be made tunable with a varicap diode and a roughly calibrated dial mounted to the pot that supplies bias voltage to the varicap diode. And of course you would need isolation on both ends of the LC circuit to maintain its integrity. Shouldn't be difficult at the low frequencys you are working with. Once you have come out of the isolation stage ( a dual supply follower wich could also incoporate level shifting and thereby forgoing the prior offset of the initial pulse should be sufficient) . The pulse could be merely injected thru a high value series resistor. The damped wave can be outputted through any kind of power stage thats required. You will probably have to manually readjust amplitude along the way, but if this is just a 'one off ' project, a little inconveniance here is no big deal. Damping as previously posted. Also, one of the many equations for "Q" is L/C which really translates to high reactance in each leg of that circuit. Of coarse, with higher L, you will also start aquiring higher R, so ther is an optimum value here due to this trade off. In my experience, this usually has been benficiial in designing these circuits. I wouldn't design a piece of test equipment in exactly this fashion, but for 'cheap and simple', it should work.

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haklesup
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Post by haklesup » Thu Jan 03, 2008 4:55 pm

Thanks you have given me a mouth full to chew on. THe parameters of the waveform are somewhat arbitrary becasue I am trying to emulate real world electrical noise which by nature is arbitrary. However if you are attempting to create a scietific test, one must control as many variables as you can.

FYI: All the research so far indicates that the magnitude of the undershoot and the rise time of the waveform from the minimum back up to VDD is where the failure will occur. The whole rest of the waveform is irrelevant because the device may have already failed in the first cycle. Ideally I will make a signal that is easily reproducable, triggers the failure mechanism and is easy to extract the numerical parameters that matter (amplitude, slew rate)

In particular I am trying to initiate CMOS latchup failure mode but this test also shows design defects in ESD protection structures and power domain isolation. While this kind of noise shouldn't happen to a real device in a real circuit, it does occasionally. Nobody expects the device to function ininterrupted, but on the other hand, we don't want it to self destruct as a result of this noise either.

This noise signal will be buffered through a wideband amplifier (DC to 1Mhz, +/-30v, +/-3A, Gain =1x, 2x, 5x or 10x). The amp has high Z and 50 ohm inputs. Anything the load does will be completely isolated from the signal source. I could do it with uA's

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Post by MrAl » Thu Jan 03, 2008 7:38 pm

Hi again hackle,

Sounds almost like you might be better off using triangular waves,
where you can allow the wave to shoot up to a pre-calculated point
and then shoot down to another calculated point. This should give
you excellent control over the rise/fall times. This wont be sine but then
you dont really need sine to simulate noise really.

A cap and resistor driven with a pulse generator where the pulse
width varies randomly would give you a nice variable noiselike
wave where you have control of min and max but allow in between
to vary randomly. If you dont like random, simply use a set of
pulses that vary but repeat after a given time period.
If you want sharper points you can use an op amp integrator instead
of a resistor and capacitor to force the waves to be almost prefect ramps
up and down forming variously sized triangle waves.

Since the amp you talk about has a high Z input then maybe you
wont need an output amplifier.
LEDs vs Bulbs, LEDs are winning.

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Post by Ron H » Sat Jan 05, 2008 10:18 pm

If this method has already been mentioned, please accept my apology. I didn't have the patience to read the entire thread.

I think I would use an analog multiplier, and apply a continuous sine wave to one input, and an exponential to the other. Your damping and frequency are now totally noninteracting, and easy to control. I sim'ed this idea with an LM1496, and it works pretty well. The LM1496 is not linear on the carrier input, and a true analog multiplier would generate less harmonic distortion.

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