sampling frequency required to resolve a pulse

It *has* to be band limited so that it has no frequency components at frequencies above the Nyquist frequency *before* it is digitised.

Fourier analysis is just one way of many to convert a time series into orthogonal basis functions. You could analyse the same problem more clumsily with any orthogonal set of basis functions you choose like Walsh functions which are used in scientific image compression.

Generally you have a pretty good idea about the front end bandwidth and use filters to ensure that the sampling theorem conditions are matched. Failure to do this properly will result in alisaing of higher frequencies reflected around the Nyquist sampling frequency.

Provided that the unknown frequencies were f < F and the length of time they were present was sufficient to distinguish f from F there isn't a problem. You have to low pass to filter out all the frequencies f' > F.

They take it as axiomatic in the definition of the sampling theorem that there are no frequency components with non-zero amplitude at frequencies above Nyquist. This condition can usually be met in practice but it can get interesting if you are making measurements in the Fourier domain and then forming an image by Fourier transform.

The condition is most obviously met in CCDs for telescopes where you can predict from the diameter of the lens that there will be no detail present in the focussed image plane finer than 1.22D/lambda. The Rayleigh criterion for a diffraction limited circular aperture.

--
Regards, 
Martin Brown

If you know *a priori* that it's a sine wave, then it needs just a few measurements total. The sampling theorem relates the sampling rate to the maximum bandwidth that can be uniquely reconstructed. You don't have to choose baseband, either--stroboscopic samplers don't, for instance.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

"Maynard A. Philbrook Jr." wrote in news: snipped-for-privacy@news.eternal-september.org:

Skin effect, skin effect. 1us pulse is a tenth harmonics so frequency is

10 MHz. Skin effect is 24 um so for fuse of this depth, you need 41 meter width if you want to send 300 A in one square milimiter cross section.

Current across L can not change Simultaneously , and neither voltage across capacitor.

For capacitor, you could use glass covered with aluminum foil so minimizing L.

:) Mass.

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Wonder how you were able to measure and supply 300 Amps for 1 us and actually get 300 amps for that 1us before L became resistive?

I had to make a test jig to generate 20k volts for 1 us, for the survivability of dipped silver mica caps, and I know it was a trick to work with lead length and layouts to eliminate the L in the circuit so not to produce SRF.

Jamie

that pops open in 10mS for 100A, so I'd like to mimic something similar to that....

want to respond to fast current spikes as well

in

did

fixturing is

For the supply i used car batteries. Then i used shielded twisted pair everywhere. For the current control resistors i had some fun learning how to form them for minimum L. Thus the test set was resistive primarily. Slammed the snot out of the gate on a monster power fet (irf450 iirc). Had some fun learning how to instrument the pulses reliably as well, self built current transformers. It was painful proving calibration on them.

?-)

meter

I have no idea what you are going about. In proving the system i went to

800 A peak and times anywhere from 250 ns width to a mere 50 A for 30 us. Shielded twisted pair 18 gauge can do things you are not yet ready to believe.

?-)

What we ended up doing was making a jig where the specimen sat in a holder. The base of the holder was round to behave like a toroid. The other side had a spark gap, yes, a spark gap.

This gap was set for a 20kV break over and the environment had to be regulated for this test to be consistence of course.

The high energy coil was directly under the holder so to minimize any lead length.

We constructed this due to a single customer, a military customer, requesting test data subjecting the caps to this punishment. Most likely lightning hits. A single 1us at 20kV pulse.

Test results showed that these caps could take this with a short recovery time ~ 1 min, for about 5 times before they would not recover to a usable state.

Then we had to supply SRF data, which was the easy part.

Jamie

Yes, you used a transmission line but you still had to contend with the DCR in that line. Hmm, I'll have to think on this for a bit.

Jamie

After about 20 more or less useless replies, you finally post some usable requirements.

Anyway, a lightning _current_ is usually simulated with a with 8/20 us pulses (8 us rise and 20 us fall time). Standard lightning _voltage_ pulses are around 1 us rise/fall times.

For short circuit analysis, you need to consider the loop resistance (actually impedance) and in practice, the feeding network impedance limits the current.

If you are using current transformers, you must also consider their frequency response.

If you do not give a rip about reproducing the pulse, put a switch in series with a diode of correct polarity, to charge the S&H cap and another switch to short the cap. SW1 "always" on and SW2 "always" off. read cap voltage; when high, turn SW1 off then SW2 on. Return to sample mode when done. Sample rate s pulse rate, which can be variable

josephkk wrote in news: snipped-for-privacy@4ax.com:

Thanks, I should learn more about twisted pair. But I know that they eliminate stray capacitors which effects rise and fall time, provided return current be equal to going current.

Charges intend to travel at the surface of conductors not whithin.If you notice the copper bus bars are not more than 2 cm thick for 60Hz.

:) Mass

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