Calculating Power of a Pulse: Tips and Considerations

[axawire]

Hi,

Im trying to calculate the power of a pulse. I know the duration of the pulse t in seconds and I know the peak current Ipeak in Amps. If need be I can also calculate the resistance R of the conductor. I know of P=RI^2 but am not sure if this holds for pulses.

Help/Tips/Suggestions

Thanks.

 

[vanesch]

Given that power is an instantaneous concept, there's no need to involve time, and it doesn't matter if it is a pulse or a continuous current. Yes, the power is given by I^2.R.

But maybe you're wondering what is the ENERGY of the pulse ? Then you will have to integrate the power over time. Assuming a constant current during time T, the energy becomes then I^2.R.T.

 

[desA]

Current is the rate of moving a bunch of charge down a wire... Would it be acceptable to assume that a pulse represents a constant current?

Perhaps you could consider a charge-time envelope, then integrate this over time, then work in charge-energy relationships to obtain a final form.

 

[vanesch]

Current is the rate of moving a bunch of charge down a wire... Would it be acceptable to assume that a pulse represents a constant current?

Depends. If it is a square-pulse generator feeding a resistor, why not ?
However, if it is some kind of discharge, it will certainly not be constant.

Perhaps you could consider a charge-time envelope, then integrate this over time, then work in charge-energy relationships to obtain a final form.

Well, you'd need to take the derivative of the charge-time curve to find back the current, SQUARE IT, and integrate it back over time.

 

[desA]

Well, you'd need to take the derivative of the charge-time curve to find back the current, SQUARE IT, and integrate it back over time.

You're finding the RMS value for current, I assume.

You could probably also perform a simple integral average of the current (charge-time envelope differentiated). Depends how you wanted to define the final energy form.

 

[vanesch]

You're finding the RMS value for current, I assume.

Well, yes. If you integrate the square of the root of the average of the square, you find, eh, the integral of the square.

You could probably also perform a simple integral average of the current (charge-time envelope differentiated). Depends how you wanted to define the final energy form.

The integral of the differentiated charge-time envelope is simply the difference between the initial and final value of the charge-time curve ; in other words, the total amount of charge displaced.
However, depending on how this is delivered to a resistance, the dissipated energy is different! In the case of a true delta-function, the dissipated energy is infinite. In the case of a square pulse, the energy is indeed <I>^2 R T. For an intermediate pulse form, the energy dissipated in the resistor will be higher than <I>^2 R T: it will be <I^2> R T.
Now, the difference, <I^2> - <I>^2 is nothing else but the variance of the current (that's why for a square pulse, both are equal: the current doesn't change and has variance 0 during the time it flows).
So with <I> alone, you can only estimate a lower bound on the dissipated energy and all variation will increase it.

 

[axawire]

Well... I do not know the exact form of the wave, but I am assuming its sinusoidal in shape (but on the positive part of the wave). Now can I actually use the RMS for current when its a pulse and not an alternating current?

Also I am not so sure about using P=R*I^2 as if I use a super conductor does this equation still apply?

My goal here is I have a rough idea of the shape of this pulse I need, but I am trying to get a ball park figure for how much energy a pulse generater would have to use to generate such pulses on a continuous basis.

Thanks.