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# Measuring the energy in a pulse

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#### riccardo

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How might someone go about measuring the energy discharge in an electrical pulse?

For example, if a capacitor is discharged into a resistor, you can trace this electrical pulse on a scope in terms of voltage or current. You can also calculate the energy using 1/2CV^2.

However, if the capacitor has some external dynamic influence such as energy from an antenna, a chemically active dielectric, mechanical forces, and so on which make calculation impossible, what would be the best way to measure the energy in the pulse directly?

Would you record the scope traces and then use excel to do some calculation on those values? (i.e measure the power on each sample and divide by time)
OR is there another way such as a dedicated device that will do the calculations on the fly?

How might someone go about measuring the energy discharge in an electrical pulse?

For example, if a capacitor is discharged into a resistor, you can trace this electrical pulse on a scope in terms of voltage or current. You can also calculate the energy using 1/2CV^2.

However, if the capacitor has some external dynamic influence such as energy from an antenna, a chemically active dielectric, mechanical forces, and so on which make calculation impossible, what would be the best way to measure the energy in the pulse directly?

Would you record the scope traces and then use excel to do some calculation on those values? (i.e measure the power on each sample and divide by time)
OR is there another way such as a dedicated device that will do the calculations on the fly?

If you are referring to to the energy lost by the capacitor, simply measure the voltage before and after the energy transfer. Once you know the two voltage measurements and the value of the capacitance, you can easily calculate the energy transfer from the capacitor to someplace else. Finding the distribution of the transferred energy into heat, light, E-M radiation, etc is another problem.

Ratch

No that wont work unless it is simply a passive capacitor. In this example, the voltage during the pulse can go up and down.

No that wont work unless it is simply a passive capacitor. In this example, the voltage during the pulse can go up and down.

Are you averring that energy is being sent into the capacitor at the same or close to the same time as the capacitor is supplying energy elsewhere? That situation is similar to the filter capacitor of a rectified sine wave. You might peruse that topic to see how that problem is analyzed.

Ratch

Yes, or that the capacitor properties alter during charge/discharge.

Yes, or that the capacitor properties alter during charge/discharge.

Without knowing more about what you are doing, all I can say is that energy input equals energy output plus energy stored. If the capacitance changes value, it will cause a voltage change, but the energy stored in the capacitor will remain the same.

Ratch

1·k·W·h = 3.6·10⁶J
e.g. the wires diffuse energy as to resistance(/heat) as to EM field as to stray capacitance caused minor oscillators - measuring the pulse energy is mostly limited to measurement setup as the fast changes are hard to get in practice with precise enough detail . . . if you can set your specific pulse to re occur periodically you can derive it's energy by some statistics and/or adequate sys. model . . .

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A current mirror might be applicable here ... your pulse drives the input side, while an open collector output side allows a capacitor to charge. I have used a similar method to read an inductive sensor, by applying a pulse to the inductor and having the back emf of the inductor drive a current mirror. The capacitor on the collector was discharged from a micro controller after the value was read with an ADC.... the micro also orchestrated the pulse to the inductor. The capacitor, if I remember right, was on the order of 330pF .

How might someone go about measuring the energy discharge in an electrical pulse?
Energy discharge is the energy that is delivered by the capacitor to some external load. There are two ways to estimate the value.

1. Look at the energy in the capacitor both before and after the discharge, assuming a known capacitor model.
2. Measure the energy that is flowing to the load by integrating the power from voltage and current measurements.

For example, if a capacitor is discharged into a resistor, you can trace this electrical pulse on a scope in terms of voltage or current. You can also calculate the energy using 1/2CV^2.
Here you are highlighting the two methods. With the resistor you can measure voltage OR current, as you say, but for an unknown load, it would be better to measure both current AND voltage. Then you can calculate the actual energy flow in general. You would then not be dependent on the ideal behavior of the load or the capacitor.

However, if the capacitor has some external dynamic influence such as energy from an antenna, a chemically active dielectric, mechanical forces, and so on which make calculation impossible, what would be the best way to measure the energy in the pulse directly?
Here you are highlighting the nonideal behavior of the capacitor. Hence, I think method 1 is the preferred method.

Would you record the scope traces and then use excel to do some calculation on those values? (i.e measure the power on each sample and divide by time)
OR is there another way such as a dedicated device that will do the calculations on the fly?
If you can get accurate voltage and current readings on and from the capacitor terminals. Then you can record the data in time and do calculations. Keep in mind that it is very possible (even likely) that measurement inaccuracy will swamp out any nonideal behavior of your capacitor or load. Hence, you would want to do various calculations for load and capacitor energy assuming models for the capacitor and load. It is very challenging to determine whether you have a measurement inaccuracy or an insufficient model fidelity.

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