# Calculation of the energy from a pulse

• Sara87
In summary, the capacitor will release pulses of energy that go through the two electrodes in a chamber. The pulses will be generated by the spark gap and will have an exponential decay. The area under the curve will tell you the total amount of energy that was delivered in any short period of time.
Sara87
Hello
I need help for a basic question (i am awful in physics)
I have two capacitors in parallel when they are charged up (18.5 kV) they release the energy to a discharge device. The discharge device releases the energy in the form of electric pulses through two electrodes in a chamber (the pulses will go through the liquid in the chamber for pulsed electric field treatment)
An exponential decay waveform is generated at the applied voltage.
What I need is to calculate the area under the discharge curve of the capacitor to have the energy of each pulse.
But i don't know which parameters, equations and ... do i need.

I would appreciate any help.

Regards,
Sara

Are you asking us how to calculate the area underneath a given curve?

I don't have the curve actually, I guess I need to draw it and yes have the area under.

The energy stored in the capacitor will be CV2/2 and that is the maximum amount of energy that will be delivered, irrespective of the time of the discharge. I would say that you are very unlikely to get a simple 'exponential' discharge because the load could well not be an Ohmic Resistance (hence no RC)

If you can measure and record the Volts across the Capacitor at a high enough sample rate, you could plot the discharge curve and calculate the energy supplied in any short instant by the difference between the energy at the start and end of the interval. That could be expensive if the total discharge time is very short. What are the time intervals involved?

Sara87
This seems like a homework question to me.

Let me to explain it better.
I have these devices as you can see in the picture attached.
The capacitor become charged up to 18.5 kV and releases the energy to the discharge switch and then the energy in form of pulses go through the electrodes in the chamber.
I am asked to calculate the energy which goes from the electrodes to the liquid in the chamber.
I guess for that I need to draw the exponential decay curve and calculate the area underneath.
I don't know how and where to start.

P.S. This is not a homework. I am a master student working on my final project

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Sara87 said:
energy in form of pulses

It isn't clear what is actually happening in this circuit.
What forms the pulses? Are you referring to some sort of high voltage oscillation due to the spark gap and some resonance in the circuit or does each pulse get generated by the 'Grey box' in the picture? What initiates the discharge? Is it when the spark gap breaks down?
Can we have a proper circuit schematic of the setup?

Sara87
The owner of the device told me they are exponential decay pulses. yes it gives high voltage pulsed electrical field (20 kV/cm) within the liquid material in a treatment chamber in a very short period of time (4 µs).
Yes the discharge will happen at the breakdown voltage of the spark gap.
Unfortunately I don't have any better picture.

Sara87 said:
The owner of the device told me they are exponential decay pulses. yes it gives high voltage pulsed electrical field (20 kV/cm) within the liquid material in a treatment chamber in a very short period of time (4 µs).
Yes the discharge will happen at the breakdown voltage of the spark gap.
Unfortunately I don't have any better picture.
Unless the discharge is through an Ohmic resistance, I don't see how the discharge can he Exponential - unless there is a large resistive component in the supply and if you treat the arc as a short circuit. But in that case, it would be very hard to estimate the energy supplied to your chamber. If this project is important to you then you should make sure that you get the theory right - unless your equipment is calibrated to tell you the correct value for the Energy transferred.
I don't want a "picture" I (you and we) want / need a proper schematic diagram to show the function of the circuit. Failing that, you just have to rely on what the 'owner' has told you. There is no simple answer to this.

Maximum energy from the power supplier unit is 200 J/s which goes to the capacitor. there will be some losses in the wires but it can be neglected. the spark gap device (PerkinElmer’s OGP ceramic-metal overvoltage spark gaps) have a resistor inside which I don't know the R value for that. When they reach the breakdown voltage they release the pulses.
I was told to calculate the
and then I will be able to calculate the area under the curve in the picture attached.

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You have the functions V(t), I(t) and τ=RC=1 μs-1.
But, energy is not the area under the curves. The axis is V(t), not V(I).
We calculate energy by:
$$E = \frac{1}{2}CV_0^2$$
To calculate C we must know the value of R.

If we have no this information we can see that the charge currency is the same to uncharge. So energy must be:$$E=\int_0^{5\tau}V(t)I(t)\,dt = V_0I_0\int_0^{5\tau}(1-e^{-t/\tau})e^{-t/\tau}\,dt \approx \frac{1}{2}CV_0^2$$ If we can assume that:
$$V_0I_0 \approx 200 (w)$$ approx the source power then we have:$$E \approx \frac{1}{2}V_0I_0\tau \approx 100\tau = 10^{-4} (J)$$per cycle.
Integral calculated from 0 to infinity and is τ/2.

Last edited:
Sara87
Cycle time is 10τ so the power is:
$$P = \frac{10^{-4}}{10^{-5}} = 10 (watts) = 5\% \text{ of power supply or less}$$

Sara87

## 1. What is the equation for calculating the energy from a pulse?

The equation for calculating the energy from a pulse is E = 1/2 * C * V^2, where E is the energy in joules, C is the capacitance in farads, and V is the voltage in volts.

## 2. How do you determine the capacitance and voltage for the energy calculation?

The capacitance and voltage can be determined by measuring the charge and voltage of the pulse using appropriate instruments, such as a capacitor meter and a voltmeter. The values can also be calculated if the electrical properties of the pulse source are known.

## 3. Can the energy from a pulse be negative?

No, the energy from a pulse cannot be negative. The equation for calculating energy only produces positive values, as both capacitance and voltage are positive quantities. A negative voltage can result in a negative energy if the pulse direction is reversed, but this is not considered a valid calculation of energy from a pulse.

## 4. How does the energy from a pulse differ from other forms of energy?

The energy from a pulse is a specific type of electrical energy that is transferred in a short duration, as opposed to continuous forms of energy like electrical power or mechanical energy. It is often measured in joules or electron volts and is typically associated with high-intensity, short-duration events such as lightning strikes or electronic pulses in circuits.

## 5. What factors can affect the accuracy of the energy calculation from a pulse?

The accuracy of the energy calculation from a pulse can be affected by various factors, including the accuracy of the instruments used to measure capacitance and voltage, any resistance in the circuit or components, and variations in pulse shape or duration. It is important to carefully consider and account for these factors when calculating the energy from a pulse.

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