# Measuring energy to charge a capacitor from 62V to 300V

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#### Flyback

##### Well-Known Member
Hello,
We are trying to measure the energy delivered to the 820uF capacitor connected to the output of our Offline Flyback SMPS when it charges this capacitor back up to 300V from 62V.

The capacitor is charged up to 300V, then the SMPS is turned OFF, then the xenon tube is flashed, then the capacitor (which discharges to 62V during the flash) is charged back up to 300V by the SMPS after the SMPS is turned back ON again. The flash rate is 1 Hertz.

Anyway, we first tried to measure the energy by capturing the capacitor voltage and the charge current on the scope over an entire charge interval from 62V to 300V. We then set up the math facility on the Wavesurfer MXs104 oscilloscope and took the integral of the instantaneous volt.current products from the start to the finish of a single recharge interval, then divided this by the recharge interval time (900ms) to get the average power over the recharge interval. The scope does this for you. We then divided this power reading by the recharge interval time in order to get the energy delivered to the capacitor in the recharge.

The problem is that this figure did not agree with the calculation which is done by simply subtracting the energy in the capacitor at 62V (0.5*C*62^2) from the energy in the capacitor at 300V (0.5*C*300^2).

In fact, the above two ways of doing the calculation differed by 6.5 Joules. The first method gave 49.5 Joules, and the second method gave 43 Joules.
The scope capture involved 16 Megasamples over the 900ms recharge interval…so that’s one sample every 56ns. However, the output current is very pulsey as it’s a high duty cycle flyback, and as such the flyback diode current is very low duty cycle……as such , I don’t feel there are enough samples being taken. However, our scope offers no more than 16 Megasamples.

We cannot afford a scope with more data memory so we wish to repeat the test with a 820uF film capacitor instead of an electrolytic just in case there was some “ESR situation” with the electrolytic one being recharged at such a low frequency (1Hz).
Do you know of vendors who cheaply sell such big film capacitors 350V and 820uF?

(incidentally the attached LTspice simulation shows how the circuit operates though doesnt have the same component values etc)

Electrolytic capacitor datasheet also attached

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#### Ratchit

##### Well-Known Member
Hello,
We are trying to measure the energy delivered to the 820uF capacitor connected to the output of our Offline Flyback SMPS when it charges this capacitor back up to 300V from 62V.

The capacitor is charged up to 300V, then the SMPS is turned OFF, then the xenon tube is flashed, then the capacitor (which discharges to 62V during the flash) is charged back up to 300V by the SMPS after the SMPS is turned back ON again. The flash rate is 1 Hertz.

Anyway, we first tried to measure the energy by capturing the capacitor voltage and the charge current on the scope over an entire charge interval from 62V to 300V. We then set up the math facility on the Wavesurfer MXs104 oscilloscope and took the integral of the instantaneous volt.current products from the start to the finish of a single recharge interval, then divided this by the recharge interval time (900ms) to get the average power over the recharge interval. The scope does this for you. We then divided this power reading by the recharge interval time in order to get the energy delivered to the capacitor in the recharge.

The problem is that this figure did not agree with the calculation which is done by simply subtracting the energy in the capacitor at 62V (0.5*C*62^2) from the energy in the capacitor at 300V (0.5*C*300^2).

In fact, the above two ways of doing the calculation differed by 6.5 Joules. The first method gave 49.5 Joules, and the second method gave 43 Joules.
The scope capture involved 16 Megasamples over the 900ms recharge interval…so that’s one sample every 56ns. However, the output current is very pulsey as it’s a high duty cycle flyback, and as such the flyback diode current is very low duty cycle……as such , I don’t feel there are enough samples being taken. However, our scope offers no more than 16 Megasamples.

We cannot afford a scope with more data memory so we wish to repeat the test with a 820uF film capacitor instead of an electrolytic just in case there was some “ESR situation” with the electrolytic one being recharged at such a low frequency (1Hz).
Do you know of vendors who cheaply sell such big film capacitors 350V and 820uF?

(incidentally the attached LTspice simulation shows how the circuit operates though doesnt have the same component values etc)

Electrolytic capacitor datasheet also attached
This appears to be the same type of problem as connecting a de-energized capacitor to a energized capacitor. Half of the energy is lost in the wires. You can read about it here. https://www.google.com/search?q=ene...ome..69i57.29412j0j8&sourceid=chrome&ie=UTF-8

Ratch

#### Flyback

##### Well-Known Member
sorry in the above, my "half.C.V^2" energy calculations are wrong because i accidentally used 1mF instead of 820uF in the calculation, but the overall point is preserved, ie, that the energy calculated with the scope method is significantly more than with the "half.C.V^2" method.

#### Flyback

##### Well-Known Member
The energy loss in the wires is minimal, as there is only about 0.5A RMS of charge curent flowing on average over the charge interval, and the wires have low resistance. There will be some extra loss due to skin effect, but not to the amount we are calculating.

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#### ronsimpson

##### Well-Known Member
as there is only about 0.5A RMS of charge curent
How are you measuring current?

#### ronsimpson

##### Well-Known Member
The problem is that this figure did not agree with the calculation which is done by simply subtracting the energy in the capacitor at 62V (0.5*C*62^2) from the energy in the capacitor at 300V (0.5*C*300^2).
Please retry your numbers based on a different thought.
You say (energy at 62V)-(energy at 300V)=?
What about (energy at 238V)? You are really only changing the charge from 62 to 300 then back to 62. So forger the 62. It is not involved in you project.

Think 0V to 238V then back to 0V. (delta V)
The 62V energy is never used.

#### kubeek

##### Well-Known Member
Please retry your numbers based on a different thought.
You say (energy at 62V)-(energy at 300V)=?
What about (energy at 238V)? You are really only changing the charge from 62 to 300 then back to 62. So forger the 62. It is not involved in you project.

Think 0V to 238V then back to 0V. (delta V)
The 62V energy is never used.
I don´t think so. Charging a cap from 0 to 100V definitely needs less energy than charging a cap from 100V to 200V. A cap (of some capacity) at 0V will have 0J stored, at 100V will have 100J and at 200V will have 400J since the relationship is quadratic. Therefore to charge it up from 100V to 200V you need to add 300J, not 100J.