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Calculating the Total Energy Released by a Capacitor up to Defined Points in Time

TAS142

Feb 21, 2018
1
Joined
Feb 21, 2018
Messages
1
Hi All,

First ever post here. I am not at all an electronics expert. In fact, I'm pretty useless, yet due to resource availability, this task has fallen on me.

Here is my situation. I currently have a device which, amongst other things, charges a capacitor such that on activation of a switch, the main power supply is removed and the capacitor kicks in which subsequently activates a pyrotechnic device used as part of a release mechanism.

Due to confidentiality reasons, I am not able to present the whole circuit diagram, but I have attached a modified snippet of the section of the circuit concerned. I'll be frank, I am not entirely sure of the function of the transistor, but I don't think this should influence my query too much. In terms of the pyro, in testing we have attached a 'dummy load' in the form of a resistor so I have been treating it as such. I guess for this purpose, the pyro can be viewed as a resistor.

Now, to get to my actual query. I have positioned a probe either side of the pyro/dummy load and connected to an oscilloscope which can give me a readout in terms of voltage or current. In both instances, on activation of the switches, the capacitor discharges and produces a discharge curve, as expected (a pretty typical looking exponential decay curve). What I am desperately trying to calculated is the total energy released up to certain time intervals (not that it impacts the process much, these time intervals are 5ms and 10ms). I have been told various things and despite using numerous attempts using various formulae and methodologies (lots of mentions of time constants, C=Q/V etc., E= I^2*R etc.), I have been unsuccessful. Historically we have used an automated programme produced by a subcontractor around 2 decades ago which did all the work for us once the device was plugged in. Unfortunately, this machine has now seen it's last days, so we need to find a manual method of it. The machine when it was working would produce a test certificate as a printout, which would present the required results. I have an extract of this certificate (attached) which provides currents and energies from which I have been trying to work backwards to try and figure out how they achieved the desired results. However, as I previously mentioned, I am failing terribly, so any guidance anyone can provide would be greatly appreciated!

circuit snip.png

cert snip.png
 

AnalogKid

Jun 10, 2015
2,884
Joined
Jun 10, 2015
Messages
2,884
The transistor is acting as an electronically-controlled on/off switch.

The total energy in a capacitor is:

E = 1/2 x C x V^2 -- Energy equals one-half times the capacitance (in farads) times the square of the voltage.

The unit is watt-seconds, abbreviated Ws, or W-s

To calculate a partial energy, calculate it at the starting voltage and at the ending voltage, and subtract. Neither voltage has to be "fully charged" or "empty".

ak
 

AnalogKid

Jun 10, 2015
2,884
Joined
Jun 10, 2015
Messages
2,884
Because Joule is a proper name, it is spelled out lower case (joule) but abbreviated with a capital letter (J).

ak

ps. I'm old, and I have old camera flashes. Watt-seconds are us.
 

Ratch

Mar 10, 2013
1,099
Joined
Mar 10, 2013
Messages
1,099
Hi All,

First ever post here. I am not at all an electronics expert. In fact, I'm pretty useless, yet due to resource availability, this task has fallen on me.

Here is my situation. I currently have a device which, amongst other things, charges a capacitor such that on activation of a switch, the main power supply is removed and the capacitor kicks in which subsequently activates a pyrotechnic device used as part of a release mechanism.

Due to confidentiality reasons, I am not able to present the whole circuit diagram, but I have attached a modified snippet of the section of the circuit concerned. I'll be frank, I am not entirely sure of the function of the transistor, but I don't think this should influence my query too much. In terms of the pyro, in testing we have attached a 'dummy load' in the form of a resistor so I have been treating it as such. I guess for this purpose, the pyro can be viewed as a resistor.

Now, to get to my actual query. I have positioned a probe either side of the pyro/dummy load and connected to an oscilloscope which can give me a readout in terms of voltage or current. In both instances, on activation of the switches, the capacitor discharges and produces a discharge curve, as expected (a pretty typical looking exponential decay curve). What I am desperately trying to calculated is the total energy released up to certain time intervals (not that it impacts the process much, these time intervals are 5ms and 10ms). I have been told various things and despite using numerous attempts using various formulae and methodologies (lots of mentions of time constants, C=Q/V etc., E= I^2*R etc.), I have been unsuccessful. Historically we have used an automated programme produced by a subcontractor around 2 decades ago which did all the work for us once the device was plugged in. Unfortunately, this machine has now seen it's last days, so we need to find a manual method of it. The machine when it was working would produce a test certificate as a printout, which would present the required results. I have an extract of this certificate (attached) which provides currents and energies from which I have been trying to work backwards to try and figure out how they achieved the desired results. However, as I previously mentioned, I am failing terribly, so any guidance anyone can provide would be greatly appreciated!

View attachment 39630

View attachment 39629

I am using some made up values because you are indefinite about whether your circuit values are in joules or millijoules, amps or milliamps, etc. I am assuming the capacitor is energized to 100 volts, and a 1k0 resistor is switched across the cap at time t = 0.

The voltage equation for the cap is:
Tas142a.JPG
The standard de-energizing voltage curve for the cap with 1k0 across it
is:
Tas142b.JPG
The energy equation for the cap is:
Tas142c.JPG
The energy curve for the cap at a particular voltage is;
Tas142d.JPG
As you can see, the cap loses 9 joules of energy in the time interval of 0 to 2 secs. From 1 to 2 secs, it loses only 2 joules. After 4 secs, it is almost depleted of energy.

If you were to give me a more precise specification without revealing the family jewels, I could give you a more definite answer.

Ratch
 
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