Measuring the energy used to recharge a 1mF electrolytic capacitor

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.

treez said:

We then divided this power reading by the recharge interval time in order to get the energy delivered to the capacitor in the recharge.

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I think you should have multiplied power with time in order to get the energy.

energy in the capacitor at 62V (0.5*C*62^2) from the energy in the capacitor at 300V (0.5*C*300^2).

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My figures for that are 1.6 Joules discharged down to 62 volts.
And 36.9 Joules charged up to 300v
So theoretically 35.3 joules required to pump it up.

But pumping it up is not so simple, because your boost inductor will be operating firstly in CCM and then switch over at some point to DCM as the output voltage rises. Plus there will be various loss mechanisms.

At the start of charging you are not going to get full energy transfer, especially if its run in current mode where peak inductor charge current is set.
Later in the charging process, energy rundown will get faster, and although you then get full energy transfer, there will be some useless dead time after rundown has completed, where nothing useful is happening.

Fastest way to charge will be to use variable frequency, where the whole thing self oscillates. Inductor charging terminates at some fixed peak current. Charging restarts when the rundown current in the inductor hits zero.
The frequency starts out low, and glides upwards as charging proceeds.
Nice, but probably not worth the extra complication of doing it that way, unless the power level is huge.

To do it conventionally at fixed frequency will require building in some extra power capability in order to transfer sufficient power in the available time.
If you require 35 Joules (or whatever it is) in one second, its going to need more grunt than just 35 averaged transferred watts.

treez said:

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)...

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Please see that

1. the energy stored does not depend on temperature. The energy should be 0.5*C*(300^2-62^2)- as you suggest.

2. The capacitor (touch with a thermocouple thermometer that comes with many multimeters) has become hot- it is rarely an ideal capacitor.

3. The electrolytic capacitors have capacitance dependent on voltage (the capacitance at 62V is not the same at 300V)

4. Yes, you will get better results (agreements) with film or ceramic capacitors.

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.

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As CataM mentioned, please fix your math. The I*V integral is already the energy amount.

It's quite simple to measure energy with a digital oscilloscope, the verbose sampling rate considerations are just pointless. The only thing you need to care for is that the measured current quantity is sufficiently filtered so that you don't get large errors by undersampling of a pulsating inverter output.

Electrolytic capacitors have certain ESR losses, I guess below 1 percent during charging. The largest error contribution in your "theoretical" versus measured energy content calculation is the 20% capacitance tolerance.

Needless to say that relevant ESR losses can be expected during discharge.

Do you know of vendors who cheaply sell such big film capacitors 350V and 820uF?

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Re-inventing the square wheel?

I think you should have multiplied power with time in order to get the energy.

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Thanks sorry thats what i meant.

My figures for that are 1.6 Joules discharged down to 62 volts.
And 36.9 Joules charged up to 300v
So theoretically 35.3 joules required to pump it up.

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Thanks, sorry i blundered when writing it out, you are correct with your figures. The point i am making is preserved though, ie that the scope method calculates significantly more energy.

As CataM mentioned, please fix your math. The I*V integral is already the energy amount.

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Thanks, sorry i blundered whilst writing it out....Hang on, if you integrate "v.i.dt" between t1 and t2, then you get an energy reading (v * i * t). Which as you know you must divide by time to get the power...or are we speaking at crossed purposes here? (either way, the scope does this for you so its academic.....the scope calculates the average power between the two cursors on the screen)

The largest error contribution in your "theoretical" versus measured energy content calculation is the 20% capacitance tolerance.

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We did measure the capacitance with an LCR meter before doing it. I admit i have contrived the numbers here for the sake of brevity of the post, but the point of the post is that the discussed scope method of measuring energy delivered is significantly more than the "half.CV^2 method".

The electrolytic capacitors have capacitance dependent on voltage (the capacitance at 62V is not the same at 300V)

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...Thanks, this could be the crux of the matter, this could be why the "half.C.V^2" method may not have worked for us.

Another point is that ESR of electrolytics varies with frequency, and we have two (or more) different frequencies going on here...we have the 1 Hertz frequency of the repeated charge/discharge, and we have the frequency of the flyback output current waveform which varies over the charging interval from about 40khz to 100khz. (its a BCM flyback as Warpspeed alluded to)

This is why i think we need to repeat with a Film capacitor, ie , to see if the electrolytic capacitor is throwing up this problem.

I think we need to check the scope is accurate by running our flyback into a constant resistive load (with some capacitance) and measuring the average current inside the output rectifier loop which is pulsey, and multiply this by the voltage across the resistor, and see if it corresponds with v^2/R. This will check that the scope can really handle these kind of pulsey waveforms accurately.

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At the moment, using the "half.c.v^2" method we are calculating some 8W of dissipation in the capacitor during the recharging.....this would kill it i believe.......when i did the recharging continuously for 10 minutes , the capacitor was barely warm, so i suspect that the "half.c.v^2" method is wrong......and possibly due to C_Mitra's suggestion about capaictance not being constant with voltage.

3. The electrolytic capacitors have capacitance dependent on voltage (the capacitance at 62V is not the same at 300V)

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Thanks, do you have a reference on this at all?

Also, we are charging the capacitor from the output of a flyback SMPS, which switchs at up to 100khz, i am wondering if this high frequency "sees" more capacitance?...ie more capacitance than what we measured on the LCR meter at 100Hz. (The LCR neter will not measure the capacitance at any frequency above 1khz, it only does it at 100Hz and 1khz. The capacitance at 1khz is coming out as being about 15uF more than at 100Hz)

Also, we are charging the capacitor from the output of a flyback SMPS, which switchs at up to 100khz, i am wondering if this high frequency "sees" more capacitance?

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It's a DC respectively low frequency charging problem, AC ripple can be neglected. You actually ask for capacitance in the 1 to 10 Hz range.

Did you notice that your test setup already does a capacitance measurement, you can derive it by calculating Cdyn = I/(dV/dt)

I would be a bit concerned about the inductance of an 820uF 300v electrolytic at 70 Khz.
It probably needs something else in parallel to soak up the very short individual current spikes.

Did you notice that your test setup already does a capacitance measurement, you can derive it by calculating Cdyn = I/(dV/dt)

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Thanks, i see your point, though our Boundary mode flyback increases its fsw as the cap voltage rises , and actually the charging current constantly reduces as the cap voltage rises.

Another point is that the xenon flash pulse draws some 150A peak, albeit the pulse is only for some 200us...but i wonder if this reaks havoc with the capacitor and makes its leakage current go high during the charge. The capacitor we used has wire leads (radial) and from searching the web, it looks like most xenon flash caps shoudl really be screw terminal or the "solid claw" type terminal.

treez said:

Thanks, i see your point, though our Boundary mode flyback increases its fsw as the cap voltage rises , and actually the charging current constantly reduces as the cap voltage rises.

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Changing switching frequency doesn't matter. If you have high-bandwidth data of the capacitor current and voltage, then you should be able to directly derive its effective capacitance and ESR as a function of its voltage. If you don't mind posting the raw data, I'd like to give it a try.

As to the origin of the error, I would suspect simple measurement errors (especially offsets) first. Also if the current and voltage measurements have different bandwidths or delays, that could induce errors in your calculated energy.

Thanks Mtwieg, We do the capture on the scope, and so i'd have to find a way to get the data off the scope. (sorry but I am certain it wouldnt be permitted for a member of staff to do this and post it here)

Please see this quote from an Epcos/TDK application note that explains well the observed energy differences ("General technical information" from https://en.tdk.eu/tdk-en/529328/pro...tic-capacitors/snap-in-capacitors#information) https://en.tdk.eu/download/530704/5...62122e90c/pdf-generaltechnicalinformation.pdf

3.2.1 AC and DC capacitance
The capacitance of a capacitor can be determined by measuring its AC impedance (taking into account amplitude and phase) or by measuring the charge it will hold when a direct voltage is applied. The two methods produce slightly different results. As a general rule, it can be said that DC voltage based measurements (DC capacitance) yield higher values (DC capacitance) than the alternating current method (AC capacitance). The factors are approximately 1.1 to 1.5 and maximum deviations occur with capacitors of low voltage ratings.

Corresponding to the most common applications (e.g. smoothing and coupling), it is most usual to determine the AC capacitance of aluminum electrolytic capacitors.

For this purpose, the capacitive component of the equivalent series circuit (the series capacitance CS) is determined by applying an alternating voltage of <0.5 V. As the AC capacitance depends on frequency and temperature, IEC 60384-1 and IEC 60384-4 prescribe a measuring frequency of 100 Hz or 120 Hz and a temperature of 20 °C (other reference values by special request).

There are also applications (e.g. discharge circuits and timing elements) in which the DC capacitance is decisive. In spite of this fact, capacitors for which the capacitance has been determined by the AC method are also used in such applications, whereby allowances are made to compensate for the difference between the two measuring methods.

However, in exceptional cases it may be necessary to determine the DC capacitance. The IEC publications do not provide any corresponding specifications. Because of this, a separate DIN standard has been defined. This standard, DIN 41328-4, describes a measuring method involving one-time, non-recurrent charging and discharging of the capacitor.

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Problem is the assumption of a constant, voltage independent capacitance which is simply not true for electrolytic capacitors (and as we know, neither for high permittivity ceramic capacitors).

In other words, the whole thread isn't but the rediscovery of phenomenon well known to capacitor experts.

Problem is the assumption of a constant, voltage independent capacitance which is simply not true for electrolytic capacitors (and as we know, neither for high permittivity ceramic capacitors).

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FvM...Thanks....Wow!.....i wasnt up on that......the factor of 1.1 to 1.5 is much much larger than i would ever have thought.

treez said:

Thanks, do you have a reference on this at all?

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No, but for electrolytic capacitors this is basically the double layer capacitance and the charge is concentrated close to the surface in an region that depends on the electric field- somewhat like a varactor diode- but then almost all diodes show similar voltage dependence but to different degrees.

I have another concern about using an electrolytic in this application, self heating.
Most really heavy duty pulse discharge circuits use proper pulse rated capacitors, quite often polypropylene and of suitably robust internal construction.

A 150 amp xenon discharge current is not too bad in something like a professional photographic flash, where discharges are few and reasonably spaced due to the forced long recharge periods.

You mention a 1Hz continuous charge and discharge cycle, which sounds more like a pumped laser or photocopy machine application. Continuous repetitive 150 Amp discharges over a prolonged period might be rather a tall order for an electrolytic, at least if a reasonable life is expected.

i believe that is a very good point......and even if we use capacitors which are said to be rated for this kind of use, you would have to ask what it might do to the capacitance value. I mean, these sort of currents are surely going to reak havoc in the internals of an electrolytic cap...and we must use 'lytics since anything else is just too big.

The interesting question is how much of the charging energy is dissipated by the capacitor ESR. I believe it can be best evaluated by acquiring the actual flash lamp I and V waveforms and calculating energy. Or more simple, determining the capacitor temperature rise.

Thanks, I agree it would be very interesting to do a scope “sample and hold” on the flash current and lamp voltage. The problem is that getting a current probe with sufficient bandwidth and current capability will be an issue…the TCP303 current probe only measures up to 150A.

Tcp303 Current probe:
**broken link removed**

As regarding temperature rise of the capacitor, I assume you are speaking of using the equation ..
Temperature rise = Energy / (mass * Specific heat capacity)
…..the problem is, we don’t know the specific heat capacity of the capacitor.
(I assume you mean having the capacitor in a perfectly insulted box and then measuring its temperature rise after x number of flash’s?)

Flash tube current can be best probed with a rogowski coil, even up to kA.

Beyond quantitative measurements can capacitor temperature rise serve as practical criterion if the pulse load might be tolerated, although it doesn't tell about possible local overheating.