# MMC calculations - UK Caps

```Terry wrote
>I have updated my MMC capacitor power and reliability calculations.  They
>now include the new and important life expectancy formulas.  The new page
>is at:

>www.peakpeak-dot-com/~terryf/tesla/misc/MMCPower4.html

Thanks for this Terry.

I worked through it see how hot our
new mmc caps might get.
I must empasise that we are taking results from
one manufacturer and apply them to another
manufacturers capacitor.

Our caps are:
0.047uF, 1500DC, 450V AC, 1800 V/uS
axial caps are 33mm long 15mm dia,
(I had to guess at the thermal
dissipation - I guessed 70 degrees
C per watt.)

I'm also assuming that the dissapation factor
tan delta is the same for all polypropylene caps. I also assumed
that Ksync would equal 1 for a static gap. It is also assumed
that all the heating occurs in the dialectric, and that the resistive
heating in the foil is not significant.

These caps are 0.047uF,
Vcap is the voltage at which the gap fires
divided by the number of caps in the string.
ie peak voltage per cap.

for the UK breaks per second is 100
(50 Hz mains)

at 200000Hz
Vcap     Temp rise
3000    13.2
2750    11.1
2500    9.2
2250    7.5
2000    5.9
1750    4.5
1500    3.3
1250    2.3
1000    1.5
750     0.8
500     0.4
250     0.1

at 100000kHz
3000    16.5
2750    13.9
2500    11.5
2250    9.3
2000    7.3
1750    5.6
1500    4.1
1250    2.9
1000    1.8
750     1.0
500     0.5
250     0.1

remember Terry was using radial caps from a
different manufacturer.
These figures should show the correct trends
but could be out by a factor of 2 or more!
We could get the catalogue from Arcotronics
and see if they give relevant figures, or we
could just try running them hard and taking their
temparature.

Terry reckons a temperature rise of
0-5 degrees as very good,
5-10 degrees as good
10-15 degrees as iffy
in terms of reliability.

I went through the life expectancy formula as well and put it
on a spread sheet.
The caps that we are using have a AC rating of 450V AC, (X)

The table shows the expected life time in hours,  (L) for the AC
voltage across each cap, (Y) = transformer AC voltage divided
by the number of caps in the string)
The formula is L= 1000000 * ( X / Y )^15
(the life time in hours is the ratio between the rated AC voltage and
the actual AC voltage raised to the power 15 and then multiplied by
one million. (looks a bit arbitary to me)

actual  Life time
Vac Cap in hours
450.00  1000000.00
500.00  205891.13
550.00  49288.70
600.00  13363.46
650.00  4022.42
700.00  1323.48
750.00  470.18
800.00  178.58
850.00  71.93
900.00  30.52
950.00  13.56
1000.00 6.28
1050.00 3.02
1100.00 1.50
1150.00 0.77
1200.00 0.41
1250.00 0.22
1300.00 0.12
1350.00 0.07
1400.00 0.04
1450.00 0.02
1500.00 0.01

This is probably very conservative - I did
subject a string of 4 of these caps to 8000 VAC in
parellel with the existing cap.
and they did survive a minutes run time!

Even 30 hours of run time is probably enough for
years of use so it might be a while before we can verify
the formula!

Do not be fooled by the numbers like 205891.13 the
formula is a best guess to start with and further skewed
when we apply it to our caps.

have fun,

Alan Sharp

```