bonitron M3534B, Customer Reference Manual

Page: 41 / 48

User’s Manual
41
7.4.6. A
VAILABLE
J
OULES
At this point, the available maximum joules for the string can be calculated.
V
Charge
= n
series
∗ V
CapMax
𝑉
𝐶ℎ𝑎𝑟𝑔𝑒
= 8 ∗ 46𝑉 = 368𝑉
The capacitor voltage at the end of the discharge
𝑉
𝐶𝑎𝑝𝐸𝑛𝑑
will be given by:
V
CapEnd
= V
end
− n
string
∗ I
peak
∗ Esr
V
CapEnd
= 320V + 8 ∗ 235A ∗ 0.01Ω = 338V
The total capacitance of the series string is given by:
C
tot
=
C
eol
n
series
∗ n
parallel
C
tot
=
132F
8
∗ 1 = 16.5F
Now, the total energy that can be delivered to the load is given by:
J
Available
=
1
2
∗ C
tot
∗ (𝑉
𝐶ℎ𝑎𝑟𝑔𝑒
2
− 𝑉
𝐶𝑎𝑝𝐸𝑛𝑑
2
)
J
Available
=
1
2
∗ 16.5F ∗ (368V
2
− 338V
2
) = 175kJ
The equivalent
𝐸𝑠𝑟
of the string is given by
Esr
tot
=
n
string
∗ Esr
n
parallel
Esr
tot
=
8 ∗ 0.01Ω
1
= 0.08Ω
The total extraction losses of the string is given by
J
LossTot
= Esr
tot
∗ I
Peak
2
∗ T
out
J
LossTot
= 0.08Ω ∗ 235A
2
∗ 2s = 9kJ
Now the total required energy can be compared.
J
Out
+ J
LossTot
< J
Available
150kJ + 9kJ < 175𝑘𝐽
This combination of capacitors will be adequate for our example application.
If the application required more energy, then capacitors can be added in
series, and the calculations redone as in 7.3.1. If the charge voltage exceeds