## Expected Life of Pulse Discharge Capacitors

Pulse discharge operation, particularly with underdamped (ringing) discharges, places large internal stresses on components. Empirical expressions have been developed to predict the life of a pulse discharge capacitor under conditions other than the nominal design. For instance, in an article by K. Salisbury, S. Lloyd, and Y.G. Chen at Maxwell Laboratories, "A transportable 50 KA Dual Mode Lightning Simulator", the following equation is given.

Lx = Lref * (Qref/Qx)^1.6 * (Vref/Vx)^7.5

where
x subscript refers to the application
ref subscript refers to the reference data
L is the expected life (in shots),
Q is the discharge waveform Q
V is the capacitor charge voltage.

Note that capacitor voltage is the most important life determinant, with a 7.5 exponent. A little reduction in voltage leads to a huge increase in life.

Voltage reversal also has a significant impact. When the voltage reverses, the mechanical stresses on the capacitor are quite high.

### Application Example

For instance, a Maxwell type 31162, is rated at 100,000 shots at 75 kV with 20% VR. (20% VR is Q = 1.4)

Now, we want to know the life in a Tesla coil at 90% reversal (a Q of 15) and a peak voltage of 42 kV. Applying the above formula:

Lx = 1E5 * ( 1.4/15)^1.6 * (75/42)^7.5 = 1E5 * .0225 * 77.37 = 1.74E5 shots.

reducing the voltage to 30 kV would increase the life by (42/30)^7.5 or 12.5 times.

If this were in a Tesla coil at 120 bps, at 42 kV, it would survive (90% probability) about 24 minutes of run time. Reducing the voltage to 30 kV would increase the life to 300 minutes, or 5 hours. Reducing the peak voltage to 20 kV is even more effective, increasing the life to 100 hours. Killing the Q down to 10 would increase the life by (15/10)^1.6 some 90 percent.

Capacitors rated for high repetition rates are necessarily overdesigned. Comparing two units from Maxwell Labs:

• 1.0 uF 40 kV 1pps 1E5 shots 2.3x5.9x27.8 inches
• 0.1 uF 40 kV 1000 pps 1E8 shots 2.3x5.9x14.8 inches

If the high reprate capacitor (with a 1000 times the life) were scaled to the capacity of the low rep rate unit, it would be about 5 times the size of the low rep rate unit. A life factor of 1000 can be achieved by increasing the rated voltage by about 2.5 times. This would require about 6.25 times the total capacitance arranged in a series parallel configuration, which correlates well with the physical size increase factor of 5.

### Q and Voltage Reversal

(these need to be verified, particularly at low Q's)

Q or voltage reversal (VR) may be computed from each other by:

Q = sqrt( 1 + 1 /( 2 /pi*ln(VR))^2)

VR = exp( - pi/2 * sqrt(1/(q^2-1)))

where VR is the voltage reversal expressed as a fraction (i.e. 0<VR<1)

Copyright 1998, Jim Lux / caplife.htm / 9 May 1998 / Back to HV Home / Back to home page / Mail to Jim