Electrolytic capacitors are major components of any power converter in use today. Proper understanding of their characteristics allows designers to better utilize them while optimizing their designs. This design note will shed some light on the main features of electrolytic capacitors.
An electric equivalent schematic of an electrolytic capacitor can be described as an equivalent series resistance (ESR), equivalent series inductance (ESL), the capacitance (C) and a parallel resistance for the leakage current (Rleak) depends on the quality of the dielectric.
Equivalent circuit of an electrolytic capacitor
When the capacitor is charged and discharged there will be some electrons stored in the dielectric. When the discharge mechanism is removed these electrons start to build up a voltage, i.e. dielectric absorption. If this causes problems, it's possible to get capacitors with a short circuit tape between the terminals.
The current through the capacitor will cause a power loss in it, due mainly to the ESR.
PLOSS = IRMS2 x ESR
ESR decreases with increasing hot-spot temperature and with increasing frequency. The hot-spot is the hottest point in the winding.
ESR as a Function of Temperature and Frequency
When the current consists of a fundamental frequency and its harmonics, you have to calculate the power loss for each harmonic and sum them to have the total power loss in the capacitor.
Ptot = P(1) + P(2) + P(3) + P(n) = I(1)2 x ESR(1) + I(2)2 x ESR(2) + I(3)2 x ESR(3) + I(n)2 x ESR(n)
The power loss causes the temperature to rise in the capacitor. The temperature at the hot-spot (Th) is decisive for the operational life (Lop) of the capacitor. Increasing Th leads to decreasing Lop. To calculate Th the thermal resistance (Rth) has to be known. At very high frequencies ESL has to be taken into consideration.
The resonant frequency (fR) depends on the capacitor. For PEG it can be above I MHz and for PEH it can vary from 1.5 kHz to 150 kHz. If the capacitor is used at a frequency greater than the resonant frequency the capacitor works like an inductor.
The hot-spot is the hottest point in the capacitor, with temperature Th. Heat will always be transported to the area with lower temperature. From the hot-spot to the ambient there are several ways for the heat to travel. Heat will be transferred through the aluminum foil and the electrolyte. If the capacitor is mounted on a heat sink some of the heat will go through the heat sink to the ambient. The total thermal resistance from hot-spot to ambient is called Rth. Below are examples of different Rth for clip mounted, stud mounted on a heat sink with a thermal resistance of 2oC/W, and a capacitor stud mounted on a heat-sink with a thermal resistance of 2oC/W with forced air of velocity 2 m/s. This is shown for capacitor type PEH20000427AM, with ambient temperature of 85oC. The negative foil is in direct contact with the aluminum case and it is a very good heat conductor. This also means that the aluminum case is the same as the negative, but it should not be used as a connection.
A correct mounting is necessary if the specified operational life time is to be fulfilled. PEH 169 and PEH200 should be mounted upright or inclined down to a horizontal position. The safety vent should be upwards. At a failure, hot conductive electrolyte and vapor can come out from the safety vent, so observe the direction of the vent.
Having stud mounting with good cooling on a chassis is preferable. When the capacitors are clip mounted there can be an air gap between the capacitor and the heat sink.
It is much easier to stud mount the capacitor compared with clip mounting. Stud mounting with a nylon cap nut gives an isolation voltage of 2.5 to 4 kV depending on the nut. When capacitors are mounted close together, it is important to have a minimum distance of 5 mm between the capacitors in order to have an acceptable air circulation.
It is important to have the right torque for the screw terminal. If the screws are too loose, there can be a bad connection. If the screws are over tightened, there is a risk the thread will be destroyed. The capacitors can't be mounted hanging in the screw terminals as the lid will break. PEG's and PEH165 and PEH300 may be mounted in any position, no accessories are needed. The PEG type should not be squeezed with a plastic strip on the body, this may cause leakage of electrolyte. At applications with high frequencies, the lead should be as short as possible to minimize the inductance and the skin effect. The mounting shown below to the left is not to be recommended. The mounting shown to the right is the preferred.
The PEG should not be mounted near any warm component. High temperatures will shorten the life time and the capacitor can be the limiting part of the construction. For applications with high vibration, as in the automotive industry, the PEG125 is recommended.
When using series connections, it is important to know the voltage across each capacitor. The tolerances of a capacitor can give a very high voltage on one capacitor while the others are subjected to lower voltages. Two 350 V capacitors with ± 20% tolerances are connected in series while a voltage of 700 V is applied across the series connection. In the worst case, one capacitor has max. capacitance and the other has min. capacitance. The capacitor with min. value will be exposed to:
n = No. of capacitors in series
To obtain correct voltage sharing between the capacitors, it is a good idea to use voltage sharing resistors. The voltage sharing resistor is calculated:
Example: C = 4700 ?F
Rvsr = 14 k?
It is important to have a high quality resistor. If the resistor fails, the capacitors will break down. For high reliability the generated power in the resistor should be less than 50% of the rated value. The tolerances of the two resistors should be better or equal to ±5%. Don't forget the time constant r, it takes some time before the voltage is shared. There are two ways to connect the voltage-sharing resistor.
In high current applications it may be necessary to use a parallel connection. Be sure the current distribution is equal in all capacitor branches. At high frequencies, inductances can give different current distribution, as in the first illustration. In the second illustration, the distribution is equal to all capacitors.
Low inductance bus bars can be built to reduce the inductance, down to less than one nH. In principle the negative side must cover the positive side.
To calculate the operational life time (Lop) you have to know the applied voltage (Vappllied), the current through the capacitor (IRMS), ambient temperature (Ta) and thermal resistance (Rth).
PLOSS = IRMS2 x ESR
Th = Ta + PLOSS x Rth
LOP = f(Th)
- First find the ESR value for the right frequency and hot-spot temperature (Th) in the ESR matrix.
- Calculate the power loss (PLOSS). If the current consists of main frequency and different harmonics, calculate the power loss for each harmonic and add up. The thermal resistance between the winding hot spot and the ambient will be found in the Rth matrix.
- Calculate Th and check if it agrees with the assumption when the ESR was chosen. If not take the new ESR value and make a new calculation. If Th is known it is easy to calculate Lop.
If applied voltage is less than rated voltage the Lop will increase. This is valid down to about 65% of rated voltage. For some capacitors the Lop will increase up to eight times. The ESR value for electrolytic capacitors depends on the temperature and frequency. Often a value at 20oC and 100 Hz is given.
With the ESR matrix it is possible to calculate the value at other temperatures and frequencies.
Capacitors can be destroyed if they are exposed to over voltage, for example transients. On the mains there are a lot of transients, it is not a pure sine wave.
UR Rated voltage
Us Surge voltage 1000 cycles with load period 30 sec and no load period 330 sec
UT Transient voltage 1000 pulses randomly applied during life time.
The over voltage can also occur when the capacitors are connected to a LC-filter.
The voltage over the capacitor will have an over shot.
To avoid high voltage when connecting the capacitors to voltage it is good to use a soft start. The switch is a semi conductor.
A filter before the rectifier stops some fast transients but not all. If the capacitor is connected to the wrong polarization it will damage the capacitor very quickly. To avoid wrong polarization the connections are turned 90o, i.e. Poka Yoka.
If the current exceeds the rated current it will shorten the life time. Shorter periods of excessive ripple current is okay as long as it's a short duration compared to the thermal time constant, r. The life time depends on the hot spot temperature. With a temperature sensor or a temperature strip it is possible to measure the temperature rise in the capacitor. The temperature should be measured directly on the aluminum.
For PEH 169 and 200 it is possible to measure the hot spot temperature with thermocouple inside the capacitor.
[an error occurred while processing this directive]The electrolytic capacitor is often used to smooth the voltage after a rectifier.
Needed capacitance to manage a certain level of ripple voltage is
P is the power load in watts.
Remember that this is the minimum required capacitance. It is important to remember the tolerances of the capacitor. During the life time the capacitance will decrease and it will also decrease with low temperatures. The ripple current from the main and from the load has to be known. First calculate the capacitor voltage charge time.
fmain is the frequency from the main. Now it is possible to calculate the capacitor voltage discharge time.
The peak value of the charge current IC is
dU is the voltage ripple (Umax - Umin).
Next the peak and RMS discharge current can be calculated.
Now the ripple current resulting from the rectification of the AC line can be made.
Drives
Continuous voltage: 750 VDC
Ripple currents: 60 A @ 4 kHz
75 A @ 8 kHz
50 A @ 12 kHz
30 A @ 16 kHz
20 A @ 32 kHz
Required capacitance: 7000 ?F
Tolerance: -10 to + 30%
Life time: 40,000 hours
Maximum ambient temperature: 700C
Forced air: 2 m/s
Heat sink: 1.0oC/W
To handle the voltage 750 VDC it is necessary to have two capacitors in series. But the tolerances of the capacitors have to be taken into consideration. If the tolerance is ±20%, the worst case gives:
Use a 450 V capacitor. If a 4700 ?F capacitor is chosen there must be three branches to fulfil the capacitance requirement. PEH200YV447DQB2 is a good selection.
First calculate the ESR values, assume hot-spot temperature to 85oC.
ESR (85oC, 4 kHz) = 13 x 0.31 = 4.0 mW
ESR (85oC, 8 kHz) = 13 x 0.30 = 3.9 mW
ESR (85oC, 12 kHz)= 13 x 0.29 = 3.8 mW
ESR (85oC, 16 kHz) = 13 x 0.29 = 3.8 mW
ESR (85oC, 32 kHz) = 13 x 0.29 = 3.8 mW
Calculate the power loss in each capacitor, we have three branches, the capacitor current is a third of the total current.
Now it is possible to calculate the hot-spot temperature. The thermal resistance comes from the Rth-matrix, thermal resistance of the heat sink is 1.0oC/W and air velocity 2 m/s.
Th = Ta + PLOSS x Rth = 70 + 5.64 x 1.5 = 78.5oC
The assumption of the hot-spot temperature was 85oC. But for this type of capacitor the ESR doesn't differ very much at this temperature so there is no need to calculate a new value.
The hot-spot temperature gives the operational life time. PEH200 450 VDC and diameter 75 mm has following Lop equation.
This solution is far below the specification. It is necessary with four branches.
Th = Ta + PLOSS x Rth = 70 + 3.17 x 1.5 = 74.8oC
The failure rate per hour is about 5.0 x 10-7. R(t) is the number of capacitors working.
? = failure rate
t = time in hours
n = number of used capacitors
Assume 80,000 capacitors are used. How many will still work at 40,000 hours?
That means 1600 capacitors have failed i.e. 2% of the total number.
