Calculating the Current Through a Bank of Capacitors

Axel Schmidt

Wednesday, July 3rd, 2019

Many times, different technologies of capacitors are needed to accomplish different tasks at the same point in a circuit. One of the most common combinations is Aluminum Electrolytic and Film capacitors. The Aluminum Electrolytic capacitors handle the bulk of the capacitance while the film capacitors help take some of the current from the Aluminum Electrolytics, all while filtering the higher frequencies that the Aluminum Electrolytics cannot.

Calculating the Current

Calculating the current through a bank of capacitors is not a tricky process but is often not approached correctly, which leads to a shorter lifetime of the capacitors chosen or an over-designed circuit where money and space is wasted. Each set of requirements has a sweet spot where the correct capacitance values, frequencies, and voltages lead to the most effective circuit with the longest lifetime. The steps below provide the equations and parameters to pay attention to when choosing capacitors to withstand voltage, current, and frequency requirements.

The first step is to calculate the impedance of each capacitor that is chosen to be in the bank using the equation below. The initial capacitors can be chosen based on estimating how their parameters (ESR and ripple current capability) will contribute given the circuit’s requirements (voltage, frequency, ripple current).

estimating how their parameters (ESR and ripple current capability) will contribute given the circuit’s requirements (voltage, frequency, ripple current)

The ESR values can be obtained from the datasheets or directly from the manufacturer if not provided in the datasheet. KEMET offers KSIM, a simulation tool which provides parameters such as ESR, capacitance, current, voltage, and other characteristics.

The ESR needs to be specified at the application frequency. Most datasheets provide the ESR at 100Hz, 10kHz, or 100kHz as shown in Figures 1 and 2. Using an ESR measured at a different frequency will result in an overestimate or underestimate of the design. The ESR determines how much current the part takes and will vary as frequencies rise and drop.

Figure 1: https://content.kemet.com/datasheets/KEM_F3046_C4AE_RADIAL.pdf

Figure 2: https://content.kemet.com/datasheets/KEM_A4011_PEG124.pdf

Once all the impedances for each capacitor are calculated, use the following equation to solve for the total impedance of the bank.

The next step is to find out how much of the total current through the bank will be going through each individual capacitor or capacitor branch. The following equation shows how to solve for this.

Refer to the datasheet or other tools to check what the ripple current capability of each part will be (example shown in Figure 3). This value will also vary based on the frequency and should be greater than the calculated value if you want to ensure the lifetime that the manufacture provides on the datasheet.

Figure 3: https://content.kemet.com/datasheets/KEM_A4011_PEG124.pdf

If the calculated value is higher than the specified current capability listed in the datasheet or by the supplier, there are a few options.

  • Verify from the manufacture the effect this could have on the lifetime of the part.
  • Add more parts in parallel to relieve the current being placed on the parts in the bank.
  • Look at different parts that have higher capabilities.
    • Note: Capacitors with lower ESR values will have higher ripple current capabilities.

Below is an example to help determine how to solve this.

Parameters

  • Total Capacitance Needed: 800 uF
  • Voltage Applied: 450 VDC
  • Ripple Current: 20 Arms
  • Frequency: 10 kHz
  • Ambient Temperature: 65°C
  • No Termination or Space Requirements

First estimation includes the following setup. The parts were chosen based off the total capacitance value, voltage rating, and current capability shown on the datasheets.

1. Obtain ESR values from the datasheets for the parts based on the specific frequency used. The frequency used in this calculation is 10 kHz.

http://www.kemet.com/Lists/ProductCatalog/Attachments/395/KEM_A4026_ALC40.pdf

http://www.kemet.com/Lists/ProductCatalog/Attachments/366/KEM_F3046_C4AE_RADIAL.pdf

Note: Not all datasheets have the ESR at the used frequency, but keep in mind as frequency decreases ESR increases.

 

2. Use the following equations to solve for the impedance of the capacitors being placed in parallel.

3. Use the following equation to solve for the total impedance of the bank.

4. Use the following equations to solve for the current through each capacitor.

5. Look back at the datasheet for the current capability of each part so that what is being put on the part (calculated value) is less than what is in the datasheet.

http://www.kemet.com/Lists/ProductCatalog/Attachments/395/KEM_A4026_ALC40.pdf

http://www.kemet.com/Lists/ProductCatalog/Attachments/366/KEM_F3046_C4AE_RADIAL.pdf

There is too much current on the Aluminum Electrolytics so different parts must be chosen. It is important to look for Aluminum Electrolytic parts that will have higher ESR values and Film capacitors that have lower ESR values to take more of the current off the Aluminum Electrolytics.

Parameters (Not Changed)

  • Total Capacitance Needed: 800uF
  • Voltage Applied: 450VDC
  • Ripple Current: 20Arms
  • Frequency: 10kHz
  • Ambient Temperature: 65°C
  • No Termination or Space Requirements

The second estimation includes the following setup. The parts were chosen based off the total capacitance value, voltage rating, and current capability shown on the datasheets. They were also chosen with the Aluminum Electrolytic capacitors having higher ESR values and the Film capacitors having lower ESR values to put more current on the Film capacitors.


1. Obtain ESR values from the datasheets for the parts based on the specific frequency used. The frequency used in this calculation is 10 kHz.

http://www.kemet.com/Lists/ProductCatalog/attachments/726/KEM_A4075_ALS70_71.pdf

http://www.kemet.com/Lists/ProductCatalog/Attachments/366/KEM_F3046_C4AE_RADIAL.pdf

Note: Not all datasheets have the ESR at the used frequency, but keep in mind as frequency decreases ESR increases.

 

2. Use the following equations to solve for the impedance of the capacitors being placed in parallel.

3. Use the following equation to solve for the total impedance of the bank.

4. Use the following equations to solve for the current through each capacitor.

5. Look back at the datasheet for the current capability of each part so that what is being put on the part (calculated value) is less than what is in the datasheet.

http://www.kemet.com/Lists/ProductCatalog/attachments/726/KEM_A4075_ALS70_71.pdf

http://www.kemet.com/Lists/ProductCatalog/Attachments/366/KEM_F3046_C4AE_RADIAL.pdf

All calculated values are below the current capability listed in the data sheets, so this is a good combination of parts.

In conclusion, using the first four capacitors (ALC40 and C4AE series) placed too much current on the Aluminum Electrolytic capacitors. This configuration will generate heat on these parts, and they will have a much shorter life than expected. The second configuration (ALC70 and C4AE series) is a good solution and the lifetime of the parts will not be negatively affected. If smaller parts are desired, the search can continue trying out various values/configurations.