# How can I select capacitors in a circuit

## This is how developers choose the right capacitor

In power converter circuits such as AC / DC power supplies, DC / DC converters, and even DC intermediate circuits, capacitive filters are required to counteract fluctuations that cause instability. The right choice ensures less or no noise at the DC output and no interference at all that is transmitted to nearby circuits.

### Key data

The choice of capacitor can have a significant impact on the reliability and longevity of an application and is made more difficult by the fact that the parameters change over temperature and operating frequency. The choice of capacitors should therefore be made with particular care.

The fluctuations in question are superimposed on the ideal, stable waveforms. Faults can have various causes. A common source of interference is the rectification of alternating current: at the corresponding DC output of a rectifier, part of the source AC content is usually superimposed. Switching regulators of all kinds generate a certain residual ripple during operation. Good designs usually try to reduce this waviness as much as possible, but cannot completely eliminate it. Designers often integrate capacitors into the circuitry to continuously absorb the energy associated with these fluctuations. Together with the corresponding discharge processes, current peaks and troughs can be minimized.

As a result, the capacitor continuously passes a varying current known as ripple. This ripple current is inevitable when the capacitor is doing its required job. It causes undesirable I2R heating when it flows through the capacitor's own equivalent series resistance (ESR). If I2R effects exceed the capacitor's ability to dissipate heat, its temperature rises and reliability is impaired. According to Arrhenius' law, this can affect the life of the components: the life is halved for every 10 ° C increase in operating temperature. Extreme heating in excess of the specified maximum temperature can destroy the capacitor by causing liquid electrolyte to dry out or boil, which can crack or ignite ceramic capacitors. A heat sink can limit the temperature rise if space and weight restrictions allow. On the other hand, calculating the ripple current and understanding the properties of suitable capacitors can help find the most space-saving and cost-effective solution.

The capacitor data sheet gives a ripple current rating, which describes the maximum ripple that the capacitor can withstand. It serves as a guide - with the understanding that this value was determined under controlled conditions. The EIA-809 or EIA / IS-535-BAAE standards are used for this purpose, although these cause some confusion. Deviations in the measurement of the ripple current capacity make it difficult to compare the value directly between capacitors from different manufacturers. However, the information in the data sheet is useful for comparing products from the same manufacturer.

### Calculation of the ripple voltage and the ripple current

In order to select the correct capacitor for the input filter of a switching regulator, the capacitance can be calculated which is required to achieve a desired voltage ripple - provided that the operating conditions of the regulator are known. If the capacitance is calculated, a suitable capacitor can be selected and the ripple current can be determined from the known ESR. This current value must be within the ripple current rating of the capacitor - provided the module is suitable for use. The selection can be difficult here, as both the ESR and the capacitance vary over the temperature, operating frequency and applied DC bias voltage.

The capacity is calculated using the following equation (Formula 1):

Formula 1 Kemet

Where C_{MIN} = required minimum capacity

I._{OUT} = Output current

dc = duty cycle (for calculation see formula 2)

Formula 2 Kemet

f_{SW} = Switching frequency

U_{P (max)} = Peak-to-peak ripple voltage

For a controller with 12 V input, 5 V output, 2 A output, 85% efficiency, 400 kHz switching frequency and a permissible input ripple voltage of 65 mV, the following applies:

Formula 3 Kemet

The selected capacitor must have this capacity at an operating frequency of the controller of

Provide 400 kHz.

The effective value of the peak-to-peak ripple voltage can be calculated as follows:

Formula 4 Kemet

The ripple current in the capacitor can then be calculated using Ohm's law - provided that the ESR of the capacitor is known.

### Take capacitor properties into account

At this point, developers must take into account the deviations in the capacitor properties depending on the operating conditions. Most designers are familiar with the temperature stability problems of Class II / III dielectrics. Few understand the size of the capacity loss due to operating frequency and applied voltage.

Recall that 19.22 µF (as calculated earlier) is the capacitance required at the controller's operating frequency (400 kHz). The ESR must also be known at this frequency in order to calculate the ripple current.

If a capacitor with a nominal capacitance of 22 µF and a nominal voltage of 16 V is selected as the next standard value above 19.22 µF, the actual capacitance of this device is 5.951 µF at 400 kHz (Fig. 1) and the ESR is 3.328 mΩ. The resulting ripple values (voltage and current) are recorded as 210 mV_{p-p}/ 74.23 mV_{eff} or 22.3 A. These are significantly greater than the nominal ripple voltage and the maximum permissible ripple current for the capacitor.

### Use simulation as an advantage

Every manufacturer of Class II components recommends simulating the component behavior taking into account the application voltage, temperature and frequency. With Kemet's online simulator K-SIM for electrical parameters, developers can assess the performance of the capacitor under various operating conditions. It is available from the Kemet Engineering Center, along with the aforementioned ripple voltage calculator, other tools and support information, including technical notes and application notes.

With K-SIM, you can quickly analyze one or more capacitors that are suitable for the respective application. Among the different characteristics, K-SIM can display the impedance and the ESR or the capacitance and voltage over the operating frequency and also predict the temperature rise depending on the ripple current and frequency. An on-screen cursor ensures accurate measurements. The S parameters of the capacitor can also be evaluated with K-SIM. Spice models and step files for components of interest are available.

With the help of this tool, a 47µF X5R capacitor with the same package size and rated voltage as the 22 µF / 16V component selected previously was identified. The capacitance value is 19.9 µF at 400 kHz with the applied DC bias and thus limits the peak-to-peak ripple voltage to 63 mV. Therefore, U is_{eff} = 22.27 mV. At 400 kHz, the ESR of this capacitor is 3.246 mΩ, which suggests that the ripple current is 6.86 A, which is below the maximum value of the capacitor.

### Conclusion

Problems related to ripple power are difficult to analyze and predict under the expected operating conditions. If left untested, the heating caused by ripple currents can impair the service life of the capacitor. However, a correct assessment of the ripple values (voltage and current) is essential to ensure that a circuit such as a switching regulator delivers the required performance over its service life. Online tools and information help calculate the required capacitance and speed up the process of choosing the right capacitor.

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