# Bypass or Decoupling Capacitor Calculator

A Bypass Capacitor is used to bypass high frequency signals and noise from power supplies. This prevents issues with Electromagnetic Interference (EMI).

The picture below shows an example of bypass capacitors at the input and output of a linear voltage regulator.

This tool provides the capacitor value that is used under the circuit conditions.

## Basic Calculator

Enter

• Impedance (Z) of the circuit in ohm. The circuit could be either a power supply module or any other electronic component
• Frequency (fn) of the signal or noise to be filtered out

## Formula

C = 1/(2Ï€*fn*Xc)

Xc is estimated at 1/10 the value of the circuit impedance.

According to this formula, Xc = 1/(2Ï€*fn*C) for a fixed value of capacitance, the impedance decreases with an increase in frequency. As a result you might assume that the capacitor you selected will filter out frequencies higher than the value you designed for (i.e. f > fn). However, that is not the case.

To understand why, let’s take a look at the impedance characteristic of a general purpose capacitor.

From the graph above impedance decreases until it reaches a minimum value at the self-resonant frequency (SRF). It increases thereafter. At this value the capacitor impedance is equal to its equivalent series resistance (calculate ESR).

At higher frequencies, the capacitor looks like an inductor. The impedance of an inductor increases with frequency. That’s the effect we see in the plot above.

If you are using a bypass capacitor in a digital design involving FPGAs or microcontrollers, the bypass calculator calculation requires the following inputs:

• Typical rise and fall times (tRISE) of the device signals
• Maximum voltage ripple (VRIPPLE) that can be tolerated
• Microcontroller’s avarage operating current (IAVE)
• Clock frequency of the microcontroller (fMICRO

## Formula

CBYPASS = ISURGE /(2*Ï€*fNOISE *VRIPPLE)

where,

ISURGE = IAVE*fNOISE/fMICRO

fNOISE =1/(2*tRISE )

Noise frequency is estimated as 0.5/tRISE. For oscilloscope bandwidth calculations however it is modeled differently at 0.35/tRISE.

## Practical Guidelines

When designing a printed circuit board, bypass capacitors should be placed as close as possible to the component pin and have a short low impedance path to ground. For instance here is what Analog Devices recommends.

As the distance between the cap and the power or ground is increased, the inductance increases and that results in a lower self-resonant frequency as explained above.

## References

[1] SimSurfing Capacitor selection software – This is a very useful tool to understand the technical specifications of a cap toward making a selection for your design.

[2] Cadence app note on How to Choose a Bypass Cap

[3] Decoupling Capacitor on Wikipedia

[4] The formula for the advanced calculator is from this appnote on EDN

[5] Rise Time on Wikipedia

[6] Pi filter design calculator for power supplies