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I'm learning about boost converters right now and have started designing one. However, I can't find the equation to calculate the input capacitor. The readings just mention that the value is listed on the datasheet and to make sure to pick a X5R or better. So, is there any way I can calculate a specific value for the input capacitor or do I just need to estimate it?

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    \$\begingroup\$ Why don't you provide your "readings" here so that we can gather up what you are seeing there? What's the device and datasheet? \$\endgroup\$ – jonk Oct 30 '16 at 23:54
  • \$\begingroup\$ @jonk ti.com/lit/an/slva372c/slva372c.pdf \$\endgroup\$ – apathak Oct 31 '16 at 0:17
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    \$\begingroup\$ I don't think there is an equation. But you could ask yourself, if the input power was disconnected, how far would the capacitor voltage drop during one complete switching cycle under peak load current? You might desire that voltage drop to be reasonable. Like 100 mV or less. Also, sometimes you might need the input ripple current to be low to avoid noise coupling into the power source supply. \$\endgroup\$ – mkeith Oct 31 '16 at 1:44
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The goal of the input capacitor is to be able to provide current both in-between switching cycles (as they are too fast for a typical power source to respond too) and any load steps (slower, but the same as previous might apply) that might happen during steady state operation.

All input capacitor estimates start with a ripple specification. The further away the switcher is from its power source and the more inductance there is between the switcher and its power source, the higher capacitor value you need at the input to handle load steps without violating your ripple or voltage drop requirement. Simulation in programs such as LTspice help here.

For the cycle by cycle switching currents you need to specify the voltage ripple allowed and have an estimate of the input load current during each switching cycle. Usually the current drawn from the input capacitor is less than the switching current itself as some portion of it is taken directly from the DC source. But a worst case assumption is to imagine the DC source being turned off at the beginning of a cycle and analyse the switcher operating for one cycle. You can then use the capacitor equation (replacing dt with the length of the switching interval) to estimate the worst case ripple (this one is ignoring the series resistance of the capacitor!)

$$\Delta V = \frac{I_{cycle}}{f_s \cdot C_{in}}$$

As you increase the capacitance the ripple decreases, it increases with lower frequency and more current. Reflected in this equation is also the scaling factor of capacitance with frequency. Switcher inductors and capacitors scale nicely with frequency! But in practise the ripple current in the capacitor will produce a ripple voltage that can be considerable. So even though the capacitor might store enough energy to fullfill the ripple requirement, the series resistance might produce a ripple voltage large enough to violate it. For the capacitor series resistance induced ripple just calculate $$R_{ESR} \cdot I_{max}$$ Keep in mind that I_{max} is the top of the current ramp during the switching cycle, which is larger than the average current.

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I would provide a source storage cap impedance based on <1% of the step load Z.

  • For low ESR ceramic cap for the step load transition edge using Zc(f) for f=1/3tr
  • Then for ripple current using RC= 10T where T=1/f , choose another C, which gives less than 10% ripple voltage based on load R from V/I

This is a starting point and depending on load current , choose ESR of the bigger cap to be <2% of step load R and check ripple current ratings often given for low ESR e-caps.

Some people forgo the calculations or testing with bad results others are "lucky" :) just using 100uF 1uF and 0.01 ceramic.

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