# Calculating size of cap & inductor for buck convertor

What is the idea of choosing inductor & capacitor value for buck DCDC convertors (no specific part number, in general)?

I've tried random one with low resistance, and it kinda works, but want to know idea behind calculation of optimal value (based on freq, and max current).

This is a basic buck converter:

The current trough the inductor is $I_L$, the voltage over the inductor is $V_L$. The voltage over the load (the resistor) and capacitor is $V_{out}$. The upper state is called the on state and the bottom state is called the off state. The switch is controlled by a PWM signal.

The relation between $V_L$ and $I_L$ is: $$V_{L}=L\frac{dI_L}{dt}$$ When the converter's switch is closed, $V_L = V_{in} - V_{out}$, so the voltage over the inductor is positive. This means the current trough the inductor will increase as described by the relation above. When the switch is closed, $V_L = - V_{out}$ (the voltage drop over the diode is neglected here). So the current trough the inductor will decrease.

The inductance limits the rate of the increase and decrease of the current. So use a larger inductor for a smaller current ripple. Because a capacitor acts like a voltage buffer here, a larger capacitor will make the voltage ripple smaller.

Everything depends of course on the frequency of the PWM signal. The higher the frequency, the smaller the time for the current to increase. So a higher frequency will decrease the current ripple.

When you make or purchase an inductor, make sure the current the inductor can handle is larger than the peak current which is the average current + 50% of the current ripple.

When you purchase a capacitor, make sure it has low ESR so minimum power losses.

Very good explanations on how to calculate the required inductance and capacitance are on this site: http://www.daycounter.com/LabBook/BuckConverter/Buck-Converter-Equations.phtml There is also a calculator which you can use to calculate the required inductance and capacitance.

Designing your own buck (or boost) converter is really fun! You have to take in account switching and conductance losses in the switch, conductance and core losses in the inductor, losses in the capacitance and diode. Designing a buck converter is looking for the frequency, C and L combination with the highest efficiency and the lowest cost. (And don't turn your converter into a radio transmitter like I did this morning :-P )

The image is from Wikipedia which has a great article on buck converters.

The choice of inductor is critical for numerous reasons:

• it dictates the ripple current sourced to the capacitors, and therefore, the ripple voltage imposed on their ESRs, which is your output ripple voltage
• it dictates at which load the converter transitions from discontinuous to continuous mode, which is important to know for feedback loop stability (a discontinuous-mode buck needs only a single-pole compensation network; a continuous-mode buck needs two), power dissipation (peak and RMS switch power is higher in a discontinuous-mode buck than in a continuous-mode buck at the same power level) and duty cycle (a discontinuous-mode buck has a dead-time component that causes the duty cycle to vary with load; a continuous-mode buck's duty cycle is essentially fixed with respect to load)
• the current slew rate of the inductor will place an upper boundary on the converter's transient response

In general, it's easier to choose the inductor you want then size the output capacitance in terms of ripple voltage; make sure the combined ESR gives you the ripple you want, and that the caps are rated appropriately for the ripple current and frequency that the inductor will be providing.

You must make sure that the inductor will not saturate out under your worst-case condition of overload, as DC current can cause the permeability of the magnetic material to roll off which will send the switching ripple high. If you're not experienced in magnetics design, it's easier to choose an off-the-shelf inductor suited for a buck (i.e. one that specifies how much current it can handle before saturating).

[It's fun playing with distributed-gap ferrite material like Sendust and Kool-Mu, which can take a lot of abuse without saturating out and blowing up your switches, but I digress...]

Linear has excellent datasheets with much information on selecting components for your SMPS. For instance when I look at the datasheet for the LTC3127 I see sections for Buck-Boost Inductor Selection, Output and Input Capacitor Selection and Capacitor Selection Example. The datasheets have detailed calculations.