Buck Converters

Overview

Buck converters use a switching element, inductor and capacitor to convert an input voltage into a lower output voltage.

The basic parts of a buck converter.
The basic parts of a buck converter.

When using a P-channel MOSFET for synchronous rectification, it’s body diode is forward-biased when the converter is in shutdown mode. This can drain the power source into the output. More advanced buck converters have extra circuitry to disconnect this P-channel MOSFET when the device is not active.

Inductor Selection

You can use the following equations to select the main inductor for a buck converter.

First, calculate the maximum average inductor current using:

$$ I_L = I_{OUT} \frac{V_{OUT}}{0.8 V_{IN}} $$

where:
\( V_{IN} \) = the input voltage to the buck regulator
\( V_{OUT} \) = the output voltage of the buck regulator

Then, calculate the value of inductance required with:

$$ L = \frac{V_{IN} (V_{OUT} – V_{IN})}{\Delta I_L \cdot f \cdot V_{OUT}} $$

where:
\( \Delta I_L \) = the desired ripple current in the inductor
\( f \) = the switching frequency
and everything else as mentioned previously

Capacitor Selection

The output capacitance is primarily determined by the maximum allowed output voltage ripple. This ripple is determined by the capacitance of the capacitor and it’s ESR (equivalent series resistance). The output capacitance of a boost converter can be found using the following equation.

C_{min} = \dfrac{I_O (V_{OUT} - V_{IN})}{f  \Delta V V_{OUT}}

where:
\Delta V = the maximum desired output voltage ripple
and everything else as mentioned previously

The actual ripple will be slightly larger than this due to the ESR of the capacitor.

\Delta V_{ESR} = I_O R_{ESR}

where:
R_{ESR} = the parasitic series resistance of the output capacitor

The total output ripple is the sum of the ripple caused by the capacitance, and the ripple cause by the ESR. Note that these equations assume a constant load. Load transients (fluctuations in the load current) will also cause voltage ripple.

Down Conversion

Some boost converters also have a built in regulator to provide regulation when the input voltage exceeds the desired output voltage. This is normally a linear regulator, so your efficiency will drop and you will have to take into account the thermal dissipation. This is normally called down conversion.

schematic-of-boost-converter-with-down-conversion-capability The internal schematic of a boost converter with in-built down conversion capability (the ability to drop the input voltage).

The price you pay for this added down conversion feature is a slightly higher cost, and slightly higher quiscent current (e.g. some of TI’s boost converters have 19uA quiscent current without down conversion, and 25uA with down conversion).

Input Voltage Range

Typically, boost IC’s with an internal switch (a converter) can support lower input voltages than those that require an external switch (a controller). A typical minimum input voltage for a converter is in the range 0.3-0.9V, while a controller’s minimum is in the range 0.9-1.8V.

BUCK Converter Calculator

This calculator can be used to calculate the values of the critical component values for a buck converter.

The non-idealities it takes into account are:

  1. The voltage drop across the switching element
  2. The voltage drop across the diode or active rectifying element.
Variable Name Symbol Value Units Notes
Input Voltage \( V_{in} \) The voltage provided to the input of the buck converter. Usually this is from a DC power supply or battery.
Output Voltage \( V_{out} \) The output voltage of a buck converter must be equal to or lower than the input voltage.
Diode Voltage Drop \( V_D \) The forward voltage drop across the diode when the diode is fully conducting. The diode may be replaced with an active switching element (such as a MOSFET), to reduce power losses. A MOSFET will have a much lower voltage drop than a diode. This is sometimes called the free-wheeling diode.
Switching Element Voltage Drop \( V_{SW} \) The voltage drop across the switching element when the switch is fully ON. The switching element is typically a MOSFET.
Duty Cycle D The duty cycle is given by the equation: $$ D = \frac{V_{out} - V_{D}}{V_{in} - V_{SW} - V_D} $$
Switching Frequency \( f_{SW} \) The switching frequency of the transistor (or other switching element).
Average Output Current \( I_{out} \) The average (DC) output current of the buck converter. Note that this is usually higher than the input current!
Percentage Output Current Ripple \( \frac{\Delta I_{out}}{I_{out}} \) The is the percentage ripple of the output current. Strictly speaking, it is the ratio between the amplitude of the output current's AC component (i.e. the ripple), and the output current's DC component (the average output current). It is recommended that this is no more than 10-20%.
Inductance L The inductance is given by the equation: $$ L = \frac{(V_{in} - V_{SW} - V_{out})\cdot D}{f_{SW} \cdot \Delta I_{out}} $$

Examples

Tiny (Nano) Buck Converters

Texas Instruments released a series of very small (3.5×3.5×1.8mm) buck converter modules in 2015. One of the most impressive features is that this includes the inductor (external capacitors are still required). One example is the LMZ20502, which can provide up to 2A of current with an input voltage range of 2.7-5.5V and a output voltage range of 0.8-3.6V.

A photo of the LMZ20502 buck converter. Image from http://www.digikey.co.nz/product-detail/en/LMZ20502SILT/296-38656-1-ND/.
A photo of the LMZ20502 buck converter. Image from http://www.digikey.co.nz/product-detail/en/LMZ20502SILT/296-38656-1-ND/.

Notice how most of the volume on the module is taken up the chip inductor (the big brown thing that dominates most of the image). The dimensions of the package are shown in the diagram below.

The dimensions of the MicroSIP component package, used by the Texas Instruments "Nano" buck converters. Image from http://www.ti.com/lit/ds/symlink/lmz20502.pdf.
The dimensions of the MicroSIP component package, used by the Texas Instruments “Nano” buck converters. Image from http://www.ti.com/lit/ds/symlink/lmz20502.pdf.