Buck Converters

Buck converters are a particular topology of switch-mode power supply (SMPSs) that use a switching element, diode (or second switch), inductor and capacitor to convert an input voltage into a lower output voltage.

The basic schematic of a buck converter. SW1 is typically a MOSFET switched by control logic (not shown).

To learn more about EMI/EMC considerations regarding buck converters, see the EMC Design Guidelines page.

How A Buck Converter Works

The output voltage of a buck converter is purely determined by the input voltage $V_{IN}$ and the percentage of time that the switch spends in the on-state during each switching cycle, $D$:

$$\begin{align} V_{OUT} = DV_{IN} \end{align}$$

$D$ is the duty cycle, and varies from $0$ to $1$. It is defined as:

$$\begin{align} D = \frac{t_{on}}{T} \end{align}$$

where:
$t_{on}$ is the on time of the switch, in seconds
$T$ is the switching period, in seconds ($t_{on} + t_{off}$)

Note

The simple equation showing $V_{OUT}$ is only dependent on $V_{IN}$ and $D$ is only true when all components act ideally (e.g. no voltage drop across the diode, no ESR in the capacitor, no resistance through the inductor) AND the inductor is in continuous conduction (i.e. current never drops to 0). In the real world there are always parasitics, however this equation is still a good first approximation to help understand how it works.

The following steps show a way to intuitively understand how a buck converter produces a lower output voltage (and derive the basic equation):

1. The average voltage across the inductor, over an entire switching cycle, must be 0 (other ways of saying is this is that the integral must be 0, or the volt-seconds must be 0). If it wasn’t, then because $V = L \frac{di}{dt}$ (the basic equation for an inductor), the current in the inductor would increase or decrease without bound (i.e. go to infinity).
2. When the switch is closed ($t_{on}$), the voltage across $L1$ is $V_{IN} - V_{OUT}$ during this phase.
3. When the switch is open ($t_{off}$), $D1$ is forward biased, and if we assume it’s a perfect diode (no forward voltage drop), the voltage across $L1$ is $-V_{OUT}$ during this phase.
4. The average (or integral) over the entire switching cycle has to be 0, so: $$\begin{align} (V_{IN} - V_{OUT})t_{on} - V_{OUT}t_{off} &= 0 \nonumber \\ V_{IN}t_{on} - V_{OUT}t_{on} - V_{OUT}t_{off} &= 0 \nonumber \\ V_{IN}t_{on} &= V_{OUT}(t_{on} + t_{off}) \nonumber \\ V_{OUT} &= \frac{t_{on}}{t_{on} + t_{off}} V_{IN} \nonumber \\ &= D V_{IN} \nonumber \end{align}$$

Tip

This analysis method of realizing the average voltage across the inductor must be 0 over an entire switching cycle also works for other switching topologies.

When the switch is closed, the current flows from the input through the inductor to the output, as shown below:

Current path when the switch is closed (during $t_{on}$ ).

When the switch opens, the input is disconnected. Because the inductor doesn’t like changes in current, it keeps a current flowing through the load by forward biasing $D1$, as shown below:

Current path when the switch is open (during $t_{off}$).

$C1$ (which is also called $C_{OUT}$) is to reduce the voltage ripple at the output/load.

Control Methods

99% of the time, you want a fixed (regulated) and stable output voltage, which does not depend on the input voltage and one which does not start to sag as you draw more current. To achieve this, it is insufficient to drive the switch at a fixed duty cycle. More complex control mechanisms with feedback are required. The most popular two are voltage-mode control and current-mode control, which are explained in the following section.

Tip

See the SMPS Control Methodologies page for general information on these control methods that is not specific to buck converters.

Voltage Mode Control

Voltage-mode (VM) control is the simplest control method, originating in approx. the 1970’s¹. It works by taking a proportion of the output voltage and comparing it with a fixed reference voltage. The difference between these two is called the error voltage and is amplified by an error amplifier. This error voltage is then fed into a comparator, with the other input being a sawtooth signal (triangular waveform). The switch is turned on at the start of the sawtooth period, and turned off when the sawtooth exceeds the error voltage. An SR latch is normally used to prevent multiple triggers per cycle due to noise. Voltage-mode control is named as such because the duty cycle is proportional to the control voltage.

The basic logical components used for voltage-mode control.

Current-Mode Control (Constant Frequency)

Current-mode (CM) control is a very common control method for buck converters.

It has the following advantages over VM:

• Simpler external frequency compensation than VM
• Faster load transient response than VM.

However, one big disadvantage is the extra control circuitry complexity. However, this is somewhat mitigated in more recent years as all of this circuitry is integrated into a cheap silicon IC.

Peak current measurement is a common way of “measuring” the average output current.

A transconductance amplifier (amplifier that converts a input voltage to an output current) is used to compare the voltage at a feedback pin (typically labelled FB) to an internal voltage reference.

PCM: Peak current mode

See the excellent SNVA555: Understanding and Applying Current-Mode Control Theory by TI for more information on current-mode control theory.

Hysteretic Control

Hysteretic control is when the output voltage is directly monitored by a comparator, rather than going through an error amplifier. If the output voltage falls or exceeds below a certain value, the buck converter switch is turned on/off. Because the control is performed by measuring the ripple in the output voltage, this method is also called the ripple control method.

There are two ways on controlling the switch:

1. Detect when the voltage falls BELOW a set threshold, and turn the switch ON for a fixed amount of time, OR
2. Detect when the voltage rises ABOVE a set threshold, and turn the switch OFF for a fixed amount of time

Hysteretic control has the benefit of being extremely fast to respond to transient current changes, since it is directly monitoring the output voltage and there is no error amplifier. It also does not need any compensation. These advantages make it suitable for powering the rapidly changing current demands of high power CPUs and FPGAs.

Calculating Buck Converter Component Values

Inductor Selection

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

In a buck converter the inductor is in series with the output, so the average inductor current is equal to the average output current:

$$\begin{align} I_L = I_{OUT} \end{align}$$

where:
$I_{OUT}$ is the output current of the buck regulator (pick your maximum)

Then, calculate the value of inductance required with:²

$$\begin{align} L = \frac{V_{OUT} (V_{IN} - V_{OUT})}{\Delta I_L \cdot f \cdot V_{IN}} \end{align}$$

where:
$V_{IN}$ is the input voltage to the buck regulator
$V_{OUT}$ is the output voltage of the buck regulator
$\Delta I_L$ = the desired ripple current in the inductor
$f$ = the switching frequency

The ripple current is typically chosen to be 20-40% of the average current². If we choose 30%, then we can calculate $\Delta I_L$ with:

$$\begin{align} \Delta I_L = 0.3I_L \end{align}$$

Caution

Aside from making sure the inductor you pick has at least the inductance calculated above, you also want to make sure that the peak inductor current is less than the inductor’s saturation current (otherwise it will stop storing energy in it’s magnetic field and stop behaving like an inductor), and the average current is less than the inductor’s rated current (otherwise it will overheat).

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 its ESR (equivalent series resistance). The minimum output capacitance for a buck converter can be found using:²

$$\begin{align} C_{min} = \dfrac{\Delta I_L}{8 f \Delta V} \end{align}$$

where:
$\Delta I_L$ = the inductor ripple current (from above)
$\Delta V$ = the maximum desired output voltage ripple
$f$ = the switching frequency

The actual ripple will be slightly larger than this due to the ESR of the capacitor. The output capacitor carries the inductor ripple current, so the ESR contributes an additional ripple voltage of:

$$\begin{align} \Delta V_{ESR} = \Delta I_L R_{ESR} \end{align}$$

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 caused by the ESR.

Note

These equations assume a constant load. Load transients (fluctuations in the load current) will also cause voltage ripple.

Buck Converter Calculator

Use the generic buck-converter design helper below to compute the duty cycle and required inductance from the supply/output voltages, diode and switch drops, switching frequency, output current and acceptable inductor ripple.

Generic buck-converter design: enter the input/output voltages, diode and switch drops, switching frequency, output current and acceptable inductor ripple to get the duty cycle and required inductance. Diode drop is 0 for synchronous (active-rectifier) topologies.

V_in

V

The voltage provided to the input of the buck converter. Usually from a DC power supply or battery.

V_out

V

The output voltage of the buck converter. Must be lower than V_in.

V_D

V

The forward voltage drop across the diode when fully conducting. For synchronous converters (active MOSFET rectifier), use 0 or the MOSFET's V_DS(on).

V_SW

V

The voltage drop across the switching element when fully ON. Typically a MOSFET's V_DS(on).

f_SW

Hz

The switching frequency of the transistor (or other switching element).

I_out

A

The average (DC) output current of the buck converter. Note: this is usually higher than the input current.

ΔI_L

%

The peak-to-peak inductor ripple current as a percentage of the average output current. Typically 10–30% for good operation.

D

24.56 %

The on/off duty cycle, D = (V_out − V_D) / (V_in − V_SW − V_D).

L

7.041 µH

The required inductance to keep the inductor ripple current below the specified percentage.

MP4558 Design Tool

The MP4558 is a buck converter IC from Monolithic Power Systems. The calculator below applies the design equations directly from its datasheet to size the frequency-setting resistor, feedback divider, inductor and capacitors for your target output voltage, switching frequency and load. The internal feedback reference voltage is $V_{FB} = 0.8\,V$.

Pick your switching frequency, set the bottom feedback resistor ($R_2$) to a value you’d actually like to use (typically $10\,k\Omega$), and the tool computes everything else.

Enter the switching frequency, output voltage, bottom feedback resistor (R₂), average load current, allowable inductor ripple current, input voltage, input and output capacitances, and output capacitor ESR. Outputs the frequency-setting resistor (R_freq), top feedback resistor (R₁), required inductance, peak inductor current, and input / output ripple voltages. All equations are taken straight from the MP4558 datasheet.

f_sw

Hz

The desired switching frequency.

V_out

V

The desired output voltage.

R₂

Ω

The resistance of the bottom resistor in the feedback divider that sets the output voltage.

I_load

A

The average load current.

ΔI_L

%

The allowable inductor ripple current, as a percentage of the average load current. Normally set to around 30%.

V_in

V

The input voltage.

C_in

F

The capacitance on the input. A larger input capacitance results in lower input voltage ripple.

C_out

F

The capacitance on the output. A larger output capacitance results in lower output voltage ripple.

R_ESR

Ω

The ESR (equivalent series resistance) of the output capacitor. A larger ESR results in larger output voltage ripple.

R_freq

195 kΩ

Resistance needed for the resistor that sets the switching frequency.

R₁

31.25 kΩ

The resistance of the top resistor in the feedback divider that sets the output voltage.

L

19.98 µH

The required inductance of the inductor.

I_L,peak

1.15 A

The peak current through the inductor. Make sure the inductor's saturation current is above this value.

ΔV_in

16.65 mV

The input ripple voltage.

ΔV_out

5.273 mV

The output ripple voltage. Lower it by increasing the output capacitance, decreasing the output capacitor's ESR, or increasing the switching frequency.

Synchronous Rectification

When using a P-channel MOSFET for synchronous rectification, its 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.

EMC

The input current “hot loop” of a buck converter is the most important part to worry about when it comes to EMC. See the EMC Design Guidelines page for more information.

Examples

Tiny (Nano) Buck Converters

Texas Instruments released a series of very small (3.5x3.5x1.8mm) 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/.

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.

Footnotes

1. Maniktala, Sanjaya (2012). Voltage-Mode, Current-Mode (and Hysteretic Control). Microsemi. Retrieved 2021-08-22, from https://www.microsemi.com/document-portal/doc_view/124786-voltage-mode-current-mode-and-hysteretic-control. ↩

2. Brigitte Hauke (2015, Aug). Basic Calculation of a Buck Converter’s Power Stage [Application Report]. Texas Instruments. Retrieved 2023-06-20, from https://www.ti.com/lit/an/slva477b/slva477b.pdf. ↩ ↩² ↩³