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# Selecting Inductors for Buck Converters

### Key Takeaways

• The conduction modes of buck converters are continuous conduction mode, critical conduction mode, and discontinuous conduction mode.

• In a buck converter, the selection of inductor determines at what conduction mode the converter is operating.

• Selecting the inductor for the buck converter above the critical value (L> Lcritical) makes the converter operate in CCM. In a buck converter, the average output voltage is lower than the input DC voltage

In electronic, industrial, medical, automotive, and telecommunication systems, different types of DC-DC converters are used. The basic operation of a DC-DC converter is to convert unregulated voltage to the desired voltage level while keeping the power constant.

DC-DC converters can be designed with or without isolation. Non-isolated DC-DC converter classifications include step-down converters (buck converters), step-up converters (boost converters), buck-boost converters, Cuk converters, and full-bridge converters. Buck and boost converters are the most basic DC-DC converter topologies. The remaining converters are either derived from these two basic topologies or a combination of them.

In a buck converter, the average output voltage is lower than the input DC voltage. The basic circuit configuration of a buck converter consists of an input DC source, solid-state switch, diode, inductor, capacitor, and load. Selecting an inductor for a buck converter plays a crucial role in determining the conduction modes of the buck converter. In this article, we will discuss buck converter conduction modes and inductor selection.

## Buck Converter Operation Buck converter schematic. Source: Rashid, M. (2001). Power Electronics Handbook. Academic Press.

As shown in the circuit above, buck converter topology is comprised of an input DC power source (Vs), semiconductor switch (S), diode (D), inductor (L), capacitor (C), and load resistor (R). There are two operating states in the buck converter, depending on the switching action. In a switching cycle, the switch remains on for a definite interval of time given by DTs, and off for (1-D)Ts duration, where D is the duty ratio and Ts is the switching period. By alternatively turning on and off the buck converter switch at switching frequency fs =1/Ts, an average output DC voltage (V0) lower than the input DC is obtained.

The output voltage of a buck converter can be given by the equation:

## V0 = DVS(1)

The two operating states in one switching cycle - the ON state and the OFF state - are described below.

1. When the switching device is turned on (ON state) - The switching device is turned on and the diode gets reverse biased. The inductor charges from the input voltage. The capacitor supplies the output current (I0) during the on-state of the switching device.
2. When the switching device is turned off (OFF state) - The switching device is turned off and the inductor current flows through the forward-biased diode. The inductor transfers some stored energy to the load. Before the inductor completely discharges, the switching device gets turned on.

## Conduction Modes of a Buck Converter

The conduction modes of a buck converter are influenced by the inductor current (IL). Based on the continuity of the inductor current flow, the conduction modes of buck converters are classified into the following.

### Continuous Conduction Mode (CCM)

If the inductor current flows continuously during the on and off states of the switch without reaching zero value for any instant of time in a switching cycle, the buck converter is operating in continuous conduction mode. Before the inductor completely discharges, the next switching cycle commences.

### Critical Conduction Mode (CRM)

If the inductor current goes to zero at the end of the switch-off period, it forms the boundary between continuous and discontinuous conduction modes, called critical conduction mode. The switch turns on immediately when the inductor current drops to zero.

### Discontinuous Conduction Mode (DCM)

When the switching device is turned off, the inductor current drops to zero and remains at zero until the commencement of the next switching cycle. Such a conduction mode is referred to as discontinuous conduction mode. During the discontinuous conduction mode, inductor voltage (VL) remains zero for a portion of the switching period and the load is supplied from the capacitor.

## Selecting an Inductor for a Buck Converter

The type of inductor selected for a buck converter determines at what conduction mode the converter is operating. Let’s see how to select the inductor value for the boundary condition between CCM and DCM, which is referred to as CRM.

At CRM, the peak inductor current iL,peak is two times the average inductor current (illustrated in the waveform below). Mathematically, you can represent the average inductor current (ILB) with the following equation:  At CRM, the peak inductor current iL,peak is two times the average inductor current. Source: Mohan, N., Undeland, T., & Robbins, W. (2022). Power Electronics: Converters, Applications, and Design (3rd Edition). Wiley.

Under CRM operation, the inductor completely discharges at the end of the switching cycle. At the boundary condition, the average inductor current (ILB) is the same as the average output current (I0B). Representing  iL,peak in equation (2) in terms of inductor voltage (V=L di/dt) and ILB= I0B gives the following equation: Rearranging  equation (3), the critical inductor value is obtained as: The given set of values Vs, V0, D, Ts, and R, I0B can be replaced by V0/ R in equation (4), and the critical value of the inductor for which the buck converter operates at the boundary condition between CCM and DCM can be calculated.

Selecting the inductor for a buck converter above the critical value (L> Lcritical) makes the converter operate in CCM, and L< Lcritical corresponds to DCM operation. The PCB design and layout tools from Cadence can help you build DC-DC converters.

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