An inductor is a common energy-storing passive component in circuits, playing roles such as filtering, boosting, and bucking in the design of switching power supplies. In the early stage of scheme design, engineers not only need to select appropriate inductance values, but also consider the current that the inductor can withstand, the DCR of the coil, mechanical dimensions, losses, and so on. If they are not familiar enough with the functions of inductors, they will often be passive in the design and consume a lot of time.

Understanding the Functions of Inductors

An inductor is the "L" in the LC filter circuit at the output of a switching power supply. In buck conversion, one end of the inductor connects to the DC output voltage, while the other end switches between the input voltage and GND according to the switching frequency.

In state 1, the inductor is connected to the input voltage via the MOSFET. In state 2, the inductor is connected to GND.  

Due to the use of this type of controller, there are two ways to ground the inductor: grounding through a diode or through a MOSFET. If the former method is adopted, the converter is called asynchronous mode. In the latter case, the converter is referred to as a synchronous mode.

In state 1, one end of the inductor is connected to the input voltage, and the other end is connected to the output voltage. For a buck converter, the input voltage must be higher than the output voltage, so a forward voltage drop is formed across the inductor.  

In state 2, the end of the inductor originally connected to the input voltage is connected to ground. For a buck converter, the output voltage is necessarily the positive terminal, so a negative voltage drop is formed across the inductor.

Inductor Voltage Calculation Formula

V=L(dI/dt).Since the current through the inductor increases when the inductor voltage is positive (State 1) and decreases when the voltage is negative (State 2),the inductor current waveform is shown in Figure 2:

From the above figure, we can see that the maximum current through the inductor is the DC current plus half of the switching peak-to-peak current. The above figure also shows the ripple current. According to the formula mentioned above, the peak current can be calculated as follows: where ton is the time in State 1, T is the switching period, and DC is the duty cycle of State 1.

Synchronous Conversion Circuit

Asynchronous Conversion Circuit

Rs: The combined resistance of the current-sensing resistor and the inductor winding resistance. Vf: The forward voltage drop of the Schottky diode. R: The total resistance in the conduction path, calculated as R=Rs+Rm, where is the MOSFET on-state resistance.

Saturation of Inductor Core

From the calculated inductor peak current, we know that as the current through the inductor increases, its inductance will decay. This is determined by the physical properties of the core material. The degree of inductance decay is critical: if the decay is too severe, the converter will not operate normally. The current at which the inductor fails due to excessive current is called the saturation current, a fundamental parameter of the inductor.

The saturation curve of power inductors in converter circuits is crucial and worthy of attention. To understand this concept, you can observe the actually measured curve of L vs. DC current.

When the current increases beyond a certain threshold, inductance drops sharply—a phenomenon known as saturation. Further current increases can cause the inductor to fail entirely.

With this saturation characteristic, we can understand why all converters specify the inductance value variation range (△L ≤ 20% or 30%) under DC output current, and why the inductor specification includes the parameter Isat. Since the change in ripple current does not significantly affect inductance, it is desired in all applications to minimize the ripple current as much as possible, as it affects the ripple of the output voltage. This is why there is always great concern about the degree of inductance attenuation under DC output current, while the inductance under ripple current is often overlooked in the specifications.

Selection of Appropriate Inductors for Switching Power Supplies

Inductors are commonly used components in switching power supplies. Due to the phase difference between their current and voltage, theoretically, the loss is zero. Inductors often serve as energy storage elements, featuring the characteristic of "opposing the incoming and retaining the outgoing," and are frequently used together with capacitors in input and output filter circuits to smooth the current.  

As magnetic components, inductors inherently face the issue of magnetic saturation. Some applications allow inductor saturation, some permit saturation starting from a certain current value, while others strictly prohibit it, requiring differentiation in specific circuits. In most cases, inductors operate in the "linear region," where the inductance value remains constant and does not change with terminal voltage or current. However, switching power supplies have a non-negligible problem: the inductor windings introduce two distributed (or parasitic) parameters. One is the unavoidable winding resistance, and the other is the distributed stray capacitance related to the winding process and materials. Stray capacitance has minimal impact at low frequencies, but its effect becomes increasingly evident as the frequency rises. When the frequency exceeds a certain value, the inductor may exhibit capacitive characteristics. If the stray capacitance is "lumped" as a single capacitor, the equivalent circuit of the inductor reveals its capacitive behavior beyond a specific frequency.  

When analyzing the operational status of an inductor in a circuit, the following characteristics must be considered:  

1. When a current I flows through an inductor L , the energy stored in the inductor is: E=0.5 × L× I2(1)  

2.In a switching cycle, the relationship between the inductor current variation (ripple current peak-to-peak value) and the voltage across the inductor is:  

 V=(L × di)/dt(2), This shows that the magnitude of the ripple current is related to the inductance value.  

3. Inductors also undergo charging and discharging processes. The current through an inductor is proportional to the integral of the voltage (volt-seconds) across it. As long as the inductor voltage changes, the current change rate di/dt will also change: a forward voltage causes the current to rise linearly, while a reverse voltage causes it to drop linearly.

Selection of Inductors for Buck-Type Switching Power Supplies

When selecting an inductor for a buck-type switching power supply, it is necessary to determine the maximum input voltage, output voltage, power switching frequency, maximum ripple current, and duty cycle. The following describes the calculation of the inductance value for a buck-type switching power supply. First, assume that the switching frequency is 300 kHz, the input voltage range is 12 V ± 10%, the output current is 1 A, and the maximum ripple current is 300 mA.

The Circuit Diagram of Buck-Type Switching Power Supply

The maximum input voltage is 13.2V, and the corresponding duty cycle is: D＝Vo/Vi＝5/13.2＝0.379(3), where Vo is the output voltage and Vi is the input voltage. When the switching transistor is on, the voltage across the inductor is: V = Vi - Vo = 8.2 V(4) . When the switching transistor is off, the voltage across the inductor is: V＝-Vo－Vd＝-5.3V(5).dt＝D/F(6).Substituting equations (2), (3), and (6) into equation (2):

Selection of Inductors for Boost-Type Switching Power Supplies

The calculation of the inductance value for a boost switching power supply, except that the relationship formula between the duty cycle and the inductor voltage is changed, other processes are the same as the calculation method of a buck switching power supply. Assuming that the switching frequency is 300 kHz, the input voltage range is 5 V ± 10%, the output current is 500 mA, and the efficiency is 80%, the maximum ripple current is 450 mA, and the corresponding duty cycle is:D=1-Vi/Vo=1-5.5/12=0.542(7).

The circuit diagram of a boost switching power supply

When the switch is turned on, the voltage across the inductor is: V = Vi = 5.5 V (8), When the switch is turned off, the voltage across the inductor is: V = Vo + Vd - Vi = 6.8 V (9), Substituting formulas 6/7/8 into formula 2 gives:

Please note that, unlike buck converters, boost converters do not continuously supply load current from the inductor. When the switching transistor is conducting, the inductor current flows through the switch to ground, while the load current is provided by the output capacitor. Therefore, the output capacitor must store sufficient energy to supply the load during this period. However, when the switch is off, the inductor current not only supplies the load but also charges the output capacitor. 

Generally, increasing the inductance value reduces output ripple but degrades the power supply's dynamic response. Therefore, the optimal inductance should be selected based on specific application requirements. Higher switching frequencies allow for smaller inductance values, reducing inductor size and saving PCB space. Consequently, modern switching power supplies trend toward higher frequencies to meet the demand for smaller electronic products.

Analysis and Application of Switching Power Supplies

Regarding Lenz's Law: In a DC-powered circuit, due to the self-inductance of the coil, an electromotive force (EMF) is induced that opposes the increase in current. Therefore, at the instant of power-on, the circuit current is effectively zero, and the entire voltage drop occurs across the coil. The current then increases gradually as the coil voltage decreases to zero, marking the end of the transient state. In switching converter operation, the inductor must not enter saturation to ensure efficient energy storage and transfer. A saturated inductor behaves like a direct DC path, losing its ability to store energy, which undermines the converter's functionality. When the switching frequency is fixed, the inductance value must be sufficiently large to prevent saturation under peak currents.

Determination of Inductance in Switching Power Supplies: At lower switching frequencies, since the on/off durations are longer, a larger inductance value is required to maintain continuous output. This allows the inductor to store more magnetic field energy. Additionally, longer switching periods result in less frequent energy replenishment, leading to relatively smaller current ripple. This principle can be explained by the formula: L = (dt/di) * uL where D = Vo/Vi (duty cycle), dt = D/F (on-time), F = switching frequency, and di = current ripple. For buck converters, D = 1 - Vi/Vo; for boost converters, D = Vo/Vi. Rearranging gives: L = D * uL / (F * di). When F decreases, L must increase proportionally. Conversely, increasing L while keeping other parameters constant reduces di (current ripple). At higher frequencies, increasing inductance raises impedance, leading to increased power loss and reduced efficiency. Generally, with fixed frequency, larger L reduces output ripple but degrades dynamic response (slower adaptation to load changes). Therefore, the optimal inductance should be selected based on application requirements to balance ripple reduction and transient performance.