Inductor is a common energy storage passive component in the circuit, which plays the role of filtering, boosting, and bucking in the design of switching power supply. In the early stage of the scheme design, the engineer should not only choose the appropriate inductance value, but also consider the current that the inductance can withstand, the DCR of the coil, the mechanical size, loss and so on. If you are not familiar with the function of the inductor, you are often passive in the design and consume a lot of time.

**Understanding the Function of Inductors**

The inductor component is the "L" in the LC filter circuit at the output of the switching power supply. In the step-down conversion, one end of the inductor is connected to the DC output voltage. The other end is connected to the input voltage or GND with switching frequency switching.

During state 1, the inductor is connected to the input voltage through the MOSFET. During state 2, the inductor is connected to GND.

Because of the use of this type of controller, the inductor can be grounded in two ways: through a diode or through a MOSFET. If it is the former way, the converter is called asynchronous way. The latter way, the converter is called synchronous way.

During 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, thus creating a forward voltage drop across the inductor.

During state 2, one end of the inductor originally connected to the input voltage is connected to ground. For a buck converter, the output voltage must be positive, so there will be a negative voltage drop across the inductor.

**Inductor voltage calculation formula**

V=L(dI/dt)

Therefore, when the voltage on the inductor is positive (state 1), the current on the inductor increases; when the voltage on the inductor is negative (state 2), the current on the inductor decreases. The current through the inductor is shown in Figure 2:

From the above figure we can see that the maximum current flowing through the inductor is the DC current plus half of the switching peak-to-peak current. The graph above is also known as ripple current. According to the above formula, we can calculate the peak current: where, ton is the time of state 1, T is the switching period, and DC is the duty cycle of state 1.

**Synchronous conversion circuit**

**Asynchronous conversion circuit**

Rs is the resistance of the inductive resistance plus the resistance of the inductance winding resistance. Vf is the forward voltage drop of the Schottky diode. R is Rs plus MOSFET on-resistance, R=Rs+Rm.

**Saturation of Inductor Core**

By having calculated the peak current of the inductor, we will know that as the current through the inductor increases, its inductance will decay. This is due to the physical properties of the core material. How much the inductance decays is critical and important: if the inductance decays too much, the converter will not work properly. When the current through the inductor is so large that the inductor fails, the current at this time is called "saturation current". This is also the basic parameter of the inductor.

It is very critical that the power inductor in the conversion circuit will have a saturation curve, which is worth noting. To understand this concept look at the actual measured LvsDC current curve:

When the current increases to a certain level, the inductance will drop sharply, which is the saturation characteristic. If the current increases, the inductor will fail.

With this saturation characteristic, we can know why the inductance value variation range (△L≤20% or 30%) under the DC output current is specified in all converters, and why is there an Isat in the inductance specification parameters. Since the ripple current changes will not seriously affect the inductance. In all applications it is desirable to keep the ripple current as small as possible because it affects the output voltage ripple. This is why people are always concerned about the attenuation of the inductance under the DC output current, but ignore the inductance under the ripple current in the specification.

**Choosing the Right Inductor for Switching Power Supplies**

Inductor is a commonly used component in switching power supply, because its current and voltage phase are different, so theoretically the loss is zero. Inductors are often energy storage components, which have the characteristics of "rejecting and staying". They are often used in input filtering and output filtering circuits together with capacitors to smooth the current.

Inductors are magnetic components and naturally have the problem of magnetic saturation. Some applications allow the inductor to saturate, some allow the inductor to saturate from a certain current value, and some do not allow the inductor to saturate, which requires distinction in specific circuits. In most cases, the inductance works in the "linear region", and the inductance value is constant at this time and does not change with the terminal voltage and current. However, there is a problem that cannot be ignored in the switching power supply, that is, the winding of the inductance will cause two distributed parameters (or parasitic parameters), one is the inevitable winding resistance, and the other is the distribution related to the winding process and material. stray capacitance. The stray capacitance has little effect at low frequency, but it gradually appears with the increase of frequency. When the frequency is higher than a certain value, the inductance may become the characteristic of capacitance. If the stray capacitance is "concentrated" into a capacitance, the capacitance characteristics after a certain frequency can be seen from the equivalent circuit of the inductance.

When analyzing the working condition of the inductor in the circuit, the following characteristics must be considered:

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

2. In a switching cycle, the relationship between the change of the inductor current (the peak-to-peak value of the ripple current) and the voltage across the inductor is: V=(L×di)/dt(2) It can be seen that the value of the ripple current is The size is related to the inductance value.

3. The inductor also has the process of charging and discharging voltage. The current across the inductor is proportional to the integral of the voltage (volts per second). As long as the inductor voltage changes, the current rate of change di/dt will also change; the forward voltage makes the current linearly increase, and the reverse voltage makes the current linearly decrease.

**Inductor selection of step-down switching power supply**

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

**Circuit diagram of step-down 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)

Among them, Vo is the output voltage, Vi is the output voltage. When the switch is turned on, the voltage across the inductor is:

V=Vi-Vo=8.2V(4)

When the switch is turned off, the voltage across the inductor is:

V=-Vo-Vd=-5.3V(5)

dt=D/F(6)

Substituting Equation 2/3/6 into Equation 2 yields:

**Inductor Selection of Boost Switching Power Supply**

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

**Circuit diagram of boost switching power supply**

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

Note that a boost power supply differs from a buck power supply in that the load current is not always provided by the inductor current. When the switch is turned on, the inductor current flows into the ground through the switch, and the load current is provided by the output capacitor, so the output capacitor must have a large enough energy storage capacity to provide the current required by the load during this period. But when the switch is turned off, the current flowing through the inductor not only provides the load, but also charges the output capacitor.

Generally speaking, the larger the inductance value is, the smaller the output ripple will be, but the dynamic response of the power supply will also be correspondingly degraded, so the selection of the inductance value can be adjusted according to the specific application requirements of the circuit to achieve the best effect. The increase of the switching frequency can make the inductance value smaller, so that the physical size of the inductance becomes smaller and saves the space of the circuit board. Therefore, the current switching power supply has a trend of developing towards high frequency to meet the requirements of smaller and smaller electronic products. .

**Analysis and Application of Switching Power Supply**

Lenz's law related content: When DC power is supplied, due to the self-inductance of the coil, the coil will generate a self-inductive electromotive force, which will hinder the increase of the coil current, so at the moment of power-on, the circuit current can be considered to be 0, At this time, all the voltage drop of the circuit falls on the coil, then the current increases slowly, the voltage at the coil terminal drops slowly until zero, and the transient process ends

During the switching operation of the converter, it is necessary to ensure that the inductor is not in saturation to ensure efficient energy storage and transfer. The saturable inductance is equivalent to a straight-through DC path in the circuit, so it cannot store energy, and it defeats the entire design of the switch-mode converter. When the switching frequency of the converter has been determined, the inductance working with it must be large enough and not saturated.

The inductance in the switching power supply is determined: the switching frequency is low, and the on and off times are relatively long, so in order to keep the output uninterrupted, the inductance value needs to be increased, so that the inductor can store more magnetic field energy. At the same time, because each switch is relatively long, the supplementary update of energy is not as timely as when the frequency is high, so the current will be relatively small. This principle can also be illustrated by the formula:

L=(dt/di)*uL

D=Vo/Vi, buck duty cycle D=1-Vi/Vo, boost duty cycle

dt=D/F,F=switching frequency

di = current ripple

Therefore, L=D*uL/(F*di), when the switching frequency of F is low, L needs to be larger; it is agreed that when L is set large, the ripple current di will be relatively reduced under other conditions At high switching frequency, increasing the inductance will increase the impedance of the inductance, increase the power loss, and reduce the efficiency. At the same time, under the condition of constant frequency, generally speaking, the larger the inductance value is, the smaller the output ripple will be, but the dynamic response of the power supply (the load power consumption is occasionally large and occasionally small, and it is correspondingly slow between the magnitude changes) will also respond accordingly. Therefore, the selection of the inductance value can be adjusted according to the specific application requirements of the circuit to achieve the best effect.