How to choose a suitable inductor for a switching power supply？

Inductance is also called a choke, which is characterized by "very large inertia" in the current flowing through it. In other words, due to the continuity of magnetic flux, the current on the inductor must be continuous, otherwise a large voltage spike will be generated. Inductance is a magnetic component, and naturally there is a problem of magnetic saturation. Some applications allow the inductor to saturate, some applications allow the inductor to enter saturation from a certain current value, and some applications do not allow the inductor to saturate, which requires distinction in specific circuits.

In most cases, the inductor works in the "linear region", at this time the inductance value is a constant, 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 materials. Stray capacitance.

Stray capacitance has little effect at low frequencies, but it gradually becomes apparent as the frequency increases. When the frequency is higher than a certain value, the inductance may become a capacitive characteristic. If the stray capacitance is "concentrated" into a capacitor, the equivalent circuit of the inductance can be used to see the capacitance characteristics that appear after a certain frequency.

When analyzing the working condition of the inductor in the circuit or drawing the voltage and current waveform, you may wish to consider the following characteristics:

1. When a 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 inductor current (peak-to-peak ripple current) and the voltage across the inductor is:V=(L×di)/dt(2)

It can be seen that the magnitude of the ripple current is related to the inductance value.

3. Just like capacitors have charging and discharging currents, inductors also have charging and discharging voltage processes. The voltage on the capacitor is proportional to the integral of the current (A·sec), and the current on the inductor is proportional to the integral of the voltage (Volt·sec). As long as the inductor voltage changes, the current rate of change di/dt will also change; the forward voltage causes the current to rise linearly, and the reverse voltage causes the current to linearly drop.

Calculating the correct inductance value is very important for choosing the right inductor and output capacitor to obtain the smallest output voltage ripple.

It can be seen from Figure 1 that the current flowing through the switching power supply inductor is composed of AC and DC components. Because the AC component has a higher frequency, it will flow into the ground through the output capacitor and generate the corresponding output ripple voltage dv. =di×RESR. This ripple voltage should be as low as possible, so as not to affect the normal operation of the power system. Generally, the peak-to-peak value is 10mV~500mV.

Figure 1: Inductor current in a switching power supply.

The size of the ripple current also affects the size of the inductor and the output capacitor. The ripple current is generally set to 10%~30% of the maximum output current. Therefore, for a step-down power supply, the peak value of the current flowing through the inductor is higher than that of the power supply. The output current is 5%~15% larger.

Inductance selection of step-down switching power supply

When choosing an inductor for a step-down switching power supply, you need to determine the maximum input voltage, output voltage, power switching frequency, maximum ripple current, and duty cycle. The following takes Figure 2 as an example to illustrate the calculation of the inductance of a step-down switching power supply. First, assume 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.

Figure 2: 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 and Vi is the output voltage. When the switch tube is turned on, the voltage on the inductor is:

V=Vi-Vo=8.2V(4)

When the switch tube is turned off, the voltage on the inductor is:

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

dt=D/F(6)

Substituting formula 2/3/6 into formula 2 gives:

Inductance selection of step-up switching power supply

For the calculation of the inductance value of the step-up switching power supply, the calculation method 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 been changed.

Take Figure 3 as an example for calculation. 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)

Figure 3: Circuit diagram of step-up switching power supply.

When the switch tube is turned on, the voltage on the inductor is:

V=Vi=5.5V(8)

When the switch tube is turned off, the voltage on the inductor is:

V=Vo+Vd-Vi=6.8V(9)

Substituting formula 6/7/8 into formula 2 gives:

Please note that the step-up power supply is different from the step-down power supply in that the load current of the former is not always provided by the inductor current. When the switch tube is turned on, the inductor current flows into the ground through the switch tube, and the load current is provided by the output capacitor. Therefore, the output capacitor must have enough energy storage capacity to provide the current required by the load during this period. However, during the switch-off period, the current flowing through the inductor not only provides the load, but also charges the output capacitor.

Generally speaking, the larger the inductance value, the smaller the output ripple, but the dynamic response of the power supply will be correspondingly worse. Therefore, the selection of the inductance value can be adjusted according to the specific application requirements of the circuit to achieve the most ideal effect.

The increase of the switching frequency can make the inductance value smaller, thereby making the physical size of the inductance smaller and saving circuit board space. Therefore, the current switching power supply has a trend toward high frequency development to meet the requirements of smaller and smaller electronic products.

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