Choosing the right inductor for a switching power supply

Inductor It is a commonly used component in switching power supply. Because its current and voltage are out of phase, the loss is theoretically zero. Inductor is often used as energy storage component, and is often used with capacitor in input filter and output filter circuit to smooth current. Inductor is also called choke, and its characteristic is that the current flowing through it has "large inertia". In other words, due to the continuous flux characteristic, the current on the inductor must be continuous, otherwise a large voltage spike will be generated.

Inductors are magnetic components, so they naturally have the problem of magnetic saturation. Some applications allow the inductor to be saturated, some allow the inductor to enter saturation from a certain current value, and some do not allow the inductor to be saturated. This requires differentiation in specific circuits. In most cases, the inductor works in the "linear region", where 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 switching power supplies, that is, the winding of the inductor will lead to two distributed parameters (or parasitic parameters), one is the inevitable winding resistance, and the other is the distributed stray capacitance related to the winding process and materials. The stray capacitance has little effect at low frequencies, but it gradually becomes apparent as the frequency increases. When the frequency is above a certain value, the inductor may become a capacitor characteristic. If the stray capacitance is "concentrated" into a capacitor, the capacitance characteristics presented after a certain frequency can be seen from the equivalent circuit of the inductor.

When analyzing the working condition of the inductor in the circuit or drawing the voltage and current waveform, it is advisable to consider the following characteristics:

1. When current I flows through 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 value of ripple current) and the voltage across the inductor is:

V＝（L×di）/dt （2）

It can be seen from this that the size of the ripple current is related to the inductance value.

3. Just as 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 (ampere-seconds), and the current on the inductor is proportional to the integral of the voltage (volt-seconds). As long as the inductor voltage changes, the current change rate di/dt will also change; forward voltage causes the current to rise linearly, and reverse voltage causes the current to fall linearly.

Calculating the correct inductor value is very important for selecting the appropriate inductor and output capacitor to obtain minimum output voltage ripple.

As can be seen from Figure 1, the current flowing through the switching power supply inductor consists of two components, AC and DC. Because the AC component has a higher frequency, it will flow into the ground through the output capacitor, generating a corresponding output ripple voltage dv=di×RESR. This ripple voltage should be as low as possible to avoid affecting the normal operation of the power supply system. Generally, the peak-to-peak value is required to be 10mV~500mV.

Figure 1: Inductor current in a switching power supply.

The size of the ripple current will also affect the size of the inductor and 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 current flowing through the inductor is 5%~15% larger than the power supply output current.

Inductor selection for step-down switching power supplies

When selecting an inductor for a step-down switching power supply, it is necessary to determine the maximum input voltage, output voltage, power supply switching frequency, maximum ripple current, and duty cycle. The following uses Figure 2 as an example to illustrate the calculation of the inductance value of a step-down switching power supply, assuming 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 a 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 is turned on, the voltage on 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 formula 2/3/6 into formula 2 yields:

Inductor selection for step-up switching power supply

For the calculation of the inductance value of the boost switching power supply, except for the change in the relationship between the duty cycle and the inductor voltage, the other processes are the same as the calculation method of the buck switching power supply. 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%, then 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 a boost switching power supply.

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

V＝Vi＝5.5V （8）

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

V＝Vo＋Vd－Vi＝6.8V （9）

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

Please note that the boost power supply is different from the buck power supply in that the load current of the former 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. However, 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, as the inductance value increases, the output ripple will decrease, but the dynamic response of the power supply will also deteriorate accordingly, so the selection of the inductance value can be adjusted according to the specific application requirements of the circuit to achieve the best effect. Increasing the switching frequency can reduce the inductance value, thereby reducing the physical size of the inductor and saving circuit board space. Therefore, the current switching power supply has a trend towards high frequency to meet the requirements of smaller and smaller electronic products.