Inductors are common passive energy storage components in circuits. They play the role of filtering, boosting, and reducing voltage in the design of switching power supplies. In the early stages of solution design, engineers must not only select the appropriate inductance value, but also consider the current that the inductor can withstand, the DCR of the coil, the mechanical size, loss, etc. If you are not familiar with the function of the inductor, you will often be passive in the design and waste a lot of time.
Understanding the Function of an Inductor
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 through the switching frequency.
During state 1, the inductor is connected to the input voltage through the MOSFET. During state 2, the inductor is connected to GND.
With this type of controller, there are two ways to connect the inductor to ground: through a diode or through a MOSFET. In the former case, the converter is called asynchronous. In the latter case, the converter is called synchronous.
During Phase 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, the inductor terminal that was originally connected to the input voltage is connected to ground. For a buck converter, the output voltage must be at the positive terminal, so a negative voltage drop will be formed on the inductor.
Inductor voltage calculation formula
V=L(dI/dt)
Therefore, when the voltage across the inductor is positive (state 1), the current through the inductor increases; when the voltage across the inductor is negative (state 2), the current through 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 above figure is also called 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 impedance of the inductive resistor plus the inductor winding resistance. Vf is the forward voltage drop of the Schottky diode. R is Rs plus the MOSFET on-resistance, R=Rs+Rm.
Saturation of the inductor core
From the calculated peak current of the inductor, we 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 the "saturation current". This is also a basic parameter of the inductor.
The power inductor in the conversion circuit has a saturation curve which is very critical and worth noting. To understand this concept, you can observe 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 further, the inductance will fail.
With this saturation characteristic, we can understand why all converters specify the inductance value variation range under DC output current (△L≤20% or 30%), and why the parameter Isat is included in the inductor specification. Since the change of ripple current will not seriously affect the inductance. In all applications, the ripple current is expected to be as small as possible because it will affect the ripple of the output voltage. This is why everyone is always concerned about the attenuation of the inductance under DC output current, and ignores the inductance under ripple current in the specification.
Choosing the right inductor for a switching power supply
Inductors are commonly used components in switching power supplies. Since their current and voltage phases are different, theoretically, the loss is zero. Inductors are often energy storage components with the characteristics of "rejecting incoming and retaining outgoing". They are often used together with capacitors in input filtering and output filtering circuits to smooth current.
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, the following characteristics must be considered:
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 in 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 that the size of the ripple current is related to the inductance value.
3. Inductors also have a charging and discharging voltage process. The current on the inductor is proportional to the integral of the voltage (volt-second). As long as the inductor voltage changes, the current change rate di/dt will also change; the forward voltage causes the current to rise linearly, and the reverse voltage causes the current to fall linearly.
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 describes the calculation of the inductor value for 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.
Step-down switching power supply circuit diagram
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
The calculation of the inductance value of the boost switching power supply is the same as that of the buck switching power supply, except that the relationship between the duty cycle and the inductor voltage has changed. Assuming 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)
Boost switching power supply circuit diagram
When the switch is on, the voltage across the inductor is: V = Vi = 5.5 V (8) When the switch is off, the voltage across the inductor is: V = Vo + Vd - Vi = 6.8 V (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.
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-induced electromotive force, which will hinder the increase of the coil current. Therefore, at the moment of power-on, the circuit current can be considered to be 0. At this time, all the voltage drops in the circuit fall on the coil, and then the current increases slowly, and the coil terminal voltage slowly decreases until it reaches zero, and the transient process ends.
During the switching operation of the converter, it is necessary to ensure that the inductor is not in a saturated state to ensure efficient energy storage and transfer. A saturated inductor is equivalent to a direct DC path in the circuit, so it cannot store energy, which will make the entire design of the switch mode converter fall short. When the switching frequency of the converter has been determined, the inductor working with it must be large enough and cannot be saturated.
Determination of inductance in switching power supply: When the switching frequency is low, the on and off time is relatively long. Therefore, in order to ensure uninterrupted output, the inductance value needs to be increased so that the inductor can store more magnetic field energy. At the same time, since each switch is relatively long, the energy replenishment and update is not as timely as when the frequency is high, so the current will be relatively small. This principle can also be explained by the formula:
L=（dt/di）*uL
D＝Vo/Vi, step-down duty cycleD＝1-Vi/Vo, step-up duty cycle
dt＝D/F，F＝switching frequency
di = current ripple
So L＝D*uL/（F*di）, when the switching frequency of F is low, L needs to be larger; agree that when L is set large, under other conditions, the ripple current di will be relatively reduced. At high switching frequencies, increasing the inductance will increase the impedance of the inductance, increase power loss, and reduce efficiency. At the same time, under the condition of constant frequency, generally speaking, the output ripple will decrease as the inductance value increases, but the dynamic response of the power supply (the load power consumption is sometimes large and sometimes small, and the response is slow between changes in size) 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 most ideal effect.
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