How to configure inductance for switching power supply?

木犯001号

How to configure inductance for switching power supply? [Copy link]

Switching power supply (SMPS) is a very efficient power converter, and its theoretical value is close to 100%. There are many types. According to the topology, there are Boost, Buck, Boost-Buck, Charge-pump, etc.; according to the switch control method, there are PWM, PFM; according to the type of switch tube, there are BJT, FET, IGBT, etc. This discussion focuses on the PWM control Buck and Boost types commonly used in data card power management. Then let us learn how to configure the appropriate inductor for the switching power supply~

The main components of a switching power supply include: input source, switch tube, energy storage inductor, control circuit, diode, load and output capacitor. Currently, most semiconductor manufacturers integrate the switch tube, control circuit and diode into a CMOS/Bipolar process power management IC, which greatly simplifies the external circuit.

As a key component of the switching power supply, the energy storage inductor plays an important role in the performance of the power supply. It is also the focus of product design engineers and the object of debugging. As the size of consumer electronic devices represented by mobile phones, PMPs, and data cards is developing towards the trend of being light, thin, compact, and fashionable, on the contrary, the stronger the product performance, the larger the inductance and capacitance required, and the larger the size. Therefore, how to reduce the size of the switching power supply inductor (the PCB area and height it occupies) while ensuring product performance is an important proposition to be discussed in this article. Designers will have to compromise between circuit performance and inductance parameters.

Everything has two sides, and switching power supplies are no exception. Bad PCB layout and wiring design will not only reduce the performance of the switching power supply, but also strengthen EMC, EMI, ground bounce, etc. The issues that should be paid attention to and the principles to be followed when laying out the switching power supply are another important topic to be discussed in this article.

1. Derivation of the switching power supply duty cycle D, inductance value L, and efficiency η formula

Buck and Boost switching power supplies have different topologies. This article will use the circuit reference models shown in Figures 1-1 and 1-2:

The reference circuit model assumes that the DCR (Direct Constant Resistance) of the inductor is zero by default.

Buck/Boost switching power supply, with the switch tube on and off, the current waveform of the energy storage inductor is shown in Figure 1-3:

As can be seen from the figure, the current waveform of the inductor is equivalent to superimposing an AC with an IP-P value of ΔI on the DC IDC. Therefore, IDC becomes the output current IO, which is mainly consumed by the load; the AC ΔI is consumed by the ESR (Equation Serial Resistance) of the load capacitor and becomes the output ripple Vripple. Therefore,

The following uses the Buck switching power supply as an example to derive the duty cycle, inductance value and efficiency formula.

In a continuous mode cycle, the switch is closed to charge the inductor. According to Kirchhoff's law:

dt is approximately: D/f (D: the ratio of the ON/OFF state of the switch tube within an oscillation period T, T=1/f, dt=D*T=D/f); D: the duty cycle is the ratio of the cycle time occupied by the high level to the entire cycle time), expand:

Where: Vi is the input voltage, VSW is the switch voltage, Vo is the output voltage, fSW is the switching frequency, and D is the duty cycle.

In a continuous mode cycle, the switch is turned on and the inductor is discharged. According to Kirchhoff's law:

r is also called the current ripple ratio, which is the ratio of the ripple current to the rated output current. For a given Buck switching power supply, this value is generally a constant. From equation (5), we can get: the larger the inductance value, the smaller I, and therefore the smaller r. However, this often requires a very large inductor to achieve this, so most Buck switching power supplies choose an r value between 0.25 and 0.5.

Substituting (6) into (5), we obtain:

So far, we have derived the D, L, Lmin, and η of the Buck switching power supply. It should be noted that all the above formulas are based on the reference circuit model and ignore the DCR of the inductor.

From formula (4), we can see that the duty cycle is only related to V(i), V(o), V(sw) and V(D). We can easily build a circuit to calculate D. This is also one of the core circuits of the switching power supply controller, but for the users of the switching power supply, we may not care about it.

From equation (8), it can be seen that the efficiency of the switching power supply is also only related to Vi, Vo, Vsw and VD. In fact, Vsw and VD are functions of the switching frequency fsw, so η is also a function of f(sw), but it cannot be guaranteed that the higher the fsw, the higher η. For a given Buck switching power supply, its SWf is fixed, so η is also a fixed value, especially after ignoring Vsw and VD, the η value is 1. Obviously, this does not conform to the actual situation. The fundamental reason is that "the reference model assumes that the energy storage inductor is an ideal inductor."

Substituting (5) into (1), we can obtain:

Therefore, the output ripple voltage can be reduced by selecting large inductors and low ESR large-capacity output capacitors.

Similarly, D, L, Lmin, and η of the Boost type switching power supply can be derived as follows:

2. Selection of minimum inductance

Formulas (7) and (12) respectively give the formulas for selecting the minimum inductance of general Buck and Boost switching power supplies. For low-power switching power supplies used in consumer electronics such as mobile phones, PMPs, and data cards, Vsw and VD are both between 0.1V and 0.3V, so formulas (7) and (12) can be simplified to obtain:

Take the PM6658 Buck power supply MSMC as an example, Vi is 3.8V, Vo is 1.2V, r is 0.3, fsw is 1.6MHz, Io_rated is 500mA, then Lmin is 3.08uH. If the selected inductor tolerance is 20%, 1.25*Lmin=3.85uH. According to the calculated value, the nearest standard inductor value is 4.7uH, so the minimum inductor value recommended by PM6658 spec is 4.7uH.

3. Inductor parameter selection

In addition to the inductance and tolerance mentioned above, the inductor also has the following important parameters: self-excitation frequency (fo), DCR, saturation current (Isat) and root mean square current (IRMS). Although there are many parameters, there is only one rule: try to ensure that the impedance of the inductor under fsw is minimized, so that the actual circuit and the ideal model are consistent, reduce the power consumption and heat of the inductor, and improve the efficiency of the power supply.

3.1 Self-excitation frequency fo

The impedance of the inductor in the ideal mode is linearly related to the frequency and will increase as the frequency increases. The actual inductor model is shown in Figure 3-1-1, which is composed of an inductor L in series with RDCR and a parasitic capacitor C in parallel, and there is a self-excitation frequency fo. When the frequency is less than fo, it is inductive, and when it is greater than fo, it is capacitive, and the impedance is the largest at fo.

Experience value: The self-excited frequency fo of the inductor is best selected to be greater than 10 times the switching frequency fsw.

3.2 DC resistance RDCR

The DC resistance RDCR of the inductor will consume some power itself, reducing the efficiency of the switching power supply. What's more, this consumption will be carried out through the inductor heating, which will reduce the inductance value of the inductor and increase the ripple current and ripple voltage. Therefore, for the switching power supply, the inductor with the smallest DCR should be selected as much as possible based on the typical or maximum DCR value provided in the chip data sheet.

3.3 Saturation current I(SAT) and root mean square current I(RMS) (inductor burnout problem)

The saturation current ISAT of an inductor refers to the maximum current that can pass through an inductor when its inductance drops by 10% to 30% of the nominal value.

The root mean square current IRMS of the inductor refers to the root mean square current that can pass through the inductor when the temperature rises from room temperature 25℃ to 65℃.

The size of ISAT and IRMS depends on the order of the inductor magnetic saturation and the temperature rising to 65℃.

When the nominal output current is greater than ISAT, the inductor is saturated, the inductance value decreases, the ripple current and ripple voltage increase, and the efficiency decreases. Therefore, the minimum value of the inductor's ISAT and IRMS should be higher than 1.3 of the rated output current of the switching power supply.

4. Inductor Type Selection

After clarifying the calculation of the minimum inductance value and the selection of inductance parameters, it is necessary to conduct a comparative analysis of some popular inductor types on the market. The following will focus on: large inductors and small inductors, winding inductors and stacked inductors, magnetically shielded inductors and unshielded inductors for comparison and explanation.

4.1 Large and small inductors of the same size

Here, "same size" refers to the roughly same physical shape of the inductor, and "size" refers to different capacities. Generally, small-capacity inductors have the following advantages:

● Lower DCR, higher efficiency and less heat at heavy load;

● Larger saturation current;

● Faster load transient response speed;

The large-capacity inductor has lower ripple current and ripple voltage, lower AC and conduction losses, and higher efficiency at light loads.

4.2 Wirewound Inductors and Multilayer Inductors

Compared with winding inductors, stacked inductors have the following advantages:

With smaller physical size, it occupies less PCB area and height space;

With lower DCR, higher efficiency at heavy load;

Has lower AC loss and higher efficiency at light load;

However, the ISAT of the stacked inductor is also small, so it will have a larger ripple current when it is heavily loaded, causing the output ripple voltage to increase accordingly.

4.3 Magnetic Shielded Inductors and Unshielded Inductors

Unshielded inductors have lower prices and smaller sizes, but they also generate EMI. Magnetic shielded inductors effectively shield EMI, so they are more suitable for EMI-sensitive applications such as wireless devices. In addition, they have lower DCR.

5. Summary of Inductor Selection

Based on the introduction in the previous sections, we can select a suitable inductor by following the steps below:

(1) Calculate Lmin and recommended inductance parameters: fo, RDC, ISAT, IRMS.

(2) Under the premise of ensuring (1), make a compromise based on the physical size requirements and cost-effectiveness: large inductor or small inductor, stacked inductor or wound inductor, magnetically shielded inductor or unshielded inductor.

6. Switching power supply layout

Taking the Buck circuit as an example, no matter whether the switch tube is closed-open or open-closed, the part where the current transient occurs is as shown in Figure (c). They are the rising or falling edges that will produce very rich harmonic components. In layman's terms, these current traces that produce transients are the so-called "AC", and the rest are "DC". Of course, the difference between AC and DC here is not the definition in traditional textbooks, but refers to the fact that the PWM frequency of the switch tube is only a component in the "AC" FFT transformation, while in "DC" such harmonic components are very low and can be ignored. So it is not surprising that the energy storage inductor belongs to "DC", after all, the inductor has the characteristic of preventing current transients. Therefore, when laying out the switching power supply, the "AC" trace is the most important and most carefully considered part. This is also the only basic law that needs to be remembered, and it applies to other laws and topologies. The figure below shows the current transient trace of the Boost circuit, and pay attention to its difference from the Buck circuit.

A 1-inch long, 50-mm wide, 1.4-mil thick (1-ounce) copper wire has a resistance of 2.5 mΩ at room temperature. If a current of 1 A flows through it, the voltage drop generated is 2.5 mV, which will not have an adverse effect on most ICs. However, the parasitic inductance of such a 1-inch long wire is 20 nH. As V=L*dI/dt shows, if the current changes rapidly, a large voltage drop may be generated. A typical Buck power supply generates a transient current of 1.2 times the output current when the switch tube is turned on and off, and a transient current of 0.8 times the output current when it is turned off and on. The switching time of FET type switch tube is 30 ns, and that of Bipolar type is 75 ns. Therefore, when a 1-inch wire in the "AC" part of the switching power supply flows through a 1A transient current, a voltage drop of 0.7 V will be generated. Compared with 2.5 mV, 0.7 V is nearly 300 times larger, so the layout of the high-speed switching part is particularly important.

The most ideal layout method is to place all peripheral devices as close as possible to the converter and reduce the length of the traces. However, this is often not possible due to the extremely limited layout space. Therefore, it is necessary to prioritize according to the severity of the transient voltage drop. For the Buck circuit, the input bypass capacitor must be placed as close to the IC as possible, followed by the input capacitor, and finally the diode, with a short and thick trace connecting one end to the SW and the other end to the ground. For the Boost circuit layout, the output bypass capacitor, output capacitor and diode are prioritized.