Analysis of Switching Power Supply Ripple Suppression in Buck Circuit

Since the switching power supply is small in size, the ripple content of the output DC voltage is larger than that of the linear power supply with the same power. How to reduce the ripple content has become a key technical difficulty in the application and manufacturing technology of switching power supplies. This article analyzes the Buck circuit to find out the factors that affect the generation of ripple and the measures to improve it.

1 Definition of ripple

The topology of the Buck type switching power supply is shown in Figure 1.

Normally, the switching power supply firstly converts the grid voltage into DC through full-wave rectification, then steps down the voltage through the transformer after high-frequency switching, and obtains a stable DC voltage output after high-frequency diode rectification and filtering. It contains a lot of harmonic interference. At the same time, the spikes caused by the leakage inductance of the transformer and the reverse recovery current of the output diode form the source of electromagnetic interference. These spikes are the output ripple. The output ripple mainly comes from four aspects: low-frequency ripple, high-frequency ripple, common-mode ripple, and ultra-high frequency resonance generated during the switching process of the power device.

2 Buck circuit ripple generation mechanism and calculation

2.1 Ripple current calculation

Definition of inductance:

λ is the coil flux; N is the number of coil turns; i is the current flowing through the coil; Φ is the coil magnetic flux. If the two ends of equation (1) are differentiated with time t as the variable, we can get:

This is known as the inductor voltage drop loop equation.

Now assume that for each individual switching cycle, the input and output voltages remain essentially unchanged when the switch is on or off. The voltages across L in the on and off states can be written out.

The voltage across L in the on state:

The voltage across L in the off state:

Vsat is the conduction voltage drop of the switch tube; VF is the conduction voltage drop of the diode.

Since Vsat and VF are very small compared to Vi and Vo, they are neglected here, and we can get:

It can be seen that Von and Voff are both constants, that is, for

, whether in the on state or in the off state:

is a constant, so we can use

replace

, substitute into formula (4) and rearrange to obtain:

It can be considered that Δi is the ripple current in the inductor coil. Substituting the time and voltage equations (2) and (3) in the on and off states into the above equations, the ripple current expressions in the on and off states are written respectively:

Δion is the on-state ripple current; ton is the on-time; Δioff is the off-state ripple current; toff is the off-time.

When the power supply is stable,

ΔiL is the absolute value of the ripple current on the coil. Substituting equations (5) and (6) into equation (7), we get:

It follows that:

fs is the switching frequency.

Substituting formula (8) into formula (5), we get:

Formula (9) is the expression of ripple current. 2.2 Ripple voltage calculation

Note that in the output section, the inductor current is divided between capacitor C and the load, and we have:

Assume that in steady state, the current output to the load remains unchanged. So:

This is also an approximation, because even if the load is constant, the current will change due to the influence of voltage ripple, but since this change is very small compared to ΔiL, it is ignored here. If it is not ignored, more complex expressions can be derived. ΔiC added to C will produce ripple voltage.

First calculate the first part. When ΔiC flows through the ideal capacitor C, the voltage change across C is:

Take the lower limit of the integral as ton/2, the upper limit of the integral as toff/2, and calculate the integral to get:

Calculate the second part. For general capacitors, they all have series equivalent inductance and series equivalent resistance (in fact, there is also parallel equivalent insulation resistance). The series equivalent inductance only works at higher frequencies and can be ignored when analyzing the switching frequency, but the series equivalent resistance ESR must be considered. When the current ΔiC flows through the ESR, a voltage drop will be generated across the ESR, and its value is:

ΔVESR will also appear at the output as part of the ripple, so the total ripple expression is the sum of equation (10) and equation (11), that is:

Vro is the total ripple; ESR is the equivalent series resistance of C.

Formula (12) is the approximate expression of the ripple voltage of the Buck type switching power supply. Each variable in it is a factor that affects the ripple. Adjusting these variables is the main method to adjust the ripple.

3 Analysis of factors affecting ripple and suppression measures

According to formula (12), the factors affecting the ripple voltage are analyzed one by one

1) First observe the factors in brackets: Take a typical value and calculate it, such as fs=300kHz, C=470μF, and you will know that

Although there are many factors to consider when calculating ESR, in general, the equivalent resistance ESR of an electrolytic capacitor and several ceramic capacitors in parallel is between a dozen and several dozen mΩ. This shows that ESR is the main factor in generating ripple, and an increase in the value of C will not significantly change the ripple.

2) Next, look at the first half of the right side of the equation

If L or fs increases, Vro becomes smaller and the ripple can be reduced. That is, increasing the inductance value and increasing the switching frequency can reduce the ripple.

3) The most easily overlooked thing is the relationship between output voltage and ripple. Examine the rate of change of Vo to Vro.

Under the condition that all other factors remain unchanged, taking the derivative of Vro with respect to Vo, we can get:

in:

make

have

, at this time the ripple of the power supply output is the largest.

Whether Vo is greater than or less than this value, the ripple will decrease. Based on this rule, the ripple of the power module with output voltage adjustment can be inferred.

4) In actual work, all adjustable factors are relatively stable and have certain actual working errors. Therefore, when considering the switching frequency, L and C values, interference factors should be considered and a compromise result affected by many factors should be selected. Other constraints should be considered when adjusting these values. The following are some constraints that need to be paid attention to when adjusting parameters:

a) Increasing the switching frequency will increase system power consumption, reduce power efficiency, increase temperature, and bring about heat dissipation problems.

b) The switching frequency is limited by the switching tube, control chip, diode and other factors and cannot be increased indefinitely.

c) Increasing the value of L will increase the size of the inductor and increase the cost, while the selection of inductors is relatively narrow.

d) Whether modifying L, C or switching frequency, pay attention to the stability of the power supply.

From the above analysis, we can know that reducing ESR can reduce ripple interference, that is, in practice, the method of connecting electrolytic and several ceramic capacitors in parallel is usually used to reduce the ESR of the output C, thereby reducing ripple interference.

4 Conclusion

This article derives the calculation formulas for ripple voltage and current through the calculation formulas of components in the Buck circuit. According to the influencing factors, the selection of inductance and capacitance is analyzed and compared, thus obtaining the method of ripple suppression. However, the problem is not completely solved, and the following issues are more worthy of attention and understanding:

1) What are the ESR characteristics of various types of electrolytic capacitors and various types of film capacitors?

2) What factors affect the ESR of various types of capacitors?

3) How to estimate the ESR of capacitors in parallel;

4) How does the relative position of the output capacitor affect the ESR?