Detailed and detailed explanation of ripple current value of inductance of power supply BUCK r

Today we will talk about value of inductor current ripple factor r of power supply BUCK. Some friends can calculate inductance BUCK ( ) are all evaluated according to r = 0.4 and some are evaluated according to r = 2 or other values. Then ripple value is different, what is impact? Why introduce concept of pulsation velocity r? Then in this article, we will discuss this matter in detail with you and use practical examples to quantify it to see what value of ripple factor r is based on. I hope explanation in this article will give engineers a deeper understanding. It's an honor to help everyone.

Before reading this article, you need to have some understanding of basic working principle of a BUCK topology and how an inductor works. If you have any needs, please leave a message and I will present it to you in a future article.

We know that for a BUCK power supply, most important core component is inductor. The inductor has three operating modes, namely discontinuous mode (DCM), critical continuous mode (BCM) and continuous mode (CCM).

For presentation, we use a picture to make it easy for everyone to compare. So, what does pulsation speed r mean? Expression in the book:

(1)

Then it means: current ripple/dc. Note that overall ripple frequency r is only discussed in BCM and CCM modes. Also note that AC component is defined as follows:

The reason for above two formulas is actually derived from volt-second law, and volt-second law only holds in BCM and CCM modes, which also indirectly explains why r value of ripple frequency is in BCM. And reason to be discussed in CCM mode.

In addition, according to basic equation of inductance The formula for inductance (tons) can be obtained:

Then, if inductor works in BCM mode, since ΔI=2*Io, then formula can be:

(2)

According to formula (1) we see that ΔI=r*Io, then 2 under denominator is actually ripple frequency r. Therefore, formula for calculating inductance can also be written in following form:

(3)

Then when we calculate BUCK inductance, we must use formula (3) to calculate inductance, but what is basis of value of ripple factor r? We know that value range of r is 0~2 (here we need to know r≠0 because BUCK power supply principle is that there must be ripple for stable operation). However, when r becomes larger, inductance L will be smaller, but Ipk will be larger. Why? Here we give an example:

Assume that load range of power supply is BUCK: Io=0A~2A. If we just work in BCM mode according to Io=2A, it will be following waveform:

If we just work in BCM mode on Io=1A, then at full load following waveform will be:

The two graphs above confirm phrase just said: larger r, larger value of Ipk. Then, if Ipk is large, magnetic circuit must be large to avoid saturation of inductor, so the cost will be high. However, according to It can be seen from formula that larger r, smaller inductance L will be. However, smaller inductance, smaller volume of inductor. Similarly, when r is taken smaller, Ipk is smaller, but L becomes larger.

Then question is, what is correct value for r? As overall volume of inductor can be relatively better.

From analysis just done, we can see that changing r affects two variables at same time: L and Ipk, so is there a variable that can cause a change in r to affect only that variable, and then use that variable to get it A what about optimal solution?

The good news is that there is a variable which is formula for energy of an inductor:

Why did you come up with this formula? In fact, he can relate inductance L to current I and express it using energy formula. Since a change in r affects both L and Ipk, inductance energy formula can be written as follows:

(4)

Some friends here might be wondering why you should use inductance energy formula to connect L and Ipk? In fact, volume of an inductor represents its ability to store energy. If you don't believe me, take a look at following formula:

(5)

Among them, μ is magnetic permeability, A is cross-sectional area of ​​the core, l is length of magnetic circuit, H is magnetic field strength, B is magnetic induction strength, N is number of turns, B is volume of magnetic core. At same time, it can be seen that V=Al, B=µH; (The formula derivation process is as follows: , and magnetomotive force F has following formula: ,So, ).

From formula (5) it can be seen that energy intensity of inductor is closely related to its volume. This is why we need to use inductance energy formula to connect L and Ipk to find optimal solution for value of r.

Okay, we've explained why ripple frequency value r is calculated using inductive energy formula. Also know the formula:

(6)

Substitute formula (3) (6) into formula (4):

(7)

When power conditions BUCK and f are defined, whole term in above formula can be considered as a constant, so above formula can be considered as a function of peak energy Epk of inductor with respect to ripple rate r .

If a known condition is given, then curve of this function is shown in figure below:

The above graph shows that at r=0.3~0.5, there is a physical inflection point. That is, trend of this curve has changed. If r continues to increase at this time, power processing power corresponding to inductor will not drop significantly. In other words, when r is 0.3 ~ 0.5, inductor Volume reduction is not particularly noticeable, but there is still a little, which will be discussed later.

r=0.3~0.5 is range commonly used in our projects, with r=0.4 being most common. At this point, we have actually explained basis of value of r. If you still have questions about some of processes, please scan QR code and submit questions to customer support.

At this point, we still have a few unanswered questions. As I just said, since value of r is after 0.3~0.5, there is still a bit of room for volume of inductor, why not usually continue to take a larger value? This is actually because if value of r continues to be large, value of Ipk will be large, and ripple current on electrolytic capacitor will be large, so on It can be seen that when Ipk becomes larger, heat dissipation of electrolytic capacitor is also larger. In other words, choice of value of r is actually ratio between volume of inductor and heat generated by capacitor, so value of r ends up being completely cut off in 0.3-0.5 range.

Some friends may wonder why some people see r value as 1, 1.5 or even 2 when designing chokes? This is actually easy to explain, because. For some high frequency tanks, high ESR electrolytic capacitors cannot be used, but ceramic capacitors. However, there is no large ESR factor in ceramic capacitors, so problem of large current ripples and high heat generation that we have just analyzed does not exist. Then it is very natural to consider value of r to be very large.