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# Origin of slope compensation

2023-10-21【Archive】

There is a knowledge point in switching power supply that is relatively difficult to explain clearly, but it plays an important role in stability of entire tilt compensation system. We plan to use a series of articles to discuss this knowledge in detail and aim to give everyone a relatively deep understanding of this content.

The first question we need to answer is why does a switching power system need tilt compensation, or what problem does tilt compensation solve? From a macro point of view, switching power supply regulation system can be divided into two parts: one is internal current loop, and other is external voltage loop. The reason why current loop is called internal loop is mainly because its adjustment speed is faster and it belongs to one-cycle adjustment. The adjustment speed of voltage loop is definitely slower than that of current loop. For output filter capacitor, voltage is integral of current. The current loop tuning result can respond to a voltage signal after tens of cycles.

When system's output or inductor current is disturbed by load changes or input voltage changes, sub-harmonic fluctuations in inductor current or inductor current may occur before voltage loop can play a regulating role. Ringing phenomenon.

The reason this is possible here is mainly because this phenomenon occurs in CCM mode and when duty cycle is over 50%. When duty cycle is less than 50%, interference current fluctuations tend to converge automatically. Let's demonstrate this graphically.

The figure above shows current disturbances caused by load changes when duty cycle is less than 50%. You can see if this perturbation will automatically converge after a few cycles. Why converge? We can derive a formula for changing perturbation current.

As you can see, when duty cycle is less than 50%, current rise during time Ton is greater than current fall during time Toff. Then trend of current jitter is closely related to ratio of two slopes.

The specific output formula is shown in figure above. Here we divide calculation into two triangles. In triangle θ0, according to ratio of tangent, proportional relationship between δIo and It (the common part of two triangles) ① can be obtained. In fact, is this tangent relationship essentially a slope? Similarly, in triangle θ1 we can also get formula ②. After simplifying these two formulas, we get relation ③. You can see if δI1 is less than δIo because m2 is less than m1, right? When duty cycle is less than 50%, is it true that m2 should be less than m1? Then, after several cycles of iterations, system converges after a gradual decrease in number of perturbations.

However, when duty cycle exceeds 50%, that is, when m2 is greater than m1, number of disturbances will increase, resulting in inductor current fluctuations, as shown in figure below.

For control system switch chip, Tone time will also fluctuate, that is, so-called alternation of large and small waves will occur. This fluctuating current does not contribute to stability of system, so we need to find a way to solve this problem. So how to solve it? This is origin of slope compensation: since in this case m2 is larger than m1, can we change overall slope relationship with slope compensation?

In next article, a deeper analysis of this issue will be carried out.

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