# Help understanding slope compensation

#### BitsNBytes

Joined Mar 22, 2021
20
Hello,

I am in need of some clarification on slope compensation. After reading some articles on Rohm, and the often suggested paper from Rob Sheehan on how to apply current mode control theory, I am just utterly confused.

For example:
1. "The Reason Why Compensation Ramp Slope must be at least 1/2 down slope" by Rohm
2. Robert Sheehan's paper " Understanding and Applying Current-Mode Control Theory "

https://techweb.rohm.com/knowledge/dentatsu/s-dentatsu/s-dentatsu03/3790

I see three different suggestions on the slope of the comp ramp, and I am sure I have read so much that I am lost.
1. Rohm paper's math is 1/2 the inductor down slope (presume independent of topology - buck, boost, buck-boost)
2. Robert's paper I swear says 2 different things between page 5 and 6: a) " By adding a compensating ramp equal to the down-slope of the inductor current ", and b) " the optimal slope of the ramp presented to the modulating comparator input is equal to the sum of the absolute values of the inductor upslope and down-slope

Is the correct comp ramp 1) 1/2 down slope, 2) down slope, 3) sum of the up and down slopes?

What in the world am I missing? Even if we presume a peak current mode control buck.

#### Papabravo

Joined Feb 24, 2006
19,854
One of the purposes of slope compensation is to prevent sub-harmonic oscillation, (Basso, 2014, pp. 173-175). in conjunction with Eq. (2.163), takes 2+ pages to develop, Basso posits:

$S_a\;>\;\cfrac{S_2}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2.163)$​
$$\text{where } S_a\text{ is the slope of the compensating signal and }S_2\text{ is the slope of the inductor discharge}$$
The accompanying text says:

This is the minimum value that guarantees the stability for all operating duty ratios. In the literature other choices are often proposed, such as compensation levels up to 75%. One should keep in mind that overcompensating a converter seriously hampers its dynamic behavior but also reduces it maximum peak current and hence available power...
I consider this a pretty definitive statement on the matter, but your mileage may vary.

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#### BitsNBytes

Joined Mar 22, 2021
20
Which book from Basso, so I can pick it up from Amazon? I know he has several.

I find it a little disappointing that this particular subject is not clear, IMO.
If I presume a fixed slope compensation ramp as some devices do, and then apply 1) 1/2 down slope, 2) downslope, finally 3) sum of up and down slopes to make sure I am choosing the optimal inductor, that leads to an increasing inductor value with the largest inductor value being calculated with the sum of the up and down slope option. If 1/2 downslope is the optimal slope balancing sub-harmonics and transient behavior then the calculated inductor value using #3 would hinder my converter's transient performance.