Introduction to Digital Power Conversion
XMC4000/1000 Family
Modulation
Application Guide 68 V1.0, 2015-01
The two expressions for the stability condition shown here are just two different outcomes from the
same calculation.
s
C
>
0,5(s
B
-
s
A
) is good as a quick check point.
If “s
B
“ is replaced by s
A
D/(1-D), then the other one appears as; (1-D)(1+s
C
/s
A
)-0,5 > 0.
This term is inverted proportional to the damping factor Q in a transfer function with two poles at half
the switching frequency; f
sw
=1/(2T).
Slope Compensation Properties
The Slope Compensation is able to move the two complex conjugated poles (~1/Q) to the left in the
high frequency transfer function stage of the loop. This enables adjustable damping of oscillations.
However, the damping factor is duty-cycle (D) dependent, and so impacted by V
IN
variations.
Maintaining Slope Compensation
(See Figure 51).
To maintain a constant damping impact that is independent of system variations, then the
Compensation Slope “s
C
” and the rising inductor current slope “s
A
” ratio “s
C
/
s
A
” should adapt to duty-
cycle (D) variations so that the stability condition for required damping stays constant:
const = (1 - D)(1 + s
C
/
s
A
) - 0.5 > 0
To keep an invariant damping with system variations, then the Slope Compensation maintenance
should satisfy:
s
C
= ((const - 0.5)V
IN
+ V
OUT
) / L
If V
OUT
is assumed to be fixed at the required target value and the damping should be constant, then
the formula would imply s
C
as a linear function of V
IN
.
Note: See also “Non-linear Slope Compensation” in section 8.8.
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