ST1S14 datasheet(17/46 Pages) STMICROELECTRONICS

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ST1S14

Closing the loop

6.1

GCO(s) control to output transfer function

The accurate control to output transfer function for a buck peak current mode converter can

be written as:

Equation 2

where R0 represents the load resistance, Ri the equivalent sensing resistor of the current

sense circuitry,

ωp the single pole introduced by the LC filter, and ωz the zero given by the

ESR of the output capacitor.

FH(s) accounts for the sampling effect performed by the PWM comparator on the output of

the error amplifier that introduces a double pole at one half of the switching frequency.

Equation 3

Equation 4

where:

Equation 5

Sn represents the ON time slope of the sensed inductor current, and Se the ON time slope

of the external ramp (VPP peak to peak amplitude) that implements the slope compensation

to avoid sub-harmonic oscillations at duty cycle over 50 %.

The sampling effect contribution FH(s) is:

Equation 6

where:

CO s

()

-------

⋅

--------------------------

–

() 0.5

–

⋅

[]

⋅

-------------------------------------------------------------------------------------------------

-----

⎝⎠

⎛⎞

-----

⎝⎠

⎛⎞

---------------------

H s

()

⋅⋅

⋅

ESR

OUT

⋅

----------------------------------

LOAD

OUT

⋅

----------------------------------------

–

() 0.5

–

⋅

OUT

⋅⋅

------------------------------------------------

------

⋅

OUT

–

------------------------------

⋅

⎝

⎜

⎛

H s

()

⋅

---------------------

-----

-------------------------------------------

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