LED5000 datasheet(44/52 Pages) STMICROELECTRONICS

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Application notes - alternative topologies

LED5000

44/51

Doc ID 023951 Rev 1

6.4

Compensation network design for alternative topologies

The small signal analysis for the alternative topologies can be written as:

Equation 74

that shares similar terms with

Equation 1 which is valid for the buck (see Equation 1). In

addition KDX depends on the topology (different for boost and buck-boost) and ωZ_RHP

(

Equation 75) is a zero in the right half plane:

Equation 75

The RHP (right half plane) zero has the same 20 dB/dec rising gain magnitude as a

conventional zero, but with 90 degree phase drop instead of lead. This characteristic cannot

be compensated with the error amplifier network so the loop gain is designed to roll off at

lower frequency in order to keep its contribution outside the small signal analysis.

Z_RHP (see Equation 75) depends on the equivalent output resistance, inductor value and

the duty cycle. As a consequence the minimum

Z_RHP over the input voltage range

determines the maximum system bandwidth:

Equation 76

the system phase margin depends on K.

This paragraph provides the equations to calculate the components of the compensation

network once selected the power components and given the BW specification.

Table 10: BB and boost parameters summarizes the KD, Km, K parameters useful for the

next calculations of the compensation network.

The DC gain of the total small loop is:

Equation 77

where Gm is the error amplifier transconductance, REA the equivalent output resistance of

the error amplifier, RCS the internal current sense gain (for these parameters refer to

Table 5: Electrical characteristics), RS the sensing resistor value, and KD can be calculated

from

Table 10

The calculation of the components composing the compensation network depends on the

relative position of the pole fp (see Equation 3) and the designed bandwidth BW.

CO s

()

LOAD

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

–

()

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

Z_RHP

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

–

⎝⎠

⎛⎞

-----

⎝⎠

⎛⎞

⋅

-----

⎝⎠

⎛⎞

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

H s

()

⋅⋅

⋅

Z_RHP

OUT

–

()

⋅

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

BW BW

MAX

≤

----

Z_RHP_MIN

⋅

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

⋅

---------

–

()

-----------

-------

⋅⋅

⋅

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