ADP2442ACPZ-R7 datasheet(23/36 Pages) AD

23 / 36 page

Data Sheet

ADP2442

Rev. B | Page 23 of 36

Correspondingly, there are three transfer functions:

)

(

)

(

)

(

COMP

OUT

REF

OUT

COMP

(14)

COMP

)

(

)

(

(15)

)

(

)

(

)

(

FILT

OUT

(16)

where:

VCOMP is the comparator voltage.

IL is the inductor current.

gm is the transconductance of the error amplifier and equals

250 µA/V.

GCS is the current sense gain and equals 2 A/V.

VOUT is the output voltage of the regulator.

VREF is the internal reference voltage and equals 0.6 V.

ZCOMP(s) is the impedance of the RC compensation network that

forms a pole at the origin and a zero, as expressed in Equation 17.

COMP

= 1

)

(

(17)

ZFILT(s) is the impedance of the output filter and is expressed as

OUT

LOAD

FILT

)

(

(18)

where s is the angular frequency, which can be written as s = 2πf.

Obtain the overall loop gain, H(s), by multiplying the three

transfer functions previously mentioned as follows:

)

(

)

(

)

(

FILT

COMP

OUT

REF

(19)

When the switching frequency (fSW), output voltage (VOUT),

output inductor (L), and output capacitor (COUT) values are

selected, the unity crossover frequency can be set to 1/12 of the

switching frequency.

At the crossover frequency, the gain of the open-loop transfer

function is unity.

H(fCROSSOVER) = 1

(20)

This yields Equation 21 for the RC compensation network

impedance at the crossover frequency.

REF

OUT

CROSSOVER

COMP

)

(

(21)

Placing s = fCROSSOVER in Equation 17,

COMP

CROSSOVER

COMP

CROSSOVER

COMP

)

(

(22)

To ensure that there is sufficient phase margin at the crossover

frequency, place the compensator zero at 1/8 of the crossover

frequency, as shown in the following equation:

CROSSOVER

COMP

ZERO

≈

(23)

Solving Equation 21, Equation 22, and Equation 23 yields the

values for the resistor and capacitor in the RC compensation

network, as shown in Equation 24 and Equation 25.

REF

OUT

CROSSOVER

COMP

(24)

COMP

ZERO

COMP

(25)

Using these equations allows calculating the compensations for

the voltage loop.

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