ADP1877ACPZ-R7 datasheet(22/32 Pages) AD

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ADP1877

Rev. 0 | Page 22 of 32

Then the power loss in the low-side MOSFET is

BODYDIODE

CLS

Note that MOSFET, RDSON, increases with increasing

temperature with a typical temperature coefficient of 0.4%/oC.

The MOSFET junction temperature rise over the ambient

temperature is

TJ = TA + θJA × PD

where:

θJA is the thermal resistance of the MOSFET package.

TA is the ambient temperature.

PD is the total power dissipated in the MOSFET.

LOOP COMPENSATION

As with most current mode step-down controller, a transcon-

ductance error amplifier is used to stabilize the external voltage

loop. Compensating the ADP1877 is fairly easy; an RC

compensator is needed between COMP and AGND. Figure 34

shows the configuration of the compensation components:

RCOMP, CCOMP, and CC2. Because CC2 is very small compared to

CCOMP, to simplify calculation, CC2 is ignored for the stability

compensation analysis.

COMPx

ADP1877

AGND

CCOMP

RCOMP

CC2

0.6V

FBx

Figure 34. Compensation Components

The open loop gain transfer function at angular frequency, s, is

given by

)

(

)

(

)

(

FILTER

COMP

OUT

REF

(1)

where:

Gm is the transconductance of the error amplifer, 500 μs.

GCS is the tranconductance of the current sense amplifier.

ZCOMP is the impedance of the compensation network.

ZFILTER is the impedance of the output filter.

VREF = 0.6 V

GCS with units of A/V is given by

MIN

DSON

(2)

where:

ACS is the current sense gain of either 3 V/V, 6 V/V, 12 V/V, or

24 V/V set by the gain resistor between DL and PGND.

RDSON_MIN is the the low-side MOSFET minimum on resistance.

Because the zero produced by the ESR of the output capacitor is

not needed to stabilize the control loop, the ESR is ignored for

analysis. Then ZFILTER is given by

OUT

FILTER

(3)

Because CC2 is very small relative to CCOMP, ZCOMP can be written

COMP

(4)

At the crossover frequency, the open loop transfer function is

unity of 0 dB, H (fCROSS) = 1. Combining Equation 1 and

Equation 3, ZCOMP at the crossover frequency can be written as

)

)(

(

)

(

REF

OUT

CROSS

COMP

(5)

The zero produced by RCOMP and CCOMP is

COMP

ZERO

(6)

At the crossover frequency, Equation 4 can be shown as

CROSS

ZERO

CROSS

COMP

CROSS

COMP

)

(

(7)

Combining Equations 5 and Equation 7 and solving for RCOMP

gives

)

(

)

(

REF

OUT

CROSS

ZERO

CROSS

COMP

(8)

Choose the crossover and zero frequencies as follows:

CROSS

(9)

CROSS

ZERO

(10)

Substituting Equation 2, Equation 9, and Equation 10 into

Equation 8 yields

)

(

)

(

REF

OUT

CROSS

DSON

COMP

(11)

where:

Gm is the transconductance of the error amplifer, 500 μs.

ACS is the current sense gain of 3 V/V, 6 V/V, 12 V/V or 24 V/V.

RDSON is on resistance of the low-side MOSFET.

VREF = 0.6 V

And combining Equation 6 and Equation 10 yields

CROSS

COMP

(12)

And lastly set CC2 to

COMP

≤

(13)

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