ADP1621ARMZ-R7 datasheet(17/32 Pages) AD

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ADP1621

Rev. A | Page 17 of 32

frequency occurs well below the frequency of the RHP zero. The

location of the RHP zero is determined by the following equation:

()

LOAD

RHP

−

(25)

where fZ,RHP is the RHP zero frequency, and RLOAD is the equivalent

load resistance or the output voltage divided by the load current.

To stabilize the regulator, ensure that the regulator crossover

frequency is less than or equal to one-fifth of the RHP zero

frequency and less than or equal to one-fifteenth of the switching

frequency. For an initial practical design, choose the crossover

frequency fC to be the lower of

f =

(26)

and

,RHP

f =

(27)

where fC is the crossover frequency, and fSW is the switching

frequency.

The regulator loop gain is

()

OUT

COMP

OUT

−

(28)

where AVL is the loop gain, VFB is the feedback regulation

voltage (typically 1.215 V), VOUT is the regulated output voltage,

D is the duty cycle, gm is the error amplifier transconductance

gain (typically 300 μS), ZCOMP is the impedance of the RC network

from COMP to GND, n is the current-sense amplifier gain

(typically 9.5), RCS is the current-sense resistance, and ZOUT is

the impedance of the load and output capacitor. In the case of

lossless current sensing, as shown in Figure 28, RCS is equal to the

on resistance, RDSON, of the external power MOSFET. Otherwise,

RCS represents the external current-sense resistor, as shown in

Figure 29.

To determine the crossover frequency, it is important to note

that at that frequency the compensation impedance, ZCOMP, is

dominated by Resistor RCOMP, and the output impedance, ZOUT,

is dominated by the impedance of the output capacitor, COUT.

When solving for the crossover frequency, the equation is

simplified to

()

−

OUT

COMP

OUT

(29)

where fC is the crossover frequency, RCOMP is the compensation

resistor, and COUT is the output capacitance.

Solving for RCOMP gives

()

OUT

COMP

−

(30)

Once the compensation resistor, RCOMP, is known, set the zero

formed by the resistor and compensation capacitor, CCOMP, to

one-fourth of the crossover frequency, or

COMP

(31)

Capacitor C2 is chosen to cancel the zero introduced by the output

capacitance ESR. Thus, C2 should be set to (see Figure 31)

COMP

OUT

ESR

(32)

where ESR represents the ESR of COUT.

For low ESR output capacitors, such as ceramic capacitors, C2

is small, generally in the range of 10 pF to 400 pF. Because of the

parasitic inductance, resistance, and capacitance of the PCB layout,

the RCOMP, CCOMP, and C2 values might need to be adjusted by

observing the load transient response of the ADP1621 to establish a

stable operating system and achieve optimal transient performance.

For most applications, RCOMP is in the range of 5 kΩ to 100 kΩ,

and CCOMP is in the range of 100 pF to 30 nF.

COMP

CCOMP

RCOMP

REF

Figure 31. Compensation Components

SLOPE COMPENSATION

The ADP1621 includes a circuit that allows adjustable slope

compensation. Slope compensation is required by current-

mode regulators to stabilize the current-control loop when

operating in continuous conduction and the switching duty

cycle is greater than 50%.

Slope compensation is achieved by internally forcing a ramping

current source out of the CS current-sense pin. By placing a resistor

between the CS pin and the current sensing device (the drain of

the external MOSFET in the case of lossless current sensing or

the source of the MOSFET if a current-sense resistor is used), a

voltage is developed across the resistor that is proportional to

the slope-compensation current.

To ensure stability of the current-mode control loop, use a

compensation voltage slope that is equal to or greater than one-

half of the current-sense representation of the inductor current

downslope. Therefore, it follows that

OUT

MIN

OFF,

SC,PK

−

(33)

where RS is the slope-compensation resistor, ISC,PK is the peak slope-

compensation current, fSW is the switching frequency, RCS is the

current-sense resistor, VOUT is the regulated output voltage, VD is the

forward-voltage drop of the diode, VIN is the input voltage, tOFF,MIN is

the minimum off time, and L is the power-stage inductor. In the

case of lossless current sensing, RCS is equal to the on resistance,

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