ADP2114ACPZ-R7 datasheet(29/40 Pages) AD

29 / 40 page

ADP2114

Rev. 0 | Page 29 of 40

The control loop can be broken down into the following three

sections:

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

function is unity. This yields Equation 16 for the compensation

network impedance at the crossover frequency.

•

VOUT to VCOMP

REF

OUT

CROSS

COMP

)

(

(16)

•

VCOMP to IL

•

IL to VOUT

Correspondingly, there are three transfer functions:

(s)

COMP

OUT

REF

OUT

COMP

(10)

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 Equation 17.

COMP

(s)

(11)

CROSS

COMP

ZERO

≈

(17)

(s)

FILT

OUT

(12)

Solving Equation 16 and Equation 17 simultaneously yields the

value for the compensation resistor and compensation

capacitor, as shown in Equation 18 and Equation 19.

where:

gm is the transconductance of the error amplifier, 550 μs.

GCS is the current sense gain, 4 A/V.

VOUT is the output voltage of the converter.

VREF is the internal reference voltage of 0.6 V.

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

forms a pole at origin and a zero as expressed in Equation 13.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

REF

OUT

CROSS

COMP

)

(

(18)

COMP

ZERO

COMP

(19)

COMP

(s)

= 1

(13)

The capacitor CC2 (as shown in Figure 77) forms a pole with the

compensation resistor, RCOMP, in the feedback loop to ensure

that the loop gain keeps rolling off well beyond the unity-gain

crossover frequency. The value of CC2, if used, is typically set to

1/40 of the compensation capacitor, CCOMP.

ZFILT

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

OUT

LOAD

FILT

(s)

(14)

where s is angular frequency that can be written as s = 2πf.

The overall loop gain, H(s), is obtained by multiplying the three

transfer functions previously mentioned as follows:

H(s)

= gM × GCS ×

OUT

REF

× ZCOMP(s) × ZFILT(s)

(15)

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

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

the unity crossover frequency of 1/12 (approximately) the

switching frequency can be targeted.

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