A8650 datasheet(23/31 Pages) ALLEGRO

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Low Input Voltage, Adjustable Frequency

2 A Synchronous Buck Regulator with EN/SYNC and Power OK

A8650

Allegro MicroSystems, LLC

115 Northeast Cutoff

Worcester, Massachusetts 01615-0036 U.S.A.

1.508.853.5000; www.allegromicro.com

typical for a design using ceramic output capacitors). Note, there

is more than 90° of total phase shift because of the double-pole at

half the switching frequency.

Next, consider the feedback resistor divider, (RFB1 and RFB2), the

error amplifier (gm), and the compensation network RZ CZ CP.

It greatly simplifies the transfer function derivation if RO>>RZ,

and CZ >> CP. In most cases, RO > 2 MΩ, 1 kΩ < RZ < 100 kΩ,

220 pF < CZ < 47 nF, and CP < 50 pF, so the following equations

are very accurate.

The low frequency gain of the control section (GC(0Hz)) is formed

by the feedback resistor divider and the error amplifier. It can be

calculated as:

GC(0Hz)

RFB2

RFB1+RFB2

VFB

VOUT

VFB

VOUT

AVOL

(24)

where

VOUT is the output voltage,

VFB is the reference voltage (0.8 V),

gm is the error amplifier transconductance (750 µA/V), and

RO is the error amplifier output impedance (AVOL/gm).

The transfer function of the Type-II compensated error amplifier

has a (very) low frequency pole (fP2) dominated by the output

error amplifier output impedance (RO) and the CZ compensation

capacitor:

fP2

2�

(25)

The transfer function of the Type-II compensated error amplifier

also has frequency zero (fZ2) dominated by the RZ resistor and

the CZ capacitor:

fZ2

2�

(26)

Lastly, the transfer function of the Type-II compensated error

amplifier has a (very) high frequency pole (fP3) dominated by the

RZ resistor and the CP capacitor:

fP3

2�

(27)

A Bode plot of the error amplifier and its compensation net-

work is shown in figure 14, fP2, fP3, and fZ2 are indicated on the

magnitude plot. Notice that the zero (fZ2 at 16 kHz) has been

placed so that it is just above the pole at fP1 previously shown in

the control-to-output Bode plot at 8.8 kHz, figure 13. Placing fZ2

just above fP1 will result in excellent phase margin, but relatively

slow transient recovery time, as will be shown later.

-20

-40

-60

-80

180

-90

-180

101

107

106

105

104

103

102

Frequency (Hz)

Double Pole at

1 MHz

fP1 = 8.8 kHz

fZ1 = 4 MHz

GCO(0Hz)= 12 dB

-20

-40

180

135

101

107

106

105

104

103

102

Frequency (Hz)

fZ2 = 16 kHz

fP2 = 45 Hz

fP3 ≈1.1MHz

GC(0Hz) = 58 dB

Figure 13. Control-to-Output Bode plot

Figure 14. Type-II compensated error amplifier Bode plot

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