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LTC3111

3111fa

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APPLICATIONS INFORMATION

A reasonable choice is to pick the frequency of the poles,

fP, to be 50 times higher than the frequency of the zeros,

fZ, which provides a peak phase boost of approximately

60° as was assumed previously. Next, the phase boost

must be centered so that the peak phase occurs at the

targetcrossoverfrequency.Thefrequencyofthemaximum

phase boost, fCENTER, is the geometric mean of the pole

and zero frequency as:

fCENTER = fP • fZ = 50 • fZ ≅ 7• fZ

Therefore, in order to center the phase boost given a factor

of 50 separation between the pole and zero frequencies,

the zero should be located at one-seventh of the crossover

frequencyandthepolesshouldbelocatedatseventhtimes

thecrossoverfrequencyasgivenbythefollowingequation:

fZ =

40kHz

= 5.71kHz

fP = 7• fC = 7•40kHz = 280kHz

Thisplacementofthepolesandzeroswillyieldapeakphase

boost of 60° that is centered at the crossover frequency,

fC. Next, in order to produce the desired target crossover

frequency, the gain of the compensation network at the

point of maximum phase boost, GCENTER, must be set to

–13.5dB. The gain of the compensated error amplifier at

the point of the phase gain is given by:

GCENTER =10•log

2•

π • fP

2•

π • fZ

(

)3 • R1•CFB

(













Assuming a multiple of 50 separation between the pole

and zero frequencies this can be simplified to the follow-

ing expression:

GCENTER = 20•log

2•

π • fC •R1•CFB









This equation completes the set of constraints needed to

determine the compensation component values. Specifi-

cally, the two zeros, fZERO1 and fZERO2, should be located

near 5.71kHz. The two poles, fPOLE2 and fPOLE3, should be

located near 280kHz and the gain should be set to provide

a gain at the crossover frequency of GCENTER = –13.5dB.

The first step in defining the compensation component

values is to pick a value for R1 that provides an acceptably

low quiescent current through the resistor divider. A value

of R1 = 1MΩ is a reasonable choice. Next, the value of CFB

can be found in order to set the error amplifier gain at the

crossover frequency to –13.5dB as follows:

GCENTER = –13.5dB= 20•log

2•

π •40kHz •1MΩ•CFB













CFB =

2•

π •40kHz •1MΩ•10

–

13.5

≅ 1000pF

The compensation poles can be set at 280kHz and the

zeros at 5.71kHz by using the expressions for the pole and

zero frequencies given in the previous sections. Setting

the frequency of the first zero, fZERO1, to 5.71kHz results

in the following value for RFB:

RFB =

2•

π •5.71kHz•1000pF

≅ 28.0kΩ

This leaves the free parameter, CPOLE, to set frequency

fPOLE1 to the common pole frequency of 280kHz as given:

CPOLE =

2•

π •280kHz •28kΩ

≅ 22pF

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