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CONSUMER ELECTRONICS

Frequency

Compensation in Switching

Regulator Design

lti f t i

 Part 2: Feedback path compensation

By Nigel Smith, Business Development Manager, Portable Power, Texas Instruments

In part one of this two-part series, the forward path of a switching converter was considered. In this

 second and nal part, the feedback path is considered as the loop is closed and the overall circuit is

compensated.

Oth i d h Th t f ti h

SWITCHING REGULATORS

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res lting freq enc response contains

Once the gain and phase re Three t pes of compensation scheme

SWITCHING REGULATORS

Power Systems Design Europe October 2007 34 35www.powersystemsdesign.com

SWITCHING REGULATORS

•Placethecompensationcircuit’s

zero(s)approximatelyoneoctavebelow

the output lter’s break frequency, and

calculate the value of K 1.Thisapproach

is relatively conservative, but avoids

the possibility of conditional stability by

ensuringthatphasestayswellabove0°

belowf c.

•Determinethenecessaryerror

amplier gain at f c and calculate the re-

quired error amplier gain at the zero(s).

•Calculatethemaximumphaselag

through the compensation circuit and,

using Table 2 or 3, and calculate the

minimum value of K  2achievingthis

phase lag. Calculate the frequency of

thecompensationcircuit’spole(s)

using.

• Calculat e the individual compo-

nentvaluesinthecompensationcircuit

required to achieve this response.

Figure 2 shows typical Bode plots for

the forward path, error amplier and

overall response of switching converter

usingType-IIIcompensation.

Each engineer has his own preferred

approach toward frequency compen-

sation, and in practice some iteration

will usually be necessary, however, the

approach described above provides a

good starting point f or inexperienced

engineers to build a stable circuit with

adequate performance.

 A general procedure for compensat-

ingaswitchingconvertercannowbe

simplied to the following:

• Generate the forward-path Bode

plots.

• Select a suitable cross-over fre-

quency. Use the rule-of-thumb that f c

should lie somewhere between one

tenth and one sixth the switching fre-

quency, but may need to be reduced if

the error amplier’s open-loop gain at

this frequency is insufcient. Determine

the forward-path gain and phase at the

crossover frequency.

• From the slope of the forward-path

gainatf c, determine whether Type-II or

Type-III compensation is required. If the

forward path slope at f c is -20dB/de-

cade, then Type-II compensation should

be used; if the slope is -40dB/decade,

thenType-IIIisnecessary.

high frequencies and a

slope of +20dB/decade

in the middle of the fre-

quency range of interest.

Type-IIIcompensationis

typically used to com-

pensatecircuitswhere

the output lter exhibits a

double-pole at the

cross-over frequency.This is done by ensuring

thatcross-overoccurs

midway up the error

amplier’s +20dB/decade

slope; the combined ef-

fect of the error amplier

and output lter slopes

is the desired -20dB/de-

cade response.

Therelativeposition

of the poles and zeros in

thecompensationcircuit

determines the overall

phaseboostoccurring

atf c. Thus, by placing

the poles and zeros at

suitable frequencies, the

desired phase margin can

be achieved. There are

a number of ways to ap-

proachthis.Onewayisto

consider the position of

the low frequency zero(s)

and high frequency

pole(s) using two factors

K 1 and K  2, as follows:

By considering the rela-

tive values of K 1 and K  2,

thephaseboostat f ccaneasily be determined from

Tables 1 and 2.

The gain of a Type-II

compensationcircuitat f c

is equal to the gain AV at

thezero.Type-IIIcom-

pensationhasagainin

dB at f c given by:

G = AV1 + 20log(K 1 )

whereA V1 is the gain at the second zero

in dB.

Type-IIIcompensationcontainstwo

zeros and two poles in addition to a pole

attheorigin.Theresultingresponse

contains an area of increased gain at

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Table 1. Phase Change through a Type-II Compensation Circuit.

Table 2. Phase Change through a Type-III Compensation Circuit.

Figure 2. System Bode Plots.