ISL8023 データシートの表示（PDF） - Intersil

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ISL8023

Compact Synchronous Buck Regulator

Intersil 

ISL8023, ISL8024

Loop Compensation Design

When there is an external resistor connected from FS to SGND,

the COMP pin is active for external loop compensation. The

ISL8023, ISL8024 uses constant frequency peak current mode

control architecture to achieve fast loop transient response. An

accurate current sensing pilot device in parallel with the upper

MOSFET is used for peak current control signal and overcurrent

protection. The inductor is not considered as a state variable

since its peak current is constant, and the system becomes

single order system. It is much easier to design a type II

compensator to stabilize the loop than to implement voltage

mode control. Peak current mode control has inherent input

voltage feed-forward function to achieve good line regulation.

Figure 42 shows the small signal model of the synchronous buck

regulator.

^iin

V^in

+

^iL LP

RLP

ILd^ 1:D Vind^

RT

vo^

Rc

Ro

Co

d^

Ti(S)

K

Fm

+

He(S)

Tv(S)

v^comp

-Av(S)

FIGURE 42. SMALL SIGNAL MODEL OF SYNCHRONOUS BUCK

REGULATOR

PWM Comparator Gain Fm:

The PWM comparator gain Fm for peak current mode control is

given by Equation 5:

Fm

=

-vˆ---c---od-ˆ--m-----p-

=

---------------1----------------

(Se + Sn)Ts

(EQ. 5)

Where Se is the slew rate of the slope compensation and Sn is

given by Equation 6:

Sn

=

Rt

V-----i-n-----–----V----o--

LP

(EQ. 6)

where Rt is trans-resistance, which is the gain of the current

amplifier.

CURRENT SAMPLING TRANSFER FUNCTION He(S):

In current loop, the current signal is sampled every switching

cycle. It has the following transfer function in Equation 7:

He(S)=

-S----2-

ωn2

+

------S--------

ωnQn

+

1

where Qn and ωn are given by Qn = –2π--, ωn= πfs

(EQ. 7)

Power Stage Transfer Functions

Transfer function F1(S) from control to output voltage is:

F1(S)

=

v-ˆ-d-ˆ-o--

=

Vi

n

---------1-----+------ω--------Se------s-------r--------

-S----2-

ωo2

+

ω-----o-S--Q-----p-

+

1

(EQ. 8)

Where

ωesr

=

------1--------

RcCo

,Qp

≈

Ro

C-----o-

LP

,ωo=

---------1---------

LPCo

Transfer function F2(S) from control to inductor current is given

by Equation 9:

F2(S) =

ˆ-Id-ˆo--

=

---------V----i--n---------

Ro + RLP

------------1-----+------ω--S------z-------------

-S----2-

ωo2

+

------S--------

ωoQp

+

1

(EQ. 9)

where

ωz

=

-------1-------

RoCo

.

Current loop gain Ti(S) is expressed as Equation 10:

Ti(S) = RtFmF2(S)He(S)

(EQ. 10)

The voltage loop gain with open current loop is Equation 11:

Tv(S) = KFmF1(S)Av(S)

(EQ. 11)

The Voltage loop gain with current loop closed is given by

Equation 12:

Lv(S)

=

-----T----v---(--S-----)----

1 + Ti(S)

(EQ. 12)

Where K

=

-V----F---B--

Vo

,

VFB

is the feedback voltage of the voltage

error amplifier. If Ti(S)>>1, then Equation 12 can be simplified as

Equation 13:

Lv(S)=

V-----F---B--

Vo

R-----o-----+----R-----L---P--

Rt

1-----+-----ω----------Se------s------r

1 + -ω-S---p-

H-A----ve---((---SS----)-)

,

ωp

≈

-------1-------

RoCo

(EQ. 13)

Equation 13 shows that the system is a single order system,

which has a single pole located at ωp before the half switching

frequency. Therefore, a simple type II compensator can be easily

used to stabilize the system.

17

FN7812.2

May 17, 2012

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