ISL6253 datasheet(18/22 Pages) INTERSIL

18 / 22 page

PWM Comparator Gain Fm

The PWM comparator gain Fm for peak current mode

control is given by:

where VPWM is the peak-peak voltage of the PWM ramp

signal.

Current Sampling Transfer Function He(S)

In current loop, the current signal is sampled every switching

cycle. It has the following transfer function:

where Qn and ωn are given by

respectively.

Power Stage Transfer Functions

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

Where

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

Current loop gain Ti(S) is expressed as the following

equation:

where RT is the trans-resistance in current loop. RT is

usually equal to the product of the current sensing resistance

of the current amplifier. For ISL6253, RT = 24R1.

The voltage gain with open current loop is:

where

, VFB is the feedback voltage of the voltage

error amplifier.

The Voltage loop gain with current loop closed is given by:

If Ti(S)>>1, then the above equation can be simplified as

follows:

Where RTV is the trans-resistance due to the current

information fed into the voltage loop. From the above

equation, it is shown that the system is a single order

system, which has a single pole located at

before the

half switching frequency. Therefore, a simple type II

compensator can be easily used to stabilize the system.

Figure 20 shows the type II compensator, and its transfer

function is expressed as follows:

dˆ

vˆcomp

-----------------

VPWM

-----------------

(EQ. 18)

He S

()

-------

nQn

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

(EQ. 19)

---

–

πf

F1 S

()

vˆo

dˆ

------

Vin

esr

------------

-------

oQp

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

---------------------------------------

(EQ. 20)

esr

RcCo

---------------

Qp Ro

-------

LCo

---------------

≈

F2 S

()

iˆo

dˆ

----

Vin

Ro RL

---------------------

------

-------

oQp

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

--------------------------------------- where

RoCo

---------------

≈

(EQ. 21)

Ti S

()

RTFmF2

()H

e S

()

(EQ. 22)

Tv S

()

KFmF1 S

()A

v S

()

(EQ. 23)

VFB

-----------

Lv S

()

Tv S

()

1Ti S

()

------------------------

(EQ. 24)

Lv S

()

VFB

-----------

Ro RL

RTV

---------------------

esr

------------

-------

----------------------

Av S

()

He S

()

----------------

RoCo

---------------

≈

(EQ. 25)

FIGURE 19. SMALL SIGNAL MODEL OF SYNCHRONOUS

BUCK REGULATOR

iin

1:D

-Av(S)

He(S)

vin

ILd

Vcomp

Tv(S)

Ti(S)

Vind

REF

COMP

REF

COMP

FIGURE 20. TYPE II COMPENSATOR

ISL6253

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