ISL85403EVAL2Z datasheet(20/25 Pages) RENESAS

20 / 25 page

ISL85403

FN8631 Rev.4.00

Page 20 of 24

Sep 28, 2020

Loop Compensation Design -

Buck

The ISL85403 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 a state variable

because its peak current is constant and the system becomes a

single order system. It is much easier to design the compensator

to stabilize the loop compared with voltage mode control. Peak

current mode control has an inherent input voltage feed-forward

function to achieve good line regulation. Figure 32 shows the

small signal model of a buck regulator.

PWM Comparator Gain Fm

The PWM comparator gain, Fm, for peak current mode control is

given by Equation 20:

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

given by Equation 21:

where Rt is the gain of the current amplifier.

Current Sampling Transfer Function He(S)

In a current loop, the current signal is sampled every switching

cycle. It has the following transfer function in Equation 22:

where Qn and n are given by

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 given

by Equation 24:

where

Current loop gain Ti(S) is expressed as Equation 25:

The voltage loop gain with open current loop is expressed in

Equation 26:

The Voltage loop gain with current loop closed is given by

Equation 27:

If Ti(S)>>1, then Equation 27 can be simplified as Equation 28:

Equation 28 shows that the system is a single order system.

Therefore, a simple type II compensator can be easily used to

stabilize the system. A type III compensator is needed to expand

the bandwidth for current mode control in some cases.

A compensator with two zeros and one pole is recommended for

this part, as shown in Figure 33.

Vin

1:D

-Av(S)

comp

He(S)

Ti(S)

(S)

Tv(S)

1:D

-Av(S)

He(S)

T(S)

FIGURE 32. SMALL SIGNAL MODEL OF BUCK REGULATOR

RLP

dˆ

vˆcomp

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

Se Sn

T

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

(EQ. 20)

Vin Vo

–

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

(EQ. 21)

He S

 S



-------



nQn

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

(EQ. 22)



---

–



f



FIGURE 33. TYPE III COMPENSATOR

F1 S



vˆo

dˆ

------

Vin



esr

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



-------



oQp

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

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

(EQ. 23)



esr

RcCo

--------------- Qp Ro

-------



LPCo

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



F2 S



Iˆo

dˆ

----

Vin

Ro RLP

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



------



-------



oQp

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

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

(EQ. 24)



RoCo

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

Ti S



RtFmF2 S

H

e S



(EQ. 25)

Tv S



KFmF1 S

A

v S



(EQ. 26)

Lv S



Tv S



1Ti S



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

(EQ. 27)

Lv S



Ro RLP

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



esr

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



-------

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

Av S



He S



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



RoCo

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



(EQ. 28)

RBIAS

VCOMP

VREF

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