FN8808 datasheet(39/44 Pages) RENESAS

39 / 44 page

ISL78227

FN8808 Rev.6.02

Page 39 of 43

Feb 28, 2025

TRANSFER FUNCTION FROM VC TO VOUT

Transfer function from error amplifier output VC to output voltage

VOUT Gvcvo(s) can be expressed as Equation 33.

The expressions of the poles and zeros are listed below:

where:

• N is the number of phases, RESR is the output capacitor’s

Equivalent Series Resistance (ESR) of the total capacitors,

RLOAD is the load resistance, Leq is the equivalent inductance

for multiphase boost with N number of phases, and L is each

phase’s inductor’s inductance.

• KISEN is the current sense gain as shown in Equation 34,

where RSENx and RSETx are per-phase current sense resistors

and setting resistors described in “Current Sense for Individual

Phase - ISENX” on page 31.

• Se/Sn is the gain of the selected compensating slope over the

sensed inductor current up-ramp. It can be calculated in

Equation 35, where KSLOPE is the gain of selected

compensating slope over the sensed IL down slope (refer to

Equation 15 on page 32).

Equation 33 shows that the system is mainly a single order

system plus a Right Half Zero (RHZ), which commonly exists for

boost converters. The main pole ωpPS is determined by load and

output capacitance and the ESR zero ωESR is the same as the

buck converter.

Because the ωRHZ changes with load, typically the boost

converter crossover frequency is set 1/5 to 1/3 of the ωRHZ

frequency.

The double pole ωn is at half of the fSW and has minimum

effects at crossover frequency for most of the cases when the

crossover frequency is fairly low.

FIGURE 64. CONCEPTUAL BLOCK DIAGRAM OF PEAK CURRENT MODE CONTROLLED BOOST REGULATOR

VREF

VOUT

RCP

CCP2

COMP

RFB2

RFB1

CCP1

ROEA

SLOPE

VIN

RSEN

VOUT

RLOAD

Resr

COUT

Gvcvo(s)

He2(s)

He1(s)

Vfb

RSET

FIGURE 65. CONCEPTUAL CONTROL BLOCK DIAGRAM

Gvcvo(s)

CURRENT MODE

CONTROL +POWER STAGE

He2(s)

ERROR AMP

VOUT

Vfb

He1(s)

VREF

Vfb



Gvcvo s

 

KDC

esr

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









RHZ

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

–











pPS

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









Qp n



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

n

-------







 2















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



(EQ. 33)

KDC

RLOAD 1 D

–







2 K

 ISEN

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

RHZ

RLOAD 1 D

–



2



Leq

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

esr

COUT Resr



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

pPS

COUT RLOAD



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



1 D

–





-------



0.5 D

–



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

n  fSW



Leq LN----

KISEN

RSENx 6500



N R

 SETx

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

(EQ. 34)

(EQ. 35)

-------

KSLOPE

VOUT

VIN

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

–















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