ISL78227 Datasheet, PDF (39/43 Pages) Intersil Corporation – 2-Phase Boost Controller with Integrated Drivers

ISL78227
Vo
RFB2
RFB1
R1
C1
Vfb
FB
+
Gm
-
VREF
He1(s)
Slope
+
Gm
-
COMP
+
Vc
-
RCP
CCP1
ROEA
CCP2
He2(s)
VIN
RSEN
L
Gvcvo(s)
Resr
COUT
VOUT
RL
FIGURE 64. CONCEPTUAL BLOCK DIAGRAM OF PEAK CURRENT MODE CONTROLLED BOOST REGULATOR
9UHI ^
䏓9IE

9IE
(UURU$PS
+HV
䏓9F
&XUUHQWPRGHFRQWURO
3RZHU6WDJH
*YFYRV
䏓9R
R_LOAD is the load resistance, L_eq is the equivalent inductance
for multiphase boost with N number of phases, L is each
phase’s inductor’s inductance.
L_eq = _N-^L--
.IE
FIGURE 65. CONCEPTUAL CONTROL BLOCK DIAGRAM
TRANSFER FUNCTION FROM V_C TO V_OUT
Transfer function from error amplifier output V_C to output voltage
V_OUT G_vcvo(s) can be expressed as Equation 33.
G_vcvos = K_DC  -_--₁-----+-----^{}_------¹_--s-p------+-_{1----}-^------_^----es--_^----s--₁^----r--^-+---^--_Q---^------¹_p--------_s--–_------_--^{---------}_n^{-----R----s--+--H--------}_^Z------_{}----_s----_n----_---₂---_-
(EQ. 33)
The expressions of the poles and zeros are listed below:
K_DC = ^R-----^L---^O-----^A_K----^DI--_S---^-_E--^--_N-¹----–-----^D-----^
_RHZ = ^R-----^L---^O-----^A----^D--_L---^_e---^-_q--¹----–-----^D-----^--²-
_esr = -_C----_O-----_U----_T--¹--_---_R-----_e---_s----_r
_pPS = _C-----_O-----_U----_T----_-²--_R-----_L---_O-----_A----_D--
Q_p
=
---------------------------------¹-----------------------------------
  1 – D  ^SS-----^en- + 0.5 + D
_n = -_f-_s-²--_w---
Where,
• N is the number of phases, R_ESR is the output capacitor’s
Equivalent Series Resistance (ESR) of the total capacitors,
• K_ISEN is the current sense gain as shown in Equation 34,
where R_SENx and R_SETx are per phase current sense resistor
and setting resistors described in “Current Sense for Individual
Phase - ISENX” on page 31.
K_ISEN = ^R-----^S----^E-_R---^N-_S---^x-_E---^-_T--⁶--_x--⁵---⁰---⁰--
(EQ. 34)
• Se/Sn is gain of the selected compensating slope over the
sensed inductor current up-ramp. It can be calculated in
Equation 36, where K_SLOPE is the gain of selected
compensating slope over the sensed IL down slope (refer to
Equation 15 on page 32).
SS_-----en-
=
K_S
LO
P
E




V_{----V-O---I-U-N---T--}
–
1

(EQ. 35)
Equation 33 shows that the system is mainly a single order
system plus a Right Half Zero (RHZ), which commonly exists for
boost converter. The main pole ω_pPS is determined by load and
output capacitance and the ESR zero ω_ESR is the same as buck
converter.
Since the ω_RHZ changes with load, typically the boost converter
crossover frequency is set 1/5 to 1/3 of the ω_RHZ frequency.
The double pole ω_n is at half of the f_SW and has minimum
effects at crossover frequency for most of the cases when the
crossover frequency is fairly low.
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FN8808.2
February 24, 2016