ISL78229 Datasheet, PDF (67/71 Pages) Intersil Corporation – 2-Phase Boost Controller with Drivers

ISL78229
9UHI ^
䏓9IE

9IE
(UURU$PS
+HV
䏓9F
&XUUHQWPRGHFRQWURO
3RZHU6WDJH
*YFYRV
.IE
䏓9R
FIGURE 75. 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 42.
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. 42)
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,
R_LOAD is the load resistance, L_eq is the equivalent inductance
for multiphase boost with N number of phases, L is the
inductance on each phase.
L_eq = _N-^L--
• K_ISEN is the current sense gain as shown in Equation 43,
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 32.
K_ISEN = ^R-----^S----^E-_R---^N-_S---^x-_E---^-_T--⁶--_x--⁵---⁰---⁰--
(EQ. 43)
• Se/Sn is gain of the selected compensating slope over the
sensed inductor current up-ramp. It can be calculated in
Equation 44, where K_SLOPE is the gain of selected
compensating slope over the sensed I_L down slope (refer to
Equation 15 on page 33).
SS_-----en-
=
K_SLOPE




V_{----V-O---I-U-N---T--}
–
1

(EQ. 44)
Equation 42 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.
COMPENSATOR DESIGN
Generally simple Type-2 compensator can be used to stabilize
the system. In the actual application, however, an extra phase
margin will be provided by a Type-3 compensator.
Vo
R1
RFB2
C1
RFB1
He1(s)
FB
+
Gm
-
Vc
COMP
Vref
RCP
CCP1
CCP2
ROEA
He2(s)
FIGURE 76. TYPE-3 COMPENSATOR
The transfer function at the error amplifier and its compensation
network will be expressed as Equation 45.
H_e2s = _V--^V---_F-^C--_B-- = g_m  Z_COMP =
(EQ. 45)
gm ₁-----+-----_s----_--_R-----_C----_P-----_C----_C-----_P-----₁-----+-----_R----_O-----_E-----^_A--¹--_---_C^+----_C-^s---^R-_P----^C-₁----^P-+---^C-_C----^C-_C----^P-_P---¹-₂---^-_--^R_----+^O-----_CE----_C-^A----_P-----₂----_C----_C-----_P-----₁---_R-----_C-----_P----_R-----_O-----_E-----_A-----_S----₂--
Submit Document Feedback ₆₇
FN8656.3
February 12, 2016