ISL78268 Datasheet, PDF (30/33 Pages) Intersil Corporation – Integrated 2A sourcing

ISL78268
INTERNAL CURRENT LOOP TRANSFER FUNCTIONS
Transfer function from control to inductor current (G_i(s)) is given
by Equation 28.
G_iS
=
---^V---^I--^N-----
R_OUT



1
+
-_--^s--_o-_
 -------------------------¹---------------------------
1
+
---------^s----------
Q_p  _n
+


-_--^s--_n-_
2
(EQ. 28)
Where,
_o
=
---------------¹----------------
C_OUT  R_OUT
Q_p  R_OUT 
C_{----O----U----T}
L
_n
=
-----------¹-------------
L  C_OUT
PWM COMPARATOR GAIN Fm
The PWM comparator gain Fm for peak current mode control is
given by Equation 29.
Fm
=
-------^D---------
V_ramp
=
-_--_m-----_a-----+-----_m1-----_S---_L----_---_---_T-
(EQ. 29)
Where m_SL is the slew rate of the slope compensation and m_a is
the inductor current slew rate while high-side MOSFET is on and
given as Equation 30.
m_a
=
R_S

V_----I_--N_{------–----}V_{----O---U----T-}
L
(EQ. 30
Where R_S is the gain of the current sense amplifier.
TOTAL V_ramp
V_c
m_SL+m_a
V_ramp
CONVERTED H/S
INDUCTOR CURRENT
mmb_a
SLOPE COMPENSATION
ADDER
t_on
t_off
m_SL
T
FIGURE 51. CONVERTED SENSE CURRENT WAVEFORM
TOTAL TRANSFER FUNCTION FROM PWM
COMPARATOR TO POWER STAGE
The total transfer function from PWM to power stage including
internal current sense loop is expressed as Equation 31
(assuming F_m*G_i(s)*R_S>>1).
G_{Ts}
=
1^------+----F^----_m^------^F---G^m----_i^--^--s^---^----^---R^----_s^-

G_vs






-^R----^o---^u---^t
R_s


-¹--₁---+--+----^----_------^e_-ss------_o^---s------r_{}
(EQ. 31)
Equation 31 shows that the system is a single order system.
Therefore, a 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
RFB1
RFB0
R1
C1
He1
FB
+
Gm
-
Vref
COMP
RCMP1
CCMP1
CCMP2
ROEA
He2
FIGURE 52. TYPE-3 COMPENSATOR
COMPENSATOR DESIGN
The transfer function at error amplifier and its compensation
network will be expressed as Equation 32.
H_e2s
=
v_{---C----O----M----P--}
v_FB
=
g_m  Z_COMP
=
(EQ. 32)
gm
--------------------------------------------------------------------------^--¹-----+-----^s---^R----^C----^M------^P----^C---^C----^M------^P----¹----^--^R----^O----^E----^A---------------------------------------------------------------------------
1
+
s
RC
MP
CCM
P
1
+
REO
A

CCM
P1
+
CC
MP
2^
+
CCMc
2CC
MP
1
R
C
MP
R
O
UT
S2
If R_OEA>>R_CMP, C_CMP1>>C_CMP2, and R_OEA = infinite, the
equation can be simplified as shown in Equation 33:
H_e2s
=
g_m  -_s----_---_C---_C----_M---¹--_P---+₁-----_^s---_-^-₁--^R---+-^C----^M_s----_^P---_R--^--_C-^C---_M-^C---^MP-----^P_---_C¹----_C---_M-----_P---₂----_
=
-^----¹-  -¹-----+------^-------^s-z-----^2----
s
1
+
----^s------
_p2
(EQ. 33)
Where,
₁
=
------^g---^m--------
C_CMP1
_z2
=
------------------¹-------------------
R_CMP  C_CMP1
_p2
=
------------------¹-------------------
R_CMP  C_CMP2
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FN8657.3
December 12, 2014