ISL8023 INTERSIL [Intersil Corporation], ISL8023 Datasheet - Page 16

• Manufacturer Part Number: ISL8023
• Description: 3A/4A Low Quiescent Current High Efficiency Synchronous Buck Regulator
• Manufacturer: INTERSIL [Intersil Corporation]

Loop Compensation Design
When there is an external resistor connected from FS to SGND,
COMP pin is active for external loop compensation. The ISL8023,
ISL8024 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 as a state variable since its peak
current is constant, and the system becomes single order
system. It is much easier to design a type II compensator to
stabilize the loop than to implement voltage mode control. Peak
current mode control has inherent input voltage feed-forward
function to achieve good line regulation. Figure 39 shows the
small signal model of the synchronous buck regulator.
PWM Comparator Gain F
The PWM comparator gain Fm for peak current mode control is
given by Equation 5:
Where, S
given by Equation 6
where, R
amplifier.
CURRENT SAMPLING TRANSFER FUNCTION H
In current loop, the current signal is sampled every switching
cycle. It has the following transfer function in Equation 7:
where, Q
F
S
H
m
n
e
FIGURE 41. SMALL SIGNAL MODEL OF SYNCHRONOUS BUCK
S ( )
=
+
+
=
V
^
i
in
R
=
^
in
--------------- -
v ˆ
comp
t
V
------------------- -
S
------ -
ω
d ˆ
t
n
e
in
2
2
n
is trans-resistance, which is the gain of the current
L
and ω
is the slew rate of the slope compensation and S
–
+
P
V
------------- -
ω
=
I L
I
o
n
REGULATOR
S
d
----------------------------- -
(
^
Q
Fm
Fm
S
n
+
n
e
are given by
1:D
1:D
d
+
^
+
1
1
S
n
V
)T
in
s
d
He(S)
He(S)
^
16
^
L i
T i (S)
T i (S)
Q
m
L
L
v
^
n
P
comp
:
=
–
R T
R T
2
-- -
π
,
-Av(S)
-Av(S)
ω
R
n
LP
=
πf
e
(S):
s
ISL8023, ISL8024
Rc
Rc
Co
T v (S)
T (S)
o v
Ro
o
^
(EQ. 5)
(EQ. 6)
(EQ. 7)
n
K
K
is
Power Stage Transfer Functions
Transfer function F
Where,
Transfer function F
by Equation 9:
where
Current loop gain T
The voltage loop gain with open current loop is Equation 11:
The Voltage loop gain with current loop closed is given by
Equation 12:
Where,
error amplifier. If T
Equation 13:
Equation 13 shows that the system is a single order system,
which has a single pole located at
frequency. Therefore, a simple type II compensator can be easily
used to stabilize the system.
F
F
T
T
L
L
i
v
1
2
v
v
S ( )
S ( )
S ( )
S ( )
S ( )
S ( )
=
=
=
=
=
=
V
-------- -
K
ω
R
V
KF
ω
---------------------- -
1
I ˆ
v ˆ o
----- -
--- -
FB
d ˆ
d ˆ
o
z
t
o
esr
T
=
F
+
m
=
v
m
R
---------------------- -
=
T
=
S ( )
V
-------- -
F
o
i
V
F
-------------
R
=
S ( )
FB
---------------------- -
R
1
+
V
2
o
R
o
o
1
S ( )A
in
S ( )H
R
t
------------ - Q
R
C
,
V
+
------------------------------------- -
------ -
ω
c
o
LP
S
1
in
V
R
C
i
1
2
2
2
o
(S)>>1, then Equation 12 can be simplified as
i
FB
(S) is expressed as Equation 10:
v
o
1
--------------------- -
LP
(S) from control to output voltage is:
(S) from control to inductor current is given
e
1
.
+
S ( )
1
,
S ( )
+
+
------------- -
ω
+
p
----------- -
ω
------------------------------------- -
------ -
ω
S
----------- -
ω
o
is the feedback voltage of the voltage
------ -
ω
S
≈
S
esr
S
Q
2
2
o
S
esr
p
R
p
+
1
o
-------------- - ω
H
A
+
------------- -
ω
+
v
e
1
o
C
----- - ω
L
S ( )
S
S ( )
----- -
ω
Q
P
o
S
z
p
,
,
+
ω
1
o
p
p
=
≈
before the half switching
---------------- -
-------------
R
L
o
1
1
P
C
o
C
o
December 22, 2011
FN7812.0
(EQ. 11)
(EQ. 12)
(EQ. 13)
(EQ. 10)
(EQ. 8)
(EQ. 9)