ISL8023AIRTAJZ-T7A Intersil, ISL8023AIRTAJZ-T7A Datasheet - Page 17

• Manufacturer Part Number: ISL8023AIRTAJZ-T7A
• Description: ISL8023 Series 2.7 - 5.5 V 3 A 4 Mhz Buck Regulator - TQFN-16
• Manufacturer: Intersil

Loop Compensation Design
When there is an external resistor connected from FS to SGND,
the 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 42 shows the small signal model of the synchronous buck
regulator.
PWM Comparator Gain F
The PWM comparator gain F
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
H
S
m
e
n
FIGURE 42. SMALL SIGNAL MODEL OF SYNCHRONOUS BUCK
( )
+
+
S
=
=
V
^
i
in
^
in
R
=
---------------- -
v ˆ
comp
t
t
n
e
V
---------------------
S
------ -
ω
d ˆ
is trans-resistance, which is the gain of the current
in
2
2
n
and ω
is the slew rate of the slope compensation and S
L
+
–
P
-------------- -
ω
=
V
I L
I
REGULATOR
n
d
o
S
^
------------------------------- -
(
Fm
Fm
Q
n
+
S
n
are given by
e
1:D
1:D
d
^
+
+
1
1
S
n
V
)T
in
d
He(S)
He(S)
s
^
m
17
^
L i
for peak current mode control is
Q
T
i
(S)
n
m
=
L
L
v
^
P
comp
–
:
2
-- -
π
,
R T
ω
n
-Av(S)
-Av(S)
R
=
LP
πf
s
e
(S):
ISL8023, ISL8024
Rc
Co
T v (S)
T (S)
o v
Ro
o
^
(EQ. 6)
(EQ. 5)
n
(EQ. 7)
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
v
v
1
2
i
v
( )
( )
( )
( )
( )
( )
S
S
S
S
S
S
=
=
=
=
=
=
K
ω
V
---------- -
ω
R
V
z
KF
----------------------- -
1
v ˆ o
----- -
I ˆ
----
d ˆ
FB
=
d ˆ
esr
o
t
o
T
F
+
=
v
=
m
V
---------- -
m
T
R
------------------------ -
=
V
( )
-------------- -
R
FB
=
F
S
i
F
o
o
------------------------ -
R
( )
V
o
1
S
2
1
+
R
-------------- - Q
R
o
C
,
( )A
in
( )H
V
S
R
S
t
c
+
o
1
-------------------------------------- -
S
------ -
ω
V
C
i
in
LP
1
2
(S)>>1, then Equation 12 can be simplified as
R
i
.
(S) is expressed as Equation 10:
2
2
o
FB
(S) from control to output voltage is:
(S) from control to inductor current is given
o
LP
v
1
+
,
e
1
--------------------- -
( )
1
( )
+
S
-------------- -
ω
+
S
is the feedback voltage of the voltage
p
+
----------- -
ω
o
-------------------------------------- -
S
------ -
ω
----------- -
ω
S
≈
Q
------ -
ω
S
esr
2
2
o
S
esr
S
R
p
p
+
o
1
+
-------------- -
ω
---------------- ω
H
A
+
1
o
v
C
------ - ω
e
L
S
------
ω
( )
Q
( )
S
P
o
S
S
z
p
ω
,
+
,
p
1
o
p
before the half switching
=
≈
------------------ -
-------------- -
R
L
o
1
P
1
C
C
o
o
May 17, 2012
FN7812.2
(EQ. 11)
(EQ. 12)
(EQ. 13)
(EQ. 10)
(EQ. 8)
(EQ. 9)