ISL6253 데이터 시트보기 (PDF) - Intersil
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ISL6253 Datasheet PDF : 22 Pages
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ISL6253
PWM Comparator Gain Fm
The PWM comparator gain Fm for peak current mode
control is given by:
Fm
=
-vˆ---c---od-ˆ--m-----p-
=
--------1---------
VPWM
(EQ. 18)
where VPWM is the peak-peak voltage of the PWM ramp
signal.
Current Sampling Transfer Function He(S)
In current loop, the current signal is sampled every switching
cycle. It has the following transfer function:
He(S)
=
-S----2- + ------S-------- + 1
ωn2 ωnQn
(EQ. 19)
where Qn and ωn are given by
Qn
=
– 2-- ,
π
ωn
=
πfs
,
respectively.
Power Stage Transfer Functions
Transfer function F1(S) from control to output voltage is:
F1(S)
=
-vˆ-d-ˆ-o-
=
1 + -----S------
Vi
n
-------------------ω----e----s---r--------
-S----2- + ------S-------- + 1
ωo2 ωoQp
(EQ. 20)
Where
ωesr
=
------1--------,
RcCo
Qp
≈
Ro
-C----o- ,
L
ωo
=
-------1-------
LCo
Transfer function F2(S) from control to inductor current is,
F2(S) = ˆi-d-ˆo- = R-----o--V--+--i--n-R-----L-
1 + --S----
----------------------ω----z------------
-S----2- + ------S-------- + 1
where
ωz
≈
-------1-------
RoCo
(EQ. 21)
ωo2 ωoQp
Current loop gain Ti(S) is expressed as the following
equation:
Ti(S) = RTFmF2(S)He(S)
(EQ. 22)
where RT is the trans-resistance in current loop. RT is
usually equal to the product of the current sensing resistance
of the current amplifier. For ISL6253, RT = 24R1.
The voltage gain with open current loop is:
Tv(S) = KFmF1(S)Av(S)
(EQ. 23)
where
K
=
V-----F---B--
Vo
,
VFB
is
the
feedback
voltage
of
the
voltage
error amplifier.
The Voltage loop gain with current loop closed is given by:
Lv(S) = 1-----T+----v-T--(--Si--(--S)-----)
(EQ. 24)
If Ti(S)>>1, then the above equation can be simplified as
follows:
Lv(S)
=
-V----F---B--
Vo
R-----o-----+----R-----L-
RTV
-1----+-----ω----------Se------s------r
1 + --S----
H-A----ve---((---SS----)-),
ωp
≈
-------1-------
RoCo
ωp
(EQ. 25)
Where RTV is the trans-resistance due to the current
information fed into the voltage loop. From the above
equation, it is shown that the system is a single order
system, which has a single pole located at ωp before the
half switching frequency. Therefore, a simple type II
compensator can be easily used to stabilize the system.
Figure 20 shows the type II compensator, and its transfer
function is expressed as follows:
i^in
v^in
+
i^L L
+
ILd^ 1:D
Vind^
RT
V^o
Rc
Ro
Co
Ti(S)
d^
K
Fm
+
He(S)
Tv(S)
V^comp -Av(S)
FIGURE 19. SMALL SIGNAL MODEL OF SYNCHRONOUS
BUCK REGULATOR
Vo
VFB
VREF
-
gm
+
VCOMP
R1
C2
C1
FIGURE 20. TYPE II COMPENSATOR
18
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