ISL6232 Datasheet, PDF (22/25 Pages) Intersil Corporation – High Efficiency System Power Supply Controller for Notebook Computers

ISL6232
Loop Compensation Design
ISL6232 uses constant frequency peak current mode control
architecture to achieve fast loop transient response. An
accurate current sensing resistor in series with the output
inductor, or DCR of the output inductor, 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 32 shows the small signal model of the synchronous
buck regulator.
^iin
V^in
+
^iL _L
ILd^ 1:D ^{Vind^}
RT
vo^
Rc
Ro
Co
d^
T _i(S)
K
Fm
+
He(S)
T _v(S)
v^comp
-Av(S)
FIGURE 32. SMALL SIGNAL MODEL OF SYNCHRONOUS
BUCK REGULATOR
PWM COMPARATOR GAIN F_M
The PWM comparator gain Fm for peak current mode
control is given by Equation 20:
F_m = _v-ˆ---_c---_o^d-ˆ--_m-----_p- = -₍--_S----_e-----+---¹-_S-----_n---₎---_T---_s-
(EQ. 20)
Where S_e is the slew rate of the slope compensation and S_n
is given by Equation 21:
S_n
=
R_t
-^V----ⁱ-ⁿ-----–----^V----^o--
L
(EQ. 21)
where R_T is trans-resistance, and is the product of the
current sensing resistance and gain of the current amplifier
in current loop.
CURRENT SAMPLING TRANSFER FUNCTION H_e(S):
In current loop, the current signal is sampled every switching
cycle. The following transfer function is shown in
Equation 22:
H_e(S)=
-^S----²-
ω_n2
+
------^S--------
ω_nQ_n
+
1
where Q_n and ω_n are given by
(EQ. 22)
Q_n = –²-_π-, = ω_n= πf_s
Power Stage Transfer Functions
Transfer function F₁(S) from control to output voltage is:
F₁(S)
=
v_{-ˆ-d-ˆ-o--}
=
V_i
n
---------¹-----+-----^{ω---------Se}------^s-------^r--------
-^S----²-
ω_o2
+
ω^-----_o^-S--Q^-----_p^-
+
1
(EQ. 23)
Where
ω_esr
=
------¹--------
R_cC_o
,Q_p
≈
R_o
-^C----^o-
L
,ω_o=
-------¹-------
LC_o
Transfer function F₂(S) from control to inductor current is
given by Equation 24:
F₂(S) =
ˆ-_{Id-ˆo-- =}
-------^V----ⁱ--ⁿ-------
R_o + R_L
------------¹-----+------^ω--^S------^z-------------
-^S----²-
ω_o2
+
------^S--------
ω_oQ_p
+
1
(EQ. 24)
where
ω_z
=
-------¹-------
R_oC_o
Current loop gain T_i(S) is expressed as Equation 25:
T_i(S) = R_TF_mF₂(S)H_e(S)
(EQ. 25)
The voltage loop gain with open current loop is shown in
Equation 26:
T_v(S) = KF_mF₁(S)A_v(S)
(EQ. 26)
The Voltage loop gain with current loop closed is given by
Equation 27:
L_v(S)
=
-----^T----^v---⁽--^S----⁾-----
1 + T_i(S)
(EQ. 27)
Where^K
=
V_-----F---B--
V_o
,
V_FB
is the feedback voltage of the voltage
error amplifier. If T_i(S)>>1, then Equation 27 can be
simplified as shown in Equation 28:
L_v(S)=
-^V----^F---^B--
V_o
R_{-----o-----+----}R_-----L-
R_T
-¹----+-----^{ω----------Se------s------r}
1 + -_ω-^S---_p-
H^{-A----ve---((---SS----)-})
,
ω_p
≈
-------¹-------
R_oC_o
(EQ. 28)
From Equation 28, 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.
22
FN9116.1
April 20, 2009