ISL78200_14 Datasheet, PDF (18/22 Pages) Intersil Corporation – 2.5A Regulator with Integrated High-Side MOSFET for Synchronous Buck or Boost Buck Converter

ISL78200
^iin
V^in
+
^iL _LP
R_LP
ILd^ 1:D ^{Vind^}
RT
vo^
Rc
Ro
Co
d^
Fm
T _i(S)
+
He(S)
Tv(S)
v^comp _-Av(S)
FIGURE 32. SMALL SIGNAL MODEL OF BUCK REGULATOR
PWM Comparator Gain F_m:
The PWM comparator gain Fm for peak current mode control is
given by Equation 16:
F_m
=
v^-ˆ--_c^---_o^-d-ˆ-_m^-----_p^--
=
--------------¹---------------
S_e + S_nT_s
(EQ. 16)
Where, S_e is the slew rate of the slope compensation and S_n is
given by Equation 17
S_n
=
R_t
V_{----i--n----–-----}V_---o-
L_P
(EQ. 17)
where, R_t is the gain of the current amplifier.
CURRENT SAMPLING TRANSFER FUNCTION H_E(S):
In current loop, the current signal is sampled every switching
cycle. It has the following transfer function in Equation 18:
H_eS=
-^S----²-
_n2
+
------^S-------
_nQ_n
+
1
where, Q_n and _n are given by
Q_n = –²-_-  _n= f_s
(EQ. 18)
Power Stage Transfer Functions
Transfer function F₁(S) from control to output voltage is:
F₁S
=
v_{-ˆ-d-ˆ-o-}
=
V_in
---------¹-----+------^--------^Se------^s------^r---------
-^S----²-
_o2
+
------^S-------
_oQ_p
+
1
(EQ. 19)
Where,
_esr
=
------¹------
R_cC_o
,Q_p

R_o
C_----o-
L_P
,_o=
--------¹--------
L_PC_o
Transfer function F₂(S) from control to inductor current is given
by Equation 20:
where
_z
=
------¹-------
R_oC_o
.
18
F₂S =
ˆ_I-d-ˆo--
=
--------^V----ⁱ-ⁿ---------
R_o + R_LP
------------¹-----+-----^---S------^z------------
-^S----²-
_o2
+
-_----_o-^S--_Q----_p-
+
1
Current loop gain T_i(S) is expressed as Equation 21:
T_iS = R_tF_mF₂SH_eS
(EQ. 20)
(EQ. 21)
The voltage loop gain with open current loop is Equation 22:
T_vS = KF_mF₁SA_vS
(EQ. 22)
The Voltage loop gain with current loop closed is given by
Equation 23:
L_vS
=
-----^T---^v---^--^S----^-----
1 + T_iS
(EQ. 23)
If T_i(S)>>1, then Equation 23 can be simplified as Equation 24:
L_vS=
-^R----^o----+-----^R----^L---^P-
R_t
1_{------+--------------}^S_{e------s------r}
1
+
--^S----
_p
-^A----^v---^--^S----^
H_eS
,
_p

------¹-------
R_oC_o
(EQ. 24)
Equation 24 shows that the system is a single order system.
Therefore, a simple type II compensator can be easily used to
stabilize the system. While type III compensator is needed to
expand the bandwidth for current mode control in some cases.
VCOMP
R2
C1
R3
C3
VO
VREF
R1
RBIAS
FIGURE 33. TYPE III COMPENSATOR
A compensator with 2 zeros and 1 pole is recommended for this
part as shown in Figure 33. Its transfer function is expressed as
Equation 25:
A_vS=
-^vˆ--c---_vˆ^o---_Om-----^p-- =
--------¹---------
S
R₁
C
1
_---¹_{-----+-----}^----------_c^S-----_z-----1^-----_---_---¹_{-----+-----}^----------_c^S-----_z-----2^-----_-
^{1 + -}_^---S-_c^---_p^-
(EQ. 25)
where,
_cz1
=
------¹------- ,
R₂C₁
_cz2 =
-_--_R----₁-----+---¹--_R----₃---_---_C---₃-- _cp=
------¹-------
R₃C₃
Compensator design goal:
Loop bandwidth f_c:


1_--
4
t
o
1^--1--0^{--}
f_s
Gain margin: >10dB
FN7641.2
December 24, 2013