ISL78201 Datasheet, PDF (20/23 Pages) Intersil Corporation – 40V 2.5A Regulator with Integrated High-side MOSFET for Synchronous Buck or Boost Buck Converter

ISL78201
^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 35. SMALL SIGNAL MODEL OF BUCK REGULATOR
PWM Comparator Gain F_m
The PWM comparator gain F_m 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_P
(EQ. 21)
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 22:
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. 22)
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. 23)
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 24:
where
_z
=
------¹-------
R_oC_o
.
F₂S =
ˆ_I-d-ˆo--
=
-_R----_o---^V-+---ⁱ-ⁿ-_R----_L---_P-
------------¹-----+-----^---S------^z------------
-^S----²-
_o2
+
------^S-------
_oQ_p
+
1
Current loop gain T_i(S) is expressed as Equation 25:
T_iS = R_tF_mF₂SH_eS
(EQ. 24)
(EQ. 25)
The voltage loop gain with open current loop is 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 = -₁----^T-+--^v--_T-^--^S-_i-_--^-_S----_
(EQ. 27)
If T_i(S)>>1, then Equation 27 can be simplified as Equation 28:
L_vS=
-^R----^o----+-----^R----^L---^P- ¹------+------^--------^Se------^s------^r -^A----^v---^--^S----^ ,
R_t
1
+
--^S----
_p
H_eS
_p

------¹-------
R_oC_o
(EQ. 28)
Equation 28 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 36. TYPE III COMPENSATOR
A compensator with 2 zeros and 1 pole is recommended for this
part as shown in Figure 36. Its transfer function is expressed as
Equation 29:
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. 29)
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
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FN8615.1
March 31, 2015