ISL6257 Datasheet, PDF (18/22 Pages) Intersil Corporation – Highly Integrated Narrow VDC Battery Charger for Notebook Computers

ISL6257
Output LC Filter Transfer Functions
The gain from the phase node to the system output and
battery depend entirely on external components. Transfer
function A_LC(s) is shown in Equation 21 and Equation 22:
A_LC
=
----------------^⎝⎛--¹-----–----^{ω----------E--s----S------R-----⎠⎞}-----------------
⎛
⎜
⎝
ω^----s-_D^-2---_P^--
+
(^---ω^----_D^----_P^-s----⋅^---Q^-----)
+
⎞
1⎟
⎠
(EQ. 21)
ω_ESR
=
--------------¹---------------
(R_ESR ⋅ C_o)
ω_DP
=
-----------¹------------
( L ⋅ C_o)
Q = R_o ⋅
--^L----
C_o
(EQ. 22)
R_BATTERY
= 100mΩ
R_BATTERY
= 50mΩ
NO BATTERY
FREQUENCY
FIGURE 22. FREQUENCY RESPONSE OF THE LC OUTPUT
FILTER
The load resistance R_O is a combination of MOSFET
r_DS(ON), inductor DCR and the internal resistance of the
battery (normally between 50mΩ and 200mΩ) in parallel with
the system. The system load may be modeled as a current
sink in parallel with a resistance. For AC analysis of the
voltage control loop this may be treated as a very high
resistance or an open circuit. The worst case for voltage
mode control is when the battery is absent. This results in
the highest Q of the LC filter and the lowest phase margin.
Voltage Control Loop
The voltage error amplifier controls the output when the
battery is not drawing current and the input current is below
the limit. Under these conditions VCOMP controls the
charger’s output because the 2 current error amplifiers (gm2
and gm3) output their maximum current and charge the
capacitor on ICOMP to its maximum voltage (limited to 1.2V
above VCOMP). With high voltage on ICOMP, the minimum
voltage buffer output equals the voltage on VCOMP. The
voltage control loop is shown in Figure 23.
RAMP GEN
V_RAMP = VDD/11
-
+
VDD
L
PHASE
I_SYSTEM
C_O
R_ESR
VCOMP
FB
CSON
R₂
C₂
R₁
C₁
-
gm1
+
V_REF
=2.1V
R₃
R₄
R_S2
R_BAT
FOR SMALL SIGNAL AC ANALYSIS, VOLTAGE SOURCES
ARE SHORT CIRCUITS AND CURRENT SOURCES ARE
OPEN CIRCUITS.
L
11
PHASE
C_O
R_ESR
R_S2
VCOMP
FB
CSON
R₂ C2
-
gm1
+
R₁ C₁
R₃
R₄
R_BAT
FIGURE 23. VOLTAGE LOOP COMPENSATOR
18
FN9288.2
January 17, 2007