ISL6255 Datasheet, PDF (18/22 Pages) Intersil Corporation – Highly Integrated Battery Charger with Automatic Power Source Selector for Notebook Computers

ISL6255, ISL6255A
TABLE 2. COMPONENT LIST (Continued)
PARTS
PART NUMBERS AND MANUFACTURER
R9
10.2kΩ, ±1%, (0805)
R10 4.7Ω, ±5%, (0805)
R12 20kΩ, ±1%, (0805)
R13 1.87kΩ, ±1%, (0805)
Loop Compensation Design
ISL6255, ISL6255A uses a constant frequency current mode
control architecture to achieve fast loop transient response.
Accurate current sensing resistors in series with the output
inductor is used to regulate the charge current, and the
sensed current signal is injected into the voltage loop to
achieve current mode control to simplify the loop
compensation design. The inductor is not considered as a
state variable for current mode control and the system
becomes a single order system. It is much easier to design a
compensator to stabilize the voltage loop than voltage mode
control. Figure 17 shows the small signal model of the
synchronous buck regulator.
PWM Comparator Gain F_m:
The PWM comparator gain Fm for peak current mode
control is given by:
F_m
=
dˆ
vˆ _comp
=¹
V_PWM
Where V_PWM is the peak-peak voltage of the PWM ramp
signal.
Current Sampling Transfer Function H_e(S):
In current loop, the current signal is sampled every switching
cycle. It has the following transfer function:
H_e (S) =
S²
ω_n2
+
S
ω_nQ_n
+1
where Q_n and
respectively.
ω_n
are
given
by
Q_n
=
−²
π
,
ω_n=π
f_s,
Power Stage Transfer Functions
Transfer function F₁(S) from control to output voltage is:
F₁ (S)
=
vˆ _o
dˆ
= V_in
1+ ^S
ω _esr
S² ₊ S
+1
ω_o2 ^ωo^Qp
Where
ω _esr
=
1
R_cC_o
,
Q_p
≈ R_o
C_{o , ωo =}
L
1
LC_o
Transfer function F₂(S) from control to inductor current is:
F₂ (S) =
iˆ_L
dˆ
= ^Vin
R_o + R_L
S²
ω
2
o
1+ ^S
ω_z
+^S
ω_oQ_p
+1
,
where
ω_z
≈¹
R_oC_o
.
Current loop gain T_i(S) is expressed as the following
equation:
T_i (S ) = R_T F_mF₂ (S)H_e (S)
where R_T is the trans-resistance in current loop. R_T is
usually equal to the product of the current sensing resistance
of the current amplifier. For ISL6255, ISL6255A, R_T=20R₁.
The voltage gain with open current loop is:
T_v (S ) = KF_mF₁ (S)A_v (S)
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closed is given by:
L_v
(S
)
=
T_v (S)
1 + T_i (S)
If T_i(S)>>1, then it can be simplified as follows:
1+ ^S
L_v (S ) =
V_FB
V_o
R_o + R_L
R_T
ω _esr
1+ ^S
A_v (S)
H_e (S)
ω_p
≈
1
R_oC_o
ω_p
From the above equation, it is shown that the system is a
single order system, which has a single pole located at ^ω_p
before the half switching frequency. Therefore, simple type II
compensator can be easily used to stabilize the system.
Figure 17 shows the voltage loop compensator, and its
transfer function is expressed as follows
iˆ_in
iˆ_L ^L
vˆ _o
vˆ _in
+
I_Ldˆ ^{1:D Vindˆ}
R_T
Rc
Ro
Co
T_i(S)
dˆ
K
Fm
+
He(S)
T_v(S)
vˆ_{comp -Av(S)}
FIGURE 17. SMALL SIGNAL MODEL OF SYNCHRONOUS
BUCK REGULATOR
18
FN9203.1
June 17, 2005