Rainbow Electronics MAX1870A - Manual (Page 24)

MAX1870A
Step-Up/Step-Down
Li+ Battery Charger
24 ______________________________________________________________________________________
Setting the LTF = 1 to solve for the unity-gain frequency
yields:
For stability, choose a crossover frequency lower than
1/10th of the switching frequency. The crossover fre-
quency must also be below the RHP zero, calculated at
maximum charge current, minimum input voltage, and
maximum battery voltage.
Choosing a crossover frequency of 13kHz and solving for
R
CV using the component values listed in Figure 1 yields:
MODE = V
CC
(4 cells) GMV = 0.1µA/mV
C OUT = 22µF GM PWM = 1.85A/V
V BATT = 16.8V f CO_CV = 13kHz
R L = 0.2Ω f OSC = 400kHz
To ensure that the compensation zero adequately can-
cels the output pole, select f
Z_CV ≤ f P_OUT .
C CV ≥ (R L / R CV ) x C OUT
C
CV ≥ 440pF
Figure 10 shows the Bode Plot of the voltage-loop fre-
quency response using the values calculated above.
Charge-Current and Wall-Adapter-Current
Loop Compensation
When the MAX1870A regulates the charge current or the
wall adapter current, the system stability does not
depend on the output capacitance. The simplified
schematic in Figure 11 describes the operation of the
MAX1870A when the charge-current loop (CCI) is in con-
trol. The simplified schematic in Figure 12 describes the
operation of the MAX1870A when the source-current
R
x C x f
GMV x GM
k
CV
OUT CO CV
PWM
= =
2
10
π
_
Ω
f GM x G
R
x C
CO CV PWM MV
CV
OUT
_
=






2π
LTF GM x
R
sC
G
PWM
CV
OUT
MV
=
Table 3. Constant Voltage Loop Poles and Zeros
NO. NAME CALCULATION DESCRIPTION
1 CCV Pole
Lowest Frequency Pole created by C CV and GMV’s finite output
resistance. Since R OGMV is very large (R OGMV > 10M Ω ), this is
a low-frequency pole.
2 CCV Zero
Voltage-Loop Compensation Zero. If this zero is lower than the
output pole, f
P_OUT , then the loop transfer function
approximates a single-pole response near the crossover
frequency. Choose C
CV to place this zero at least 1 decade
below crossover to ensure adequate phase margin.
3
Output
Pole
Outp ut P ol e For m ed w i th the E ffecti ve Load Resi stance R L and the
Outp ut C ap aci tance C
OU T
. R
L
i nfl uences the D C g ai n b ut d oes not
affect the stab i l i ty of the system or the cr ossover fr eq uency.
4
Output
Zero
Output ESR Zero. This zero can keep the loop from crossing
unity gain if f
Z_OUT is less than the desired crossover
frequency. Therefore, choose a capacitor with an ESR zero
greater than the crossover frequency.
5 RHP Zero
S tep - U p M od e RH P Z er o. Thi s zer o occur s b ecause of the i ni ti al
op p osi ng r esp onse of a step - up conver ter . E ffor ts to i ncr ease the
i nd uctor cur r ent r esul t i n an i m m ed i ate d ecr ease i n cur r ent
d el i ver ed , al thoug h eventual l y r esul t i n an i ncr ease i n cur r ent
d el i ver ed . Thi s zer o i s d ep end ent on char g e cur r ent and m ay
cause the system to g o unstab l e at hi g h cur r ents w hen i n step - up
m od e. A r i g ht- hal f- p l ane zer o i s d etr i m ental to b oth p hase and
g ai n. To ensur e stab i l i ty und er m axi m um l oad i n step - up m od e,
the cr ossover fr eq uency m ust b e l ow er than hal f of f
R H P Z .
f
x R C
P CV
OGMV CV
_
=
1
2π
f
x R C
Z CV
CV CV
_
=
1
2π
f
x R C
P OUT
L OUT
_
=
1
2π
f
x R C
Z OUT
ESR OUT
_
=
1
2π
f
V
x L I
V
x L I V
RHPZ
IN
L
IN
OUT OUT
=
=
2
2
2
π
π