Rainbow Electronics MAX1870A - Manual (Page 25)

MAX1870A
Step-Up/Step-Down
Li+ Battery Charger
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loop (CCS) is in control. Since the output capacitor’s
impedance has little effect on the response of the current
loop, only a single pole is required to compensate this
loop. A
CSI and A CSS are the internal gains of the current-
sense amplifiers. RS2 is the charge current-sense resis-
tor. RS1a and RS1b are the adapter current-sense
resistors. R
OGMI
and R
OGMS
are the equivalent output
impedance of the GMI and GMS amplifiers, which are
greater than 10MΩ. GMI is the charge-current amplifier
transconductance (2.4µA/mV). GMS is the adapter-cur-
rent amplifier transconductance (1.7µA/mV.) GM
PWM is
the DC-DC converter transconductance (1.85A/V).
Use the following equation to calculate the loop transfer
function:
which describes a single-pole system. Since GM PWM =
the loop-transfer function simplifies to:
Use the following equations to calculate the crossover
frequency:
For stability, choose a crossover frequency lower than
1/10th of the switching frequency and lower than half of
the RHP zero.
C
CI = 10 GMI / (2π x f OSC ), C CS = 10 GMS / (2π x f OSC )
This zero is inversely proportional to charge current
and may cause the system to go unstable at high cur-
rents when in step-up mode. A right-half-plane zero is
detrimental to both phase and gain. To also ensure sta-
bility under maximum load in step-up mode, the CCI
crossover frequency must also be lower than f
RHPZ .
The right-half-plane zero does not affect CCS.
Choosing a crossover frequency of 30kHz and using
the component values listed in Figure 1 yields C
CI and
C CS_ > 10nF. Values for C CI / C CS greater than ten
times the minimum value may slow down the current
loop response excessively. Figure 13 shows the Bode
Plot of the input-current frequency response using the
values calculated above.
MOSFET Drivers
DHI and DBST are optimized for driving moderately-
sized power MOSFETs. Use low-inductance and low-
resistance traces from driver outputs to MOSFET gates.
DHI typically sources 1.6A and sinks 0.8A to or from
the gate of the p-channel MOSFET. DHI swings from
VHP to VHN. VHN is a negative LDO that regulates with
respect to VHP to provide high-side gate drive.
Connect VHP to DCIN. Bypass VHN with a 1µF capaci-
tor to VHP.
f
V
x L I
V
L I V
RHPZ WorstCase
IN MIN
L
IN MIN
OUTMAX OUTMAX
_
_ _
= =
2 2
2
π π
f
GMI
C
f
GMS
C
CO CI
CI
CO CS
CS
_ _
, = =
2 2 π π
LTF GM
R
sR x C
OGM
OGM C
=
+
_
_
_ _
1
1
A x RS
CS _
_
LTF GM x A x RS x GM
R
sR x C
PWM CS
OGM
OGM C
=
+
_ _ _
_
_ _
1
CCV LOOP RESPONSE
MAGNITUDE (dB)
-135
-90
-45
0 80
60
40
20
-40
-20
0
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E-01
FREQUENCY (Hz)
MAG
PHASE
Figure 10. CCV Loop Response
GM
PWM
REF
GMI
R OGMI
C CI
CCI
RS2
A CSI
CSI
Figure 11. CCI Simplified Loop Diagram