Rainbow Electronics MAX1801 User Manual
Page 11
MAX1801
Digital Camera Step-Up Slave
DC-DC Controller
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11
Since the external gate drive (DL) swings between IN
and GND, use a MOSFET whose on-resistance is spec-
ified at or below V
IN
. The gate charge, Qg, includes all
capacitance associated with gate charging and helps
to predict the transition time required to drive the MOS-
FET between on and off states. The power dissipated in
the MOSFET is due to on-resistance and transition loss-
es. The on-resistance loss is:
P
1
≈ D I
L
2
R
DS(ON)
where D is the duty cycle, I
L
is the average inductor
current, and R
DS(ON)
is the on-resistance of the MOS-
FET. The transition loss is approximately:
where V
OUT
is the output voltage, I
L
is the average
inductor current, f
OSC
is the converter switching fre-
quency, and t
T
is the transition time. The transition time
is approximately Q
g
/ I
G
, where Q
g
is the total gate
charge and I
G
is the gate drive current (typically 0.5A).
The total power dissipation in the MOSFET is:
P
MOSFET
= P
1
+ P
2
Diode Selection
For low-output-voltage applications, use a Schottky
diode to rectify the output voltage because of the
diode’s low forward voltage and fast recovery time.
Schottky diodes exhibit significant leakage current at
high reverse voltages and high temperatures. Thus, for
high-voltage, high-temperature applications, use ultra-
fast junction rectifiers.
Compensation Design
MAX1801 converters use voltage mode to regulate their
output voltages. The following explains how to compen-
sate the control system for optimal performance. The
compensation differs depending on whether the induc-
tor current is continuous or discontinuous.
Discontinuous Inductor Current
For discontinuous inductor current, the PWM converter
has a single pole. The pole frequency and DC gain of
the PWM controller are dependent on the operating
duty cycle, which is:
D = (2 L f
OSC
/ R
E
)
1/2
where R
E
is the equivalent load resistance, or:
R
E
= V
IN2
R
LOAD
/ (V
OUT
(V
OUT
– V
IN
))
The frequency of the single pole due to the PWM con-
verter is:
P
O
= (2 V
OUT
– V
IN
) / (2
π
(V
OUT
– V
IN
) R
LOAD
C
OUT
)
And the DC gain of the PWM controller is:
A
VO
= 2 V
OUT
(V
OUT
– V
IN
) R
LOAD
/ ((2 V
OUT
– V
IN
) D)
Note that the pole frequency decreases and the DC
gain increases proportionally as the load resistance
(RLOAD) is increased. Since the crossover frequency
is the product of the pole frequency and the DC gain, it
remains independent of the load.
The gain through the voltage-divider is:
A
VDV
= V
REF
/ V
OUT
And the DC gain of the error amplifier is A
VEA
= 2000V/V.
Thus, the DC loop gain is:
A
VDC
= A
VDV
A
VEA
A
VO
The compensation resistor-capacitor pair at COMP cause
a pole and zero at frequencies (in Hz):
P
C
= G
EA
/ (4000
π
C
C
) = 1 / (4 x 10
7
π
C
C
)
Z
C
= 1 / (2
π
R
C
C
C
)
And the ESR of the output filter capacitor causes a zero
in the loop response at the frequency (in Hz):
Z
O
= 1 / (2
π
C
OUT
ESR)
The DC gain and the poles and zeros are shown in the
Bode plot of Figure 4.
To achieve a stable circuit with the Bode plot of Figure
4, perform the following procedure:
P
V
I f
t
OUT L OSC T
2
3
≈
FREQUENCY
A
VDC
GAIN
(dB)
PHASE
180°
90°
0°
O
-20
80
60
40
20
PHASE
GAIN
Z
C
= P
O
P
C
Z
O
Figure 4. MAX1801 Discontinuous-Current, Voltage-Mode,
Step-Up Converter Bode Plot