Datasheet

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SLUS395J - FEBRUARY 2000 - REVISED MARCH 2009
12
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APPLICATION INFORMATION
voltage loop (continued)
C
f
+
1
ǒ
2 p f
R
G
VA
R
IN
Ǔ
In this example C
f
equals 150 nF. Resistor R
f
sets the dc gain of the error amplifier and thus determines the
frequency of the pole of the error amplifier. The location of the pole can be found by setting the gain of the loop
equation to one and solving for the crossover frequency. The frequency, expressed in terms of input power, can
be calculated by the equation:
f
VI
2
+
P
IN
ǒ
(
2 p
)
2
DV
VAOUT
V
OUT
R
IN
C
OUT
C
f
Ǔ
f
VI
for this converter is 10 Hz. A derivation of this equation can be found in the Unitrode Power Supply Design
Seminar SEM1000, Topic 1, [A 250-kHz, 500-W Power Factor Correction Circuit Employing Zero Voltage
Transitions].
Solving for R
f
becomes:
R
f
+
1
ǒ
2 p f
VI
C
f
Ǔ
or R
f
equals 100 kΩ.
Due to the low output impedance of the voltage amplifier, capacitor C
Z
was added in series with R
F
to reduce
loading on the voltage divider. To ensure the voltage loop crossed over at f
VI
, C
Z
was selected to add a zero
at a 10th of f
VI
. For this design a 2.2-µF capacitor was chosen for C
Z
. The following equation can be used to
calculate C
Z
.
C
Z
+
1
2 p
f
VI
10
R
f
current loop
The gain of the power stage is:
G
ID
(s) +
ǒ
V
OUT
R
SENSE
Ǔ
ǒ
s L
BOOST
V
P
Ǔ
R
SENSE
has been chosen to give the desired differential voltage for the current sense amplifier at the desired
current limit point. In this example, a current limit of 4 A and a reasonable differential voltage to the current amp
of 1 V gives a R
SENSE
value of 0.25 Ω. V
P
in this equation is the voltage swing of the oscillator ramp, 4 V for
the UCC3817. Setting the crossover frequency of the system to 1/10th of the switching frequency, or 10 kHz,
requires a power stage gain at that frequency of 0.383. In order for the system to have a gain of 1 at the crossover
frequency, the current amplifier needs to have a gain of 1/G
ID
at that frequency. G
EA
, the current amplifier gain
is then:
G
EA
+
1
G
ID
+
1
0.383
+ 2.611