ꢀ ꢁꢁꢂ ꢃ ꢄ ꢅ ꢆ ꢀ ꢁꢁ ꢂ ꢃꢄ ꢃ ꢆ ꢀꢁ ꢁꢇ ꢃ ꢄ ꢅ ꢆ ꢀꢁ ꢁꢇ ꢃ ꢄ ꢃ
ꢈ ꢉꢁꢊ ꢋꢌ ꢍꢋꢎ ꢏꢐ ꢑꢒꢁ ꢓꢋ ꢐ ꢍ ꢐꢏ ꢐꢏ ꢔꢀ ꢕꢒꢓꢋ ꢐ
ꢖ
SLUS395J - FEBRUARY 2000 - REVISED MARCH 2009
APPLICATION INFORMATION
voltage loop (continued)
1
C +
f
ǒ
INǓ
2 p f G
R
R
VA
In this example C equals 150 nF. Resistor R sets the dc gain of the error amplifier and thus determines the
f
f
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:
P
2
IN
f
+
VI
2
ǒ 2 p
(
)
CfǓ
DV
V
R C
IN
OUT
VAOUT
OUT
f
for this converter is 10 Hz. A derivation of this equation can be found in the Unitrode Power Supply Design
VI
Seminar SEM1000, Topic 1, [A 250-kHz, 500-W Power Factor Correction Circuit Employing Zero Voltage
Transitions].
Solving for R becomes:
f
1
R +
f
ǒ
CfǓ
2 p f
VI
or R equals 100 kΩ.
f
Due to the low output impedance of the voltage amplifier, capacitor C was added in series with R to reduce
Z
F
loading on the voltage divider. To ensure the voltage loop crossed over at f , C was selected to add a zero
VI
Z
at a 10th of f . For this design a 2.2-µF capacitor was chosen for C . The following equation can be used to
VI
Z
calculate C .
Z
1
C
+
Z
f
VI
2 p
R
f
10
current loop
The gain of the power stage is:
ǒVOUT SENSEǓ
R
G
(s) +
ID
ǒ
PǓ
s L
V
BOOST
R
has been chosen to give the desired differential voltage for the current sense amplifier at the desired
SENSE
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 value of 0.25 Ω. V in this equation is the voltage swing of the oscillator ramp, 4 V for
SENSE
P
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 at that frequency. G , the current amplifier gain
ID
EA
is then:
1
1
G
+
+
+ 2.611
EA
0.383
G
ID
12
www.ti.com
TI [ TEXAS INSTRUMENTS ]
