?/DIV>
V
rms
V
out
+ 1
Calculating the Loop Gain
At this point in the design process, all of the parameters
involved in this calculation have been determined with the
exception of the pole- -zero pair on the output of the voltage
error amplifier.
All equations give gains in absolute numbers. It is
necessary to convert these to the decibel format using the
following formula:
A(dB) = 20 Log
10
(A)
For example, the voltage divider would be:
A =
5.6 k
560 k + 5.6 k
= 0.0099
A(dB) = 20 Log
10
0.0099 = - -40 dB
Thegainoftheloopwillvaryastheinputvoltagechanges.
It is recommended that the compensation for the error
amplifierbecalculatedunderhighline,fullloadconditions.
Thisshould be the greatest bandwidth that the unit will see.
By necessity, the unity gain (0 dB) loop bandwidth for a
PFC unit, must be less than the line frequency. If the
bandwidth approaches or exceeds the line frequency, the
voltage  error  amplifier  signal  will  have  frequency
components in its output that are greater than the line
frequency. These components will cause distortion in the
outputofthereferenceamplifier,whichisusedtoshapethe
current waveform. This in turn will cause distortion in the
current and reduce the power factor.
Typically the maximum bandwidth for a 60 Hz PFC
converter is 10 Hz, and slightly less for a 50 Hz system. This
canbeadjustedtomeettheparticularrequirementsofasystem.
The unity gain bandwidth is determined by the frequency at
which the loop gain passes through the 0 dB level.
For stability purposes, the gain should pass through 0 dB
withaslopeof- -20dBforapproximatelyondecadeoneither
sideoftheunitygainfrequency.Thisassuresaphasemargin
of greater than 45?
Thegaincanbecalculatedgraphicallyusingtheequations
of Figure 18 as follows:
Divider:
Calculate V?V
o
in dB, this value is constant so it
will not change with frequency.
OptocouplerTransfer:
CalculateV
fb
/V
ea
usingtheequation
provided. Convert this value into dB.
ReferenceSignal:
CalculateV
ref
/V
fb
usingthepeaklevelof
the AC input signal at high line that will be seen on pin 9.
Convert this to dB. This is also a constant value.
Modulator and Output Stage:
Calculate the gain in dB for
DI
o
/DV
ref
for the modulator, and also the gain in dB for the
outputstage(DV
out
/DI
in
).Calculatethepolefrequency.The
gainwillbeconstantforallfrequencieslessthanf
p
.Starting
at the pole frequency, this gain will drop off at a rate of
20 dB/decade.
Plot the sum of all of the calculated values. Be sure to
include the output pole. It should resemble the plot of
Figure 45. This plot shows a gain of 34 dB until the pole of
the output filter is reached at 3 Hz. After that, the gain is
reduced at a rate of 20 dB/decade.