Datasheet

   
   
SLUS419C − AUGUST 1999 − REVISED NOVEMBER 2001
25
www.ti.com
TYPICAL APPLICATION
R16 +
V
F
I
TL431 (min)
R13 +
V
REF
* V
VERR (max)
I
OP (min)
To compensate the loop, it is necessary to estimate or measure the control-to-output gain’s frequency response
G
CO
(s). The frequency response for G
CO
(s) was measured with a network analyzer and the measured
frequency response is shown in Figure 15.
Figure 14
OPTOISOLATOR TRANSFER FUNCTION
(GAIN AND PHASE)
vs.
FREQUENCY
−20
0
100
20
−60
−40
60
40
60
180
120
0
−60
−180
−120
1 k 10 k 100 k
f − Frequency − Hz
Gain − dB
Phase − Degrees
PHASE
GAIN
Figure 15
100 1 k 10 k 100 k
−40
−50
−20
−30
0
−10
20
10
30
50
40
−144
−180
−72
−108
0
−36
72
36
108
180
144
Gain − dB
Phase − Degrees
POWER STAGE CONTROL-TO-OUTPUT TRANSFER
FUNCTION (GAIN AND PHASE)
vs.
FREQUENCY
f − Frequency − Hz
GAIN
PHASE
After determining the frequency response of G
CO
(s) it is necessary to define some closed loop frequency
response design goals. The following equation describes the frequency response of the loop gain (T(s)
dB
) of
the system in decibels. Typically, the loop is designed to crossover at a frequency below one-sixth
of the
switching frequency. In order for this design example to have good transient response, the design goal is to have
the loop gain crossover at approximately 1 kHz, which is less than one-sixth of the switching frequency. The
gain crossover frequency for this design example is referenced as f
C
.
T(s) dB + G
C
(s) ) G
CO
(s) ) H(s)
The compensation network that is used (G
C
(s)) has three poles and one zero. One pole occurs at the origin,
and a second pole is caused by the limitations of the opto-isolator. The third pole is set to attenuate the
high-frequency gain and needs to be set to one-half of the switching frequency. The zero is set at the desired
crossover frequency.
The following equations can be used to select R35, C14 and C15, where G
CO
(s), G
OPTO
(s), and H(s) are the
gains in decibels (dB) of each control block at the desired f
C
. From the graphs in Figures 14 and 15 it can be
observed at the desired crossover frequency G
CO
(s) is approximately 0 dB and G
OPTO
(s) is approximately
(43)
(44)
(45)