A Generalized Tuning Procedure - Allegro MicroSystems A8600 Manual

A8600
The transfer function of the Type-II compensated error amplifier
also has frequency zero (f
Z2
the CZx capacitor:
f
=
P2x
2�
×
Lastly, the transfer function of the Type-II compensated error
amplifier has a higher frequency pole (f
resistor and the CPx capacitor:
60 G 0Hz = 45.6 dB
CO
40
f = 54 Hz
P2
20
0
-20
-40
-60
180
90
0
-90
-180
1 2
10 10 10
Frequency (Hz)
Figure 26. Compensated error amplifier Bode plot (SW3)
60
40
20
0
-20
-40
-60
180
90
0
-90
-180
10 1 10 2 10
Frequency (Hz)
Figure 27. Bode plot of the complete SW3 system (red curve)
Quadruple Output Regulator with Two High-Side Switches,
) dominated by the RZx resistor and
1
R C
×
Zx Zx
) dominated by the RZx
P3
f = 3.8 kHz
Z1
f = 315 kHz
P3
3 4 5
10 10
f = 36 kHz
C
PM = 66°
3 10 4 10 5
BU/ACC Voltage Detectors, and Mute Delay
f
P3x
A Bode plot of the error amplifier and its compensation network
is shown in figure 26, in which f
(34)
the magnitude plot. Notice that the zero (f
placed so that it is in the vicinity of the pole at f
shown at 1.9 kHz in the control-to-output Bode plot, figure 25.
Placing f just above f
Z2
but relatively slow transient recovery time, as we will see later.
Finally, we take a look at the combined Bode plot of both the
control-to-output and the compensated error amplifier; see the red
curve shown in figure 27. Careful examination of this plot shows
that the magnitude and phase of the entire system (red trace) are
simply the sum of the error amplifier response (blue trace) and
the control-to-output response (green trace). As shown in fig-
ure 27, the bandwidth (f
margin is 66 degrees.

A Generalized Tuning Procedure

1) Choose the system bandwidth, f
which the magnitude of the gain will cross 0 dB. Recommended
values for f based on the PWM switching frequency, are in the
C ,
6 range: f / 20 < f
10
SW
provide a better transient response, and a lower value of f
make it easier to obtain higher gain and phase margins.
3.32
3.30
3.28
3.26
3.24
3.22
3.20
10 6 440 480
Figure 28. Transient recovery comparison for f
9 kHz / 57°
1
=
2� R C
× ×
Zx Px
, f , and f
P2 P3
at 3.8 kHz) has been
Z2
will result in excellent phase margin,
P1
) of this system is 36 kHz and the phase
c
, which is the frequency at
C
< f / 10. A higher value of f
C SW
9 kHz / 57°
3.8 kHz / 66°
520 560 600 640 680
Recovery Time (µs)
at 3.8 kHz / 66° and
Z2
Allegro MicroSystems, LLC
115 Northeast Cutoff
Worcester, Massachusetts 01615-0036 U.S.A.
1.508.853.5000; www.allegromicro.com
(35)
are indicated on
Z2
previously
P1
will generally
C
will
C
720 760 800
43