
Control Loop Design
(Continued)
When Q is higher than 0.5, there will be a double-pole at half
the switching frequency f
n
. When Q is lower than 0.5, the
double-pole is damped and becomes two separate poles.
The lower the Q value is, the farther apart the two poles are.
When Q is too low (such as Q = 0.05 or lower), one of the
two high frequency poles may move well into the low fre-
quency region. When Q is too high (such as Q = 5 or higher),
there will be significant peaking at half the switching fre-
quency and the phase will rapidly go to 180 near it. This
typically results in a lower cross-over frequency so that the
peaking in the loop gain is well below the 0dB line.
Q is a function of duty cycle and the deepness of the ramp
compensation (m
). See Equation (34) The larger the duty
cycle, the higher the Q value. The deeper the ramp compen-
sation, the lower the Q value. When the inductor current
ramp is too much smaller than the compensation ramp, one
of the two high frequency poles will move far into the low
frequency region and form a double-pole with the existing
low frequency pole f
p
. That makes it a voltage-mode control.
The ramp compensation becomes deeper when inductance
is increased, or input voltage is decreased, or sense resis-
tance is decreased.
In the case of Channel 1 of LM2633, if L = 1 to 3μH, V
= 5
to 24V, V
o
= 0.925 to 2V, R
ds
= 5 to 20m
, the Q value will
be between 0.65 and 0.2.
Audio Susceptibility
Audio susceptibility is the transfer function from input to
output. In a typical power supply design, it is desirable to
have as much attenuation in that transfer function as pos-
sible so that noise appearing at the input has little effect on
the output. The open-loop audio susceptibility given by the
model in Figure 7 is:
(47)
The closed-loop audio susceptibility is simply:
(48)
where H(s) is the compensation transfer function defined by:
(49)
It can be seen from Equation (47) that if m
c
is equal to
1/(2D’)+0.5, then the open-loop audio susceptibility is zero.
Unfortunately, the transfer function is rather sensitive to the
value of m
c
around the critical value and thus this phenom-
enon is of little value.
The open-loop and closed-loop audio susceptibility of the
previous example is shown in Figure 16 It can be told, both
from the model and from Equation (47) that open-loop gain
of audio susceptibility is just a level shift of the loop gain.
Closed-loop audio susceptibility starts to depart from its
open-loop counterpart when frequency drops below the
cross-over frequency.
Adjusting the Output Voltages of the Switching
Channels
Channel 1 output voltage is normally adjusted through the
VID pins. Channel 2 output voltage is adjusted through an
external voltage divider, as shown in Figure 17
The equation to find the value of R
2
when R
1
has been
selected is:
(50)
where V
is equal to the internal reference voltage con-
nected to the non-inverting input of the Channel 2 error
20000878
FIGURE 15. How Control-Output Transfer Function
Changes with Q Values
20000882
FIGURE 16. Example Audio Susceptibility Gain
200008B7
FIGURE 17. Setting the Ch2 Output Voltage
L
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