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APPLICATIONS INFORMATION
Most electrolytic and tantalum capacitors come
with adequate ESR value to generate a zero below
power supplies’ crossover frequency. This is cru-
cial to a stable close loop system. However, this
same system can become unstable if ceramic out-
put capacitors are used. The low ESR associated
with ceramic capacitors can push the ESR zero
above the crossover frequency and often higher
than 1MHz. In this case, type III compensation is
In SP6123, G M (error amplifier transconductance)
and R OUT (error amplifier output impedance) are
specified at 0.6ms and 3M ? , respectively.
For frequencies above the second zero f Z2 , the
feedback gain rises at 20dB/dec and is equal to
A FB = 2 π fR Z C 1
However, the error amplifier gain A EA declines
at -20dB/dec due to C P .
required to provide additional low frequency zero for
adequate phase margin and thus stable operation.
A EA =
G M
2 π fC P
f Z1 =
= 6kHz
f Z2 =
= 11.7kHz
2 π (R 2 // R 3 )C Z G M R OUT
The design of type III compensation using
SP6123 transconductance error amplifier is quite
straightforward. First, the resonant frequency of
the LC output filter could be derived from
1
f r = = 11.6kHz
2 π√ L 1 C OUT
The values and references used in all the calcula-
tions agree with the schematic shown in Figure 3.
Select values of R2, C1, R Z and C Z to place two
zeros below or equal to the LC resonant fre-
quency. Those two zeros are located at:
1
2 π R 2 C 1
1
2 π R Z C Z
There is low frequency pole determined by both
the error amplifier gain and feedback gain. It
occurs at
1
f P1 = = 3.25Hz
200
Phase
100
0
Gain
-100
-200
When A FB is less than A EA , the compensated
error amplifier gain is dominated by A FB . As a
result, it shows up as a positive 20dB/dec slope.
However, when the rising A FB crosses the fall-
ing A EA at one particular frequency, the com-
pensated error amplifier gain is now solely de-
termined by A EA . Therefore, the 20dB/dec slope
is converted to a -20dB/dec slope, and the bode
plot demonstrates a double pole at this fre-
quency which is equal to
1 GM
f P2 = 2 π C P C 1 R Z = 221kHz
Select C P such that f P2 is located at least a decade
higher than the crossover frequency.
As shown in Figure 4, this type III compensation
generates a close loop system with 50 degree phase
margin and crossover frequency at 20kHz. This
ensures a stable regulated power supply with tight
DC regulation and fast transient response.
10Hz
100Hz
100Hz
1.0kHz
10kHz
1.0MHz
10MHz
Frequency
Figure 4. Bode Plot for schematic shown in Figure 3. V IN = 3.3V and V OUT = 1.6V, no load.
Date: 9/13/04
SP6123 Low Voltage, Synchronous Step Down PWM Controller
14
? Copyright 2004 Sipex Corporation
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