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Wide-Input, High-Frequency, Triple-Output Supplies
with Voltage Monitor and Power-On Reset
When the output capacitance is comprised of parallel-
ing n number of identical capacitors whose values are
C EACH with ESR of R ESR_EACH , then:
C OUT = n × C EACH and
the -40dB/decade slope of the LC double pole, and the
resultant compensated loop crosses over at the
desired -20dB/decade slope. The error amplifier has a
dominant pole at very low frequency ( ≈ 0Hz), and two
separate zeros at:
R ESR =
R ESR _ EACH
n
f Z 1 =
1
2 π × R 3 × C 5
and f Z 2 =
1
2 π × ( R 1 + R 4 ) × C 11
Thus the resulting f ZESR is the same as that of each
capacitor.
and poles at:
2 π × R 3 × ? ?
The crossover frequency (f C ), which is the frequency
when the closed-loop gain is equal to unity, should be
the smaller of 1/5th the switching frequency or 100kHz
(see the Switching-Frequency Setting section):
f P 2 =
1
2 π × R 4 × C 11
and f P 3 =
1
? C 5 × C12 ?
? C 5 + C 12 ?
f C ≤ S or 100 kHz
f
5
The loop-gain equation at the crossover frequency is:
G EA ( fc ) G MOD ( fc ) = 1
The error-amplifier equivalent circuit and its gain vs.
frequency plot are shown below in Figure 3.
In this case, f Z2 and f P1 are selected to have the convert-
ers’ closed-loop crossover frequency, f C , occur when the
error-amplifier gain has a +20dB/decade slope between
f Z2 and f P2 . The error-amplifier gain at f C is:
where G EA(fc) is the error-amplifier gain at f C , and
G MOD( f c) is the power modular gain at f C .
The loop compensation is affected by the choice of out-
G EA ( fc ) =
1
G MOD ( fc )
put-filter capacitor used, due to the position of its ESR
The gain of the error amplifier between f Z1 and f Z2 is:
G EA ( fZ 1 - fZ 2 ) = G EA ( fc ) Z 2 =
zero frequency with respect to the desired closed-loop
crossover frequency. Ceramic capacitors are used for
higher switching frequencies (above 750kHz) because
of low capacitance and low ESR; therefore, the ESR
zero frequency is higher than the closed-loop crossover
frequency. While electrolytic capacitors (e.g., tantalum,
solid polymer, oscon, etc.) are needed for lower switch-
ing frequencies, because of high capacitance and ESR,
f
f C
C12
f Z 2
f C G MOD ( fc )
the ESR zero frequency is typically lower than the
closed-loop crossover frequency. Thus the compensa-
tion design procedure is separated into two cases:
V OUT1
C11
R4
R3
C5
Case 1: Ceramic Output Capacitor (operating at
high switching frequencies, f ZESR > f C )
R1
R2
REF
EA
COMP
G MOD ( fc ) = G MOD ( DC ) ? PMOD ?
The modulator gain at f C is:
? f ?
? f C ?
2
GAIN
(dB)
CLOSED-LOOP GAIN
EA GAIN
Since the crossover frequency is lower than the output
capacitors’ ESR zero frequency and higher than the LC
f Z1
f Z2
f P2
f P3
FREQUENCY
double-pole frequency, the error-amplifier gain must
have a +20dB/decade slope at f C . This +20dB/decade
slope of the error amplifier at crossover then adds to
f C
Figure 3. Case 1: Error-Amplifier Compensation Circuit (Closed-
Loop and Error-Amplifier Gain Plot)
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