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RC5054A
PRODUCT SPECIFICATION
8
P
4.
Place 1
ST
Pole at the ESR Zero
5.
Place 2
ND
Pole at Half the Switching Frequency
6.
Check Gain against Error Amplifier’s Open-Loop Gain
7.
Estimate Phase Margin - Repeat if Necessary
Compensation Break Frequency Equations
p
R2
C1
·
·
Figure 6 shows an asymptotic plot of the DC-DC converter’s
gain vs. frequency. The actual Modulator Gain has a high
gain peak due to the high Q factor of the output filter and is
not shown in Figure 6. Using the above guidelines should
give a Compensation Gain similar to the curve plotted.
The open loop error amplifier gain bounds the compensation
gain. Check the compensation gain at F
P2
with the capabili-
ties of the error amplifier. The Closed Loop Gain is con-
structed on the log-log graph of Figure 6 by adding the
Modulator Gain (in dB) to the Compensation Gain (in dB).
This is equivalent to multiplying the modulator transfer func-
tion to the compensation transfer function and plotting the
gain.
The compensation gain uses external impedance networks
Z
FB
and Z
IN
to provide a stable, high bandwidth (BW) over-
all loop. A stable control loop has a gain crossing with
-20dB/decade slope and a phase margin greater than 45
degrees. Include worst case component variations when
determining phase margin.
Figure 6. Asymptotic Bode Plot of Converter Gain
Component Selection Guidelines
Output Capacitor Selection
An output capacitor is required to filter the output and supply
the load transient current. The filtering requirements are a
function of the switching frequency and the ripple current.
The load transient requirements are a function of the slew
rate (di/dt) and the magnitude of the transient load current.
These requirements are generally met with a mix of capaci-
tors and careful layout.
Modern microprocessors produce transient load rates above
1A/ns. High frequency capacitors initially supply the tran-
sient and slow the current load rate seen by the bulk capaci-
tors. The bulk filter capacitor values are generally determined
by the ESR (effective series resistance) and voltage rating
requirements rather than actual capacitance requirements.
High frequency decoupling capacitors should be placed as
close to the power pins of the load as physically possible. Be
careful not to add inductance in the circuit board wiring that
could cancel the usefulness of these low inductance compo-
nents. Consult with the manufacturer of the load on specific
decoupling requirements. For example, Intel recommends
that the high frequency decoupling for the Pentium Pro be
composed of at least forty (40) 1
m
F ceramic capacitors in the
1206 surface-mount package.
Use only specialized low-ESR capacitors intended for
switching-regulator applications for the bulk capacitors. The
bulk capacitor’s ESR will determine the output ripple voltage
and the initial voltage drop after a high slew-rate transient.
An aluminum electrolytic capacitor’s ESR value is related to
the case size with lower ESR available in larger case sizes.
However, the equivalent series inductance (ESL) of these
capacitors increases with case size and can reduce the useful-
ness of the capacitor to high slew-rate transient loading.
Unfortunately, ESL is not a specified parameter. Work with
your capacitor supplier and measure the capacitor’s imped-
ance with frequency to select a suitable component. In most
cases, multiple electrolytic capacitors of small case size per-
form better than a single large case capacitor.
Output Inductor Selection
The output inductor is selected to meet the output voltage
ripple requirements and minimize the converter’s response
time to the load transient. The inductor value determines the
converter’s ripple current and the ripple voltage is a function
of the ripple current. The ripple voltage and current are
approximated by the following equations:
Increasing the value of inductance reduces the ripple current
and voltage. However, the large inductance values reduce the
converter’s response time to a load transient.
One of the parameters limiting the converter’s response to
a load transient is the time required to change the inductor
current. Given a sufficiently fast control loop design, the
RC5054A will provide either 0% or 100% duty cycle in
response to a load transient. The response time is the time
F
Z1
2
=
F
P1
2
p
R2
C2
C2
·
+
C1
è
·
·
-----------------------1
=
F
Z2
+
p
R1
R3
(
)
C3
·
·
2
=
F
P2
p
R3
C3
·
·
2
=
100
80
60
40
20
0
-20
-40
-60
F
P1
F
Z2
10M
1M
100K
10K
1K
100
10
OPEN LOOP
ERROR AMP GAIN
F
Z1
F
P2
20LOG
(R2/R1)
F
LC
F
ESR
COMPENSATION
GAIN
G
FREQUENCY (Hz)
20LOG
(V
IN
/
D
V
OSC
)
MODULATOR
GAIN
CLOSED LOOP
GAIN
D
I
V
----------–
V
L
′
FS
V
V
IN
--------------
·
=
D
V
OUT
D
I
ESR
′
=