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RC5039
PRODUCT SPECIFICATION
8
P
Feedback Compensation
Figure 6 highlights the voltage-mode control loop for a buck
converter. The output voltage (V
OUT
) is regulated to the ref-
erence voltage level. The error amplifier (Error Amp) output
(V
E/A
) is compared with the oscillator (OSC) triangular
wave to provide a pulse-width modulated (PWM) wave with
an amplitude of V
IN
at the PHASE node. The PWM wave is
smoothed by the output filter (L
O
and C
O
).
The modulator transfer function is the small-signal transfer
function of V
OUT
/V
E/A
. This function is dominated by a DC
Gain and the output filter (L
O
and C
O
), with a double pole
break frequency at F
LC
and a zero at F
ESR
. The DC Gain of
the modulator is simply the input voltage (V
IN
) divided by
the peak-to-peak oscillator voltage
D
V
OSC
.
Figure 6. Voltage-Mode Buck Converter Compensation
Modulator Break Frequency Equations
The compensation network consists of the error amplifier
(internal to the RC5039) and the impedance networks Z
IN
and Z
FB
. The goal of the compensation network is to provide
a closed loop transfer function with the highest 0dB crossing
frequency (f
0dB
) and adequate phase margin. Phase margin
V
OUT
OSC
REFERENCE
LO
CO
ESR
V
IN
D
V
OSC
ERROR
AMP
PWM
DRIVER
(PARASITIC)
Z
FB
+
-
DACOUT
R1
R3
R2
C3
C2
C1
COMP
V
OUT
FB
Z
FB
RC5039
Z
IN
COMPARATOR
DETAILED COMPENSATION COMPONENTS
PHASE
V
E/A
+
-
+
-
Z
IN
F
LC
L
O
2
p
C
O
·
·
-----------------1
=
F
ESR
p
ESR
C
O
·
·
2
=
is the difference between the closed loop phase at f
0dB
and
180
°
. The equations below relate the compensation network’s
poles, zeros and gain to the components (R1, R2, R3, C1, C2,
and C3) in Figure 6. Use these guidelines for locating the
poles and zeros of the compensation network:
1.
Pick Gain (R2/R1) for desired converter bandwidth
2.
Place 1
ST
Zero Below Filter’s Double Pole (~75% F
LC
)
3.
Place 2
ND
Zero at Filter’s Double Pole
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
Figure 7 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 7. 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 7 by adding the
Modulator Gain (in dB) to the Compensation Gain (in dB).
This is equivalent to multiplying the modulator transfer
function to the compensation transfer function and plotting
the gain.
Figure 7. Asymptotic Bode Plot of Converter Gain
F
Z1
2
p
R2
C1
·
·
---------------1
=
F
P1
2
p
R2
C1
C2
C2
·
+
C1
è
·
·
-----------------------1
=
F
Z2
+
p
R1
R3
(
)
C3
·
·
2
=
F
P2
2
p
R3
C3
·
·
---------------1
=
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
/DV
OSC
)
MODULATOR
GAIN
CLOSED LOOP
GAIN