2-137
Feedback Compensation
Figure 7 highlights the voltage-mode control loop for a
synchronous-rectified buck converter. The output voltage
(Vout) is regulated to the Reference 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 Vin at the
PHASE node. The PWM wave is smoothed by the output
filter (Lo and Co).
The modulator transfer function is the small-signal transfer
function of Vout/V
E/A
. This function is dominated by a DC
Gain and the output filter (Lo and Co), 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 (Vin) divided by the
peak-to-peak oscillator voltage
V
OSC
.
Modulator Break Frequency Equations
The compensation network consists of the error amplifier
(internal to the HIP6007) 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
is the difference between the closed loop phase at f
0dB
and
180
o
.
The equations below relate the compensation
network’s poles, zeros and gain to the components (R1, R2,
R3, C1, C2, and C3) in Figure 8. Use these guidelines for
locating the poles and zeros of the compensation network:
Compensation Break Frequency Equations
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
Figure 8 shows an asymptotic plot of the DC-DC converter’s
gain vs frequency. The actual Modulator Gain has a high gain
peak do to the high Q factor of the output filter and is not
shown in Figure 8. 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 capabilities of
the error amplifier. The Closed Loop Gain is constructed on
the log-log graph of Figure 8 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.
The compensation gain uses external impedance networks
Z
FB
and Z
IN
to provide a stable, high bandwidth (BW) overall
loop. A stable control loop has a gain crossing with
-20dB/decade slope and a phase margin greater than 45
o
.
Include worst case component variations when determining
phase margin.
FIGURE 7. VOLTAGE - MODE BUCK CONVERTER
COMPENSATION DESIGN
V
OUT
OSC
REFERENCE
L
O
C
O
ESR
V
IN
V
OSC
ERROR
AMP
PWM
DRIVER
(PARASITIC)
-
+
REF
R1
R3
R2
C3
C2
C1
COMP
V
OUT
FB
Z
FB
HIP6007
Z
IN
COMPARATOR
DRIVER
DETAILED COMPENSATION COMPONENTS
PHASE
V
E/A
+
-
+
-
Z
IN
Z
FB
F
LC =
L
O
2
π
C
O
--------------------------------------
F
ESR
=
O
)
--------------------------------------------
F
Z1
=
---------------------------------
F
P1
=
2
π
R2
---------------------
-----------------------------------------------------
F
Z2
=
----------------------------------------------------
F
P2
=
---------------------------------
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
F
LC
F
ESR
COMPENSATION
GAIN
G
FREQUENCY (Hz)
20LOG
(V
IN
/
V
OSC
)
MODULATOR
GAIN
20LOG
(R2/R1)
CLOSED LOOP
GAIN
FIGURE 8. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN
HIP6007