8
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
V
OSC
.
Modulator Break Frequency Equations
The compensation network consists of the error amplifier
(internal to the HIP6015) 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 degrees
.
The equations below relate
the compensation network’s poles, zeros and gain to the
components (R
1
, R
2
, R
3
, C
1
, C
2
, and C
3
) in Figure 8. Use
these guidelines for locating the poles and zeros of the
compensation network:
1. Pick Gain (R
2
/R
1
) 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 8 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 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
degrees. Include worst case component variations when
determining phase margin.
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
capacitors and careful layout.
Modern microprocessors produce transient load rates above
1A/ns. High frequency capacitors initially supply the transient
V
OUT
OSC
REFERENCE
L
O
C
O
ESR
V
IN
V
OSC
ERROR
AMP
PWM
DRIVER
(PARASITIC)
FIGURE 7. VOLTAGE-MODE BUCK CONVERTER
COMPENSATION DESIGN
Z
IN
Z
FB
DACOUT
R
1
R
3
R
2
C
3
C
2
C
1
COMP
V
OUT
FB
Z
FB
HIP6015
Z
IN
COMPARATOR
DETAILED COMPENSATION COMPONENTS
V
E/A
+
-
+
-
+
-
PHASE
F
LC
L
O
2
π
C
O
--------------------------------------
=
F
ESR
O
)
--------------------------------------------
=
F
Z2
1
R
3
)
C
3
-----------------------+
=
F
P1
2
π
R
2
3
1
2
C
2
+
--------------------
----------------------------------------------------
=
F
P2
3
---------------------------------
=
F
Z1
2
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
F
LC
F
ESR
COMPENSATION
GAIN
G
FREQUENCY (Hz)
20LOG
(V
IN
/
V
OSC
)
MODULATOR
GAIN
FIGURE 8. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN
20LOG
(R
2
/R
1
)
CLOSED LOOP
GAIN
HIP6015