8
Figure 8 highlights the voltage-mode control loop for a buck
converter. The output voltage (V
OUT
) 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 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
V
OSC.
Modulator Break Frequency Equations
The compensation network consists of the error amplifier
(internal to the HIP6008) 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:
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 9 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 9. 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 9 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 and slow the current load rate seen by the bulk
capacitors. 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
components. 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
μ
F ceramic
capacitors in the 1206 surface-mount package.
F
LC =
L
O
2
π
C
O
--------------------------------------
F
ESR
=
O
)
-------------------------------------------
1
=
---------------------------------
F
P1
=
2
π
R2
---------------------
-----------------------------------------------------
2
=
----------------------------------------------------
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
20LOG
(R2/R1)
F
LC
F
ESR
COMPENSATION
GAIN
G
FREQUENCY (Hz)
20LOG
(V
IN
/
V
OSC
)
MODULATOR
GAIN
FIGURE 9. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN
CLOSED LOOP
GAIN
HIP6008