
6
FN9083.2
January 20, 2005
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 ISL6520B) 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 4. 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 5 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 5. 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 graph of Figure 5 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 components and loads are capable of producing 
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.
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 
usefulness 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 
impedance with frequency to select a suitable component. In 
most cases, multiple electrolytic capacitors of small case size 
perform better than a single large case capacitor.
FLC
2
π
 x LO x CO
--------------------1
=
FESR
2
 x ESR x CO
-------------------1
=
F
Z1
π
 x R
2
 x C
1
2
=
F
Z2
+
π
 x R
1
R
3
)
 x C
3
2
=
F
P1
2
π
 x R
2
 x 
C
 x C
2
1
+
C
2
C
---------------------------1
=
F
P2
π
 x R
3
 x C
3
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
(R
2
/R
1
)
F
LC
F
ESR
COMPENSATION
GAIN
CLOSED LOOP
 GAIN
G
FREQUENCY (Hz)
20LOG
(V
IN
/
V
OSC
)
MODULATOR
GAIN
FIGURE 5. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN
ISL6520B