7

6. Check Gain against Error Amplifier’s Open-Loop Gain.

7. Estimate Phase Margin - Repeat if Necessary.

Compensation Break Frequency Equations

Figure 6 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 6. Using the above guidelines should give a

Compensation Gain similar to the curve plotted. The open

loop error amplifier gain bounds the compensation gain.

the error amplifier. The Closed Loop Gain is constructed on

the graph of Figure 6 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

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.

Refer to the evaluation board application note (available

soon) for a complete reference design schematic and bill of

materials for a typical Residential Gateway application.

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.

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.

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.

Output Inductor Selection

The output inductor is selected to meet the output voltage

ripple requirements and minimize the converter’s response

time to the load transient. The inductor value determines the

converter’s ripple current and the ripple voltage is a function

of the ripple current. The ripple voltage and current are

approximated by the following equations:

Increasing the value of inductance reduces the ripple current

and voltage. However, the large inductance values reduce

the converter’s response time to a load transient.

One of the parameters limiting the converter’s response to

a load transient is the time required to change the inductor

current. Given a sufficiently fast control loop design, the

ISL6431 will provide either 0% or 100% duty cycle in

response to a load transient. The response time is the time

required to slew the inductor current from an initial current

value to the transient current level. During this interval the

difference between the inductor current and the transient

current level must be supplied by the output capacitor.

Minimizing the response time can minimize the output

capacitance required.

F

Z1

1

2

π xR

------------------------------------

=

F

Z2

1

2

π xR

1

R

3

+

() xC

3

-------------------------------------------------------

=

F

P1

1

2

π xR

C

C

1

C

2

+

----------------------







---------------------------------------------------------

=

F

P2

1

2

π xR

------------------------------------

=

100

80

60

40

20

0

-20

-40

-60

10M

1M

100K

10K

1K

100

10

OPEN LOOP

ERROR AMP GAIN

20LOG

COMPENSATION

FREQUENCY (Hz)

GAIN

20LOG

MODULATOR

GAIN

FIGURE 6. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN

CLOSED LOOP

GAIN

∆I =

FsxL

x

ISL6431