HIP6004E

FN4997 Rev 3.00

Page 9 of 14

November 10, 2015

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

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

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.

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 HIP6004E 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.

The response time to a transient is different for the application

of load and the removal of load. The following equations give

the approximate response time interval for application and

removal of a transient load:

1

2

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

=

1

2

+

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

=

1

2

+

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







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

=

1

2

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

=

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 8. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN

CLOSED LOOP

GAIN

I=

Fs x L

x