8

The modulator transfer function is the small-signal transfer

peak-to-peak oscillator voltage

Modulator Break Frequency Equations

The compensation network consists of the error amplifier

a closed loop transfer function with the highest 0dB crossing

180 degrees

. 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

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.

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

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

µF ceramic

capacitors in the 1206 surface-mount package.

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

F

LC

1

2

π

L

O

C

O

•

•

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

=

F

ESR

1

2

π ESR C

O

•

•

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

=

F

Z1

1

2

π R2

•

C1

•

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

=

F

Z2

2

π

R1

R3

+

() C3

•

•

=

F

P1

1

2

π R

2

C1

C2

•

C1

C2

+

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





•

•

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

=

F

P2

1

2

π R3

•

C3

•

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

=

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 9. ASYMPTOTIC BODE PLOT OF CONVERTER GAIN

CLOSED LOOP

GAIN

HIP6004