9

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

locating the poles and zeros of the compensation network:

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

7. Estimate Phase Margin - Repeat if Necessary.

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.

the error 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

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.

FIGURE 7. VOLTAGE-MODE BUCK CONVERTER

COMPENSATION DESIGN

REFERENCE

ESR

ERROR

AMP

PWM

DRIVER

(PARASITIC)

+

-

DACOUT

COMP

FB

HIP6004B

COMPARATOR

DRIVER

DETAILED COMPENSATION COMPONENTS

PHASE

+

-

+

-

OSC

F

LC

1

2

π x L

O

x C

O

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

=

F

ESR

1

2

π x ESR x C

O

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

=

F

Z1

1

2

π x R

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

=

F

Z2

1

2

π x R

1

R

3

+

() x C

3

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

=

F

P1

1

2

π x R

C

C

1

C

2

+

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







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

=

F

P2

1

2

π x R

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

=

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

HIP6004B