LM5642 datasheet(21/24 Pages) NSC

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Loop Compensation (Continued)

As shown in Figure 11, the control-output transfer function

consists of one pole (fp), one zero (fz), and a double pole at

fn (half the switching frequency). The following can be done

to create a -20dB /decade roll-off of the loop gain: Place the

first pole at 0Hz, the first zero at fp, the second pole at fz,

and the second zero at fn. The resulting output-control trans-

fer function is shown in Figure 12.

The control-output corner frequencies, and thus the desired

compensation corner frequencies, can be determined ap-

proximately by the following equations:

(29)

(30)

Since fp is determined by the output network, it will shift with

loading (Ro). It is best to use a minimum Iout value of

approximately 100mA when determining the maximum Ro

value.

Example: Re=20m

Ω, Co=100uF, Romax=5V/100mA=50Ω:

(31)

(32)

First determine the minimum frequency (fpmin) of the pole

across the expected load range, then place the first compen-

sation zero at or below that value. Once fpmin is determined,

Rc1 should be calculated using:

(33)

Where B is the desired gain in V/V at fp (fz1), gm is the

transconductance of the error amplifier, and R1 and R2 are

the feedback resistors. A gain value around 10dB (3.3v/v) is

generally a good starting point.

Example: B=3.3v/v, gm=650m, R1=20K

Ω, R2=60.4KΩ:

(34)

Bandwidth will vary proportional to the value of Rc1. Next,

Cc1 can be determined with the following equation:

(35)

Example: fpmin=695Hz, Rc1=20K

Ω:

(36)

The compensation network (Figure 13) will also introduce a

low frequency pole which will be close to 0Hz.

A second pole should also be placed at fz. This pole can be

created with a single capacitor Cc2 and a shorted Rc2 (see

Figure 13). The minimum value for this capacitor can be

calculated by:

(37)

Cc2 may not be necessary, however it does create a more

stable control loop. This is especially important with high

load currents and in current sharing mode.

Example: fz=80kHz, Rc1= 20K

Ω:

(38)

A second zero can also be added with a resistor in series

with Cc2. If used, this zero should be placed at fn, where the

control to output gain rolls off at -40dB/dec. Generally, fn will

be well below the 0dB level and thus will have little effect on

stability. Rc2 can be calculated with the following equation:

(39)

20060114

FIGURE 11. Control-Output Transfer Function

20060112

FIGURE 12. Output-Control Transfer Function

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