LM2633 datasheet(31/40 Pages) NSC

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Control Loop Design (Continued)

(18)

Where

D’ = 1−D

(19)

(20)

e =Vm •f

(21)

(22)

i =Rds •ρ

(23)

e is the correction ramp slope, Sn is the on-time slope of the

current sense waveform, V

m is the peak-peak value of the

correction ramp, f is the PWM frequency, V

in is input voltage,

i is the transfer resistance from inductor current to ramp

voltage, R

ds is the top FET on-resistance and ρ is the gain of

the current sense amplifier.

The coefficient of the first current source is:

(24)

and the coefficient of the second current source is:

(25)

The output capacitance of the PWM switch is:

(26)

The DC resistance of the FET switches and of the inductor is

not included here because its value is usually much smaller

than the load resistance.

Control-Output Transfer Function

The control (COMPx pin) voltage in a peak-current mode

scheme such as that of the LM2633 is the current command.

At any instant that voltage determines the level of the induc-

tor current (from an average-model point of view). The

control-output transfer function is a description of the

small-signal behavior of the power stage and is obtained by

letting the small signal component of the input voltage be

zero. The expression for the control-output transfer function

is:

(27)

Where

α =LC

sC(R+Re)

(28)

β =g

oLC(R + Re)+Cs(CRRe + L)

(29)

γ = C(R+R

e)+go(CRRe +L)+CsR

(30)

δ = 1+g

(31)

For a reasonable design, the output filter has large attenua-

tion at large complex frequencies (i.e. large s values). At s

values where 1/sC is smaller than R

e, the power stage can

be reduced to the one shown in

Figure 8.

The transfer function can be re-written as:

(32)

Where

(33)

(34)

All the R

e terms are omitted in the denominator because

their values are negligible compared to other terms.

Since the denominator of the control-output transfer function

is a third-order polynomial, and its coefficients are positive

real numbers, the transfer function either has one real pole

and two complex poles that are complex conjugates or has

three real poles. Thus it can be approximately written in the

following format:

(35)

Where

(36)

and

(37)

where

(38)

and

200008D5

FIGURE 8. Simplified Power Stage at High Frequencies

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