1

(in Hz)

1

(in Hz)

(in Amps)

2Lfs

0.144 fs

L >

(

)

D

D'

2

-1

(

)

D

D'

+1

(in H)

LM5000

www.ti.com

SNVS176D – MAY 2004 – REVISED MARCH 2007

COMPENSATION

This section will present a general design procedure to help insure a stable and operational circuit. The designs

in this datasheet are optimized for particular requirements. If different conversions are required, some of the

components may need to be changed to ensure stability. Below is a set of general guidelines in designing a

stable circuit for continuous conduction operation (loads greater than 100mA), in most all cases this will provide

for stability during discontinuous operation as well. The power components and their effects will be determined

first, then the compensation components will be chosen to produce stability.

INDUCTOR SELECTION

To ensure stability at duty cycles above 50%, the inductor must have some minimum value determined by the

minimum input voltage and the maximum output voltage. This equation is:

(5)

This equation is only good for duty cycles greater than 50% (D>0.5).

(6)

The inductor ripple current is important for a few reasons. One reason is because the peak switch current will be

the average inductor current (input current) plus

reach its current limit during normal operation. The inductor must also be sized accordingly. It should have a

saturation current rating higher than the peak inductor current expected. The output voltage ripple is also affected

by the total ripple current.

DC GAIN AND OPEN-LOOP GAIN

Since the control stage of the converter forms a complete feedback loop with the power components, it forms a

closed-loop system that must be stabilized to avoid positive feedback and instability. A value for open-loop DC

gain will be required, from which you can calculate, or place, poles and zeros to determine the crossover

frequency and the phase margin. A high phase margin (greater than 45°) is desired for the best stability and

transient response. For the purpose of stabilizing the LM5000, choosing a crossover point well below where the

right half plane zero is located will ensure sufficient phase margin. A discussion of the right half plane zero and

checking the crossover using the DC gain will follow.

OUTPUT CAPACITOR SELECTION

The choice of output capacitors is somewhat more arbitrary. It is recommended that low ESR (Equivalent Series

Higher ESR capacitors may be used but will require more compensation which will be explained later on in the

section. The ESR is also important because it determines the output voltage ripple according to the approximate

equation:

(7)

After choosing the output capacitor you can determine a pole-zero pair introduced into the control loop by the

following equations:

(8)

(9)

ESR of the output capacitor is generally very high frequency if the ESR is small. If low ESR capacitors are used

it can be neglected. If higher ESR capacitors are used see the High Output Capacitor ESR Compensation

section.

Copyright © 2004–2007, Texas Instruments Incorporated

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