'iL =

(in Amps)

VIND

2Lfs

VINRDSON

0.144 fs

L >

(

)

D

D'

2

-1

(

)

D

D'

+1

(in H)

Hz

1

2S(RC + RO)CC

fPC =

Hz

1

fZC =

2SRCCC

LM5000

SNVS176D – MAY 2004 – REVISED MARCH 2007

www.ti.com

To keep a current programmed control converter stable above duty cycles of 50%, the inductor must meet

certain criteria. The inductor, along with input and output voltage, will determine the slope of the current through

the inductor (see Figure 22 (a)). If the slope of the inductor current is too great, the circuit will be unstable above

duty cycles of 50%.

The LM5000 provides a compensation pin (COMP) to customize the voltage loop feedback. It is recommended

that a series combination of RC and CC be used for the compensation network, as shown in Figure 19. The

series combination of RC and CC introduces pole-zero pair according to the following equations:

(3)

where

•

RO is the output impedance of the error amplifier, 850kΩ

(4)

For most applications, performance can be optimized by choosing values within the range 5k

Ω ≤ RC ≤ 20kΩ and

680pF

≤ CC ≤ 4.7nF.

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:

where

•

fs is the switching frequency

•

D is the duty cycle

•

RDSON is the ON resistance of the internal switch

(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

ΔiL. Care must be taken to make sure that the switch will not

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.

12

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