20059117

Basic Application Circuit

DUTY CYCLE

The maximum duty cycle of the switching regulator deter-

mines the maximum boost ratio of output-to-input voltage

that the converter can attain in continuous mode of opera-

tion. The duty cycle for a given boost application is defined

as:

This applies for continuous mode operation.

INDUCTANCE VALUE

The first question we are usually asked is: “How small can I

make the inductor?” (because they are the largest sized

component and usually the most costly). The answer is not

simple and involves trade-offs in performance. Larger induc-

tors mean less inductor ripple current, which typically means

less output voltage ripple (for a given size of output capaci-

tor). Larger inductors also mean more load power can be

delivered because the energy stored during each switching

cycle is:

E = L/2 X (lp)

2

Where “lp” is the peak inductor current. An important point to

observe is that the LM2731 will limit its switch current based

on peak current. This means that since lp(max) is fixed,

increasing L will increase the maximum amount of power

available to the load. Conversely, using too little inductance

may limit the amount of load current which can be drawn

from the output.

Best performance is usually obtained when the converter is

operated in “continuous” mode at the load current range of

interest, typically giving better load regulation and less out-

put ripple. Continuous operation is defined as not allowing

the inductor current to drop to zero during the cycle. It should

be noted that all boost converters shift over to discontinuous

operation as the output load is reduced far enough, but a

larger inductor stays “continuous” over a wider load current

range.

To better understand these trade-offs, a typical application

circuit (5V to 12V boost with a 10 µH inductor) will be

analyzed. We will assume:

V

Since the frequency is 1.6 MHz (nominal), the period is

approximately 0.625 µs. The duty cycle will be 62.5%, which

means the ON time of the switch is 0.390 µs. It should be

noted that when the switch is ON, the voltage across the

inductor is approximately 4.5V.

Using the equation:

V = L (di/dt)

We can then calculate the di/dt rate of the inductor which is

found to be 0.45 A/µs during the ON time. Using these facts,

we can then show what the inductor current will look like

during operation:

20059118

10 µH Inductor Current,

5V–12V Boost (LM2731X)

During the 0.390 µs ON time, the inductor current ramps up

0.176A and ramps down an equal amount during the OFF

time. This is defined as the inductor “ripple current”. It can

also be seen that if the load current drops to about 33 mA,

the inductor current will begin touching the zero axis which

means it will be in discontinuous mode. A similar analysis

can be performed on any boost converter, to make sure the

ripple current is reasonable and continuous operation will be

maintained at the typical load current values.

MAXIMUM SWITCH CURRENT

The maximum FET switch current available before the cur-

rent limiter cuts in is dependent on duty cycle of the appli-

cation. This is illustrated in the graphs below which show

typical values of switch current for both the "X" and "Y"

versions as a function of effective (actual) duty cycle:

www.national.com

13