(

)

(

)

OUT

D

IN

IN

OUT(crit)

OUT

D

SW

2

2

V

V

V

V

I

2

V

V

L

+

-

´

=

´

+

´ ¦

´

OUT

D

IN

OUT

SW

IN

2 (V

V

V ) L I

D

V

´

+

-

´ ´

´ ¦

=

OUT

D

IN

OUT

V

V

V

D

V

V

D

+

-

=

+

TPS55340

www.ti.com

SLVSBD4B – MAY 2012 – REVISED OCTOBER 2012

DETERMINING THE DUTY CYCLE

The input to output voltage conversion ratio of the TPS55340 is limited by the worst case maximum duty cycle of

89% and the minimum duty cycle which is determined by the minimum on-time of 77 ns and the switching

frequency. The minimum duty cycle can be estimated with Equation 7. With a 600 kHz switching frequency the

minimum duty cycle is 4%.

(7)

The duty cycle at which the converter operates is dependent on the mode in which the converter is running. If the

converter is running in discontinuous conduction mode (DCM), where the inductor current ramps to zero at the

end of each cycle, the duty cycle varies with changes of the load much more than it does when running in

continuous conduction mode (CCM). In continuous conduction mode, where the inductor maintains a minimum

dc current, the duty cycle is related primarily to the input and output voltages as computed below. Assume a 0.5

input of 12 V, the duty cycle is 51%.

(8)

At light loads the converter will operate in DCM. In this case the duty cycle is a function of the load, input and

output voltages, inductance and switching frequency as computed below. This can be calculated only after an

inductance is chosen in the following section. While operating in DCM with very light load conditions the duty

cycle demand will force the TPS55340 to operate with the minimum on time. The converter will then begin pulse

skipping which can increase the output ripple.

(9)

All converters using a diode as the freewheeling or catch component have a load current level at which they

transit from discontinuous conduction mode to continuous conduction mode. This is the point where the inductor

current just falls to zero during the off-time of the power switch. At higher load currents, the inductor current does

not fall to zero and diode and switch current assume a trapezoidal wave shape as opposed to a triangular wave

shape. The load current boundary between discontinuous conduction and continuous conduction can be found

for a set of converter parameters as follows.

(10)

For loads higher than the result of the Equation 10, the duty cycle is given by Equation 8. For loads less than the

results of Equation 10, the duty cycle is given Equation 9. For Equation 7 through Equation 10, the variable

definitions are as follows.

•

•

•

•

•

L is the inductor value in H

•

Unless otherwise stated, the design equations that follow assume that the converter is running in continuous

conduction mode, which typically results in a higher efficiency for the power levels of this converter.

SELECTING THE INDUCTOR (L1)

The selection of the inductor affects steady state operation as well as transient behavior and loop stability. These

factors make it the most important component in power regulator design. There are three important inductor

specifications: inductor value, DC resistance and saturation current. Considering inductor value alone is not

enough. Inductor values can have ±20% tolerance with no current bias. When the inductor current approaches

saturation level, the effective inductance can fall to a fraction of the zero current value.

Copyright © 2012, Texas Instruments Incorporated

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