LT3757 datasheet(23/38 Pages) AD

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LTC7840

Rev 0

For more information www.analog.com

Maximum Duty Cycle Limitations

Another operating extreme occurs at high duty cycle,

when the input voltage is low and the output voltage is

high. In this case:

DMAX =

VO + VF – VIN(MIN)

VO + VF

⎛

⎝⎜

⎞

⎠⎟

A single-ended boost converter needs a minimum off-

time every cycle in order to allow energy transfer from

the input inductor to the output capacitor. This minimum

off-time translates to a maximum duty cycle for the con-

verter. The equation above can be rearranged to obtain

the maximum output voltage for a given minimum input

or maximum duty cycle.

VO(MAX) =

VIN

1– DMAX

– VF

The equation for DMAX above can be used as an initial

guideline for determining the maximum duty cycle of the

application circuit. However, losses in the inductor, input

and output capacitors, the power MOSFETs, the sense

resistors and the controller (gate drive losses) all contrib-

ute to an increasing of the duty cycle. The effect of these

losses will be to decrease the maximum output voltage

for a given minimum input voltage.

After the initial calculations have been completed for an

application circuit, it is important to build a prototype of

the circuit and measure it over the entire input voltage

range, from light load to full load, and over temperature,

in order to verify proper operation of the circuit.

Peak and Average Input Currents

The control circuit in the LTC7840 measures the input

current (by means of resistors in the sources of the power

MOSFETs), so the output current needs to be reflected

back to the input in order to dimension the power

MOSFETs properly. Based on the fact that, ideally, the

output power is equal to the input power, the maximum

average input current is:

IIN(MAX) =

IO(MAX)

1– DMAX

The peak current in each inductor is:

IIN(PK) =

• 1

+ χ

⎛

⎝⎜

⎞

⎠⎟ •

IO(MAX)

1– DMAX

where n represents the number of phases and χ repre-

sents the percentage peak-to-peak ripple current in the

inductor. For example, if the design goal is to have 30%

ripple current in the inductor, then χ = 0.30, and the peak

current is 15% greater than the average.

Inductor Selection

Given an input voltage range, operating frequency and

ripple current, the inductor value can be determined using

the following equation:

L =

VIN(MIN)

∆IL • f

• DMAX

where:

∆IL =

•

IO(MAX)

1– DMAX

Choosing a larger value of ∆IL allows the use of a lower

value inductor but results in higher output voltage ripple,

greater core losses, and higher ripple current ratings for

the input and output capacitors. A reasonable starting

point is 30% ripple current in the inductor (χ = 0.3), or:

∆IL =

0.3

•

IO(MAX)

1– DMAX

The inductor saturation current rating needs to be higher

than the worst-case peak inductor current during an

overload condition. If IO(MAX) is the maximum rated load

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