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LTC3872

3872fa

APPLICATIO S I FOR ATIO

Output Voltage Programming

The output voltage is set by a resistor divider according

to the following formula:

O =+

⎛

⎝⎜

⎞

⎠⎟

.•

The external resistor divider is connected to the output

as shown in the Typical Application on the front page,

allowing remote voltage sensing.

Application Circuits

A basic LTC3872 application circuit is shown on the front

page of this datasheet. External component selection is

driven by the characteristics of the load and the input

supply.

Duty Cycle Considerations

For a boost converter operating in a continuous conduction

mode (CCM), the duty cycle of the main switch is:

⎛

⎝⎜

⎞

⎠⎟

–

where VD is the forward voltage of the boost diode. For

converters where the input voltage is close to the output

voltage, the duty cycle is low and for converters that develop

a high output voltage from a low voltage input supply, the

duty cycle is high. The LTC3872 has a built-in circuit that

allows the extension of the maximum duty cycle while

keeping the minimum switch off time unchanged. This

is accomplished by reducing the clock frequency when

the duty cycle is close to 80%. This function allows the

user to obtain high output voltages from low input supply

voltages. The shift of frequency with duty cycle is shown

in the Typical Performance Characteristics section.

The Peak and Average Input Currents

The control circuit in the LTC3872 is measuring the input

current (either by using the RDS(ON) of the power MOSFET

or by using a sense resistor in the MOSFET source), so

the output current needs to be reﬂected back to the input

in order to dimension the power MOSFET properly. Based

on the fact that, ideally, the output power is equal to the

input power, the maximum average input current is:

The peak input current is

IN MAX

OMAX

MAX

IN PEAK

OMAX

MAX

()

–

•

–

⎛

⎝⎜

⎞

⎠⎟

Ripple Current IL and the χ Factor

The constant χ in the equation above represents the

percentage peak-to-peak ripple current in the inductor,

relative to its maximum value. For example, if 30% ripple

current is chosen, then χ = 0.30, and the peak current is

15% greater than the average.

For a current mode boost regulator operating in CCM,

slope compensation must be added for duty cycles above

50% in order to avoid subharmonic oscillation. For the

LTC3872, this ramp compensation is internal. Having an

internally ﬁxed ramp compensation waveform, however,

does place some constraints on the value of the inductor

and the operating frequency. If too large an inductor is

used, the resulting current ramp (IL) will be small relative

to the internal ramp compensation (at duty cycles above

50%), and the converter operation will approach voltage

mode (ramp compensation reduces the gain of the current

loop). If too small an inductor is used, but the converter

is still operating in CCM (continuous conduction mode),

the internal ramp compensation may be inadequate to

prevent subharmonic oscillation. To ensure good current

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