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A4407

2.2 MHz Constant On-Time Buck Regulator With Two External and Two Internal Linear Regulators

Allegro MicroSystems 

A4407

2.2 MHz Constant On-Time Buck Regulator

With Two External and Two Internal Linear Regulators

Application Information

Component Selection

Buck On-Time and Switching Frequency

In order for the switcher to maintain regulation, the energy that is

transferred to the inductor during the on-time must be transferred

to the capacitor during the off-time. Because of this relationship,

the load current and IR drops, as well as the input and output

voltages, affect the on-time of the converter. The equation that

governs switcher on-time is:

tON

=

TSW [VREG + (RL × Ipeak) +Vf + (RSENSE × Ipe

VIN + Vf – (RDS(on) × Ipeak)

(8)

The effects of the voltage drop on the inductor and trace resis-

tance affect the switching frequency. However, the frequency

variation due to these factors is small, and is covered in the varia-

tion of the switcher period, which is ±25% of the target. Remov-

ing these current dependant terms simplifies the equation:

tON

=

VREG + Vf + (RSENSE × Ipeak)

VIN + Vf – (RDS(on) × Ipeak)

×

1

fSW

(9)

Be sure to use worst-case sense voltage and forward voltage

of the diode including any effects due to temperature. For the

example provided, assume a 1 A converter with a supply voltage

of 13.5 V. The output voltage is 5.45 V, Vf is 0.45 V, RSENSE ×

Ipeak is 0.34 V, RDS(on) × Ipeak is 0.15 V, and the target frequency

is 2.2 MHz. Applying equation 9, we can solve for tON:

5.45 (V) + 0.45 (V) + 0.34 (V)

1

tON = 13.5 (V) + 0.45 (V) – 0.15 (V) × 2.2 (MHz)

= 205 ns

The formulas above describe how tON changes based on input and

load conditions. Because load changes are minimal and the out-

put voltage is fixed, the only factor that affects the on-time is the

input voltage. The converter is able to maintain a constant period

over a varying supply voltage because the on-time changes based

on the input voltage. The current into the TON pin is derived

from a resistor tied to VIN, which sets the on-time proportional to

the supply voltage. Selecting the resistor value based on the tON

calculated above is done using the following formula:

RTON

=

VIN × (tON – 5 (ns) )

6.36 × 10–12

(10)

When the resistor is selected and a suitable tON is found, tON must

be demonstrated that it does not, under worst-case conditions,

exceed the minimum on-time or minimum off-time of the con-

verter. The minimum on-time occurs at maximum input voltage

and minimum load. The maximum off-time occurs at minimum

supply voltage and maximum load. For supply voltages above

6.5 V but below 8.6 V, refer to the section entitled Low Voltage

Operation.

Low Voltage Operation

The converter can run at very low input voltages; for example,

with a 5.25 V output, the minimum input supply can be as low

as 5.5 V. When operating at high frequencies, the on-time of the

converter must be very short because the available period is short.

At high input voltages the converter should not violate the mini-

mum on-time, tON(min) , and at low input voltages the converter

should not violate the minimum off-time, tOFF(min) . Rather than

limit the supply voltage range, the converter solves this problem

by automatically increasing the period. With the period extended,

the converter does not violate the minimum on-time or off-time

specifications. If the input voltage is between 8.6 and 31 V, the

converter will maintain a constant period. When calculating worst

case on- and off-times, make sure to use the highest switching

frequency if the supply voltage is in that range.

When operating at voltages below 8.6 V, additional care must

be taken when selecting the inductor and diode. At low voltages

the maximum current may be limited, due to the IR drops in the

current path. When selecting external components for low voltage

operation, the IR drops must be considered when determining

on-time, so the complete formula (equation 8) should be used to

make sure the converter does not violate the timing specification.

Inductor Selection

Choosing the proper inductor is critical to the correct operation of

the switcher. The converter is capable of running at frequencies

above 2 MHz, making it possible to use small inductor values and

reducing cost and board area.

The inductor value determines the ripple current. It is important

to size the inductor so that under worst-case conditions the over-

current threshold equals the average current minus half the ripple

current plus reasonable margin. When the ripple current is too

large, the converter reaches current limit. Typically, peak-to-peak

ripple current should be limited to 20% to 25% of the maximum

average load current.

Allegro MicroSystems, Inc.

19

115 Northeast Cutoff

Worcester, Massachusetts 01615-0036 U.S.A.

1.508.853.5000; www.allegromicro.com

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