Constant On-T ime Buck Regulator
W ith One External and Two Internal Linear Regulators
A4405
18
Allegro MicroSystems, LLC
115 Northeast Cutoff
Worcester, Massachusetts 01615-0036 U.S.A.
1.508.853.5000; www.allegromicro.com
Application Information
Switcher 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 relation-
ship, the load current and IR drops, as well as input and output
voltages, affect the on-time of the converter. The formula that
governs switcher on-time is shown below:
=
tON VIN –
RDS(on)
×
IPEAK
+
Vf
TSW
×
{VVREG
+
[(RL
+
RSENSE)
×
IPEAK]
+
Vf }.
(7)
where Vf is the forward voltage on the diode DBUCK in the Typi-
cal Application Circuit schematic.
The effects of the voltage drop on the inductor and trace resis-
tance will 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 formula:
=
tON VIN –
RDS(on)
×
IPEAK
+
Vf
(1/ fSW)
×
(VVREG
+
RSENSE
×
IPEAK
)
+
Vf.
(8)
Be sure to use the worst-case sense voltage and forward voltage
of the diode DBUCK , including any effects due to temperature.
For an example: 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 0.20 V, RDS(ON) × IPEAK is 0.15 V, and the required frequency
is 2.2 MHz. Substituting into equation 8, we can solve for tON:
tON = 1 / 2.2 (MHz) ×
[(5.45+0.20+0.45) / (13.5 – 0.15 + 0.45)]
= 201 (ns) .
The formulas above describe how tON changes based on input
and load conditions. Because load changes are minimal and the
output voltage is fixed, the only factor that will affect 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 terminal is
derived from a resistor tied to VIN, which sets the on-time pro-
portional 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 . (9)
After the resistor is selected and a suitable tON is found, it must
be demonstrated that tON does not, under worst-case condi-
tions, exceed the minimum on-time or minimum off-time of
the converter. 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
below 8.3 V and above 6.5 V, refer to the Low Voltage Opera-
tion section.
Low Voltage Operation
The converter can run at very low input voltages; 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 minimum on-time,
tON(min), while 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 will not violate the minimum on-time or off-time
specifications. If the input voltage is between 8.3 and 31 V, the
converter maintains a constant period. When calculating worst
case on-times and off-times, make sure to use the highest switch-
ing frequency if the supply voltage is in that range.
When operating at voltages below 8.3 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 volt-
age operation, the IR drops must be considered for determining
on-time, so the complete equation (formula 8) should be used to
make sure the converter does not violate the timing specification.
Inductor Selection
Choosing the right inductor is critical to the correct operation of
the switcher. The converter is capable of running at frequencies
above 2 MHz, this makes it possible to use small inductor values,
which reduces cost and board area.
The inductor value is what determines the ripple current. It is
important to size the inductor so that under worst-case condi-
tions ITRIP equals IAV G , minus half of the ripple current, plus a
reasonable margin. If the ripple current is too large, the converter
will activate the current limit function. Typically peak-to-peak