LTC3872-1_15 Datasheet, PDF (8/20 Pages) Linear Technology – No RSENSE Current Mode Boost DC/DC Controller

LTC3872-1
Applications Information
Output Voltage Programming
The output voltage is set by a resistor divider according
to the following formula:
V_O
=
1.2V
•
₁₊
R2
R1


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 LTC3872-1 application circuit is shown on the front
page of this data sheet. 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 conduc-
tion mode (CCM), the duty cycle of the main switch is:
D=
^V_O ^{+ V}_D
 V_O +
– V_IN
V_D


where V_D 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 minimum on-time of
the LTC3872-1 is typically around 250ns. This time limits
the minimum duty cycle of the LTC3872-1. The maximum
duty cycle of the LTC3872-1 is around 90%. Although
frequency foldback feature of the regular LTC3872 enables
the user to obtain higher output voltage, it also increases
inductor ripple current.
The Peak and Average Input Currents
The control circuit in the LTC3872-1 is measuring the input
current (either by using the R_DS(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:
I_IN(MAX)
=
I_O(MAX)
1– D_MAX
The peak input current is:
I_IN(PEAK)
=
₁₊
χ
2
•
I_O(MAX)
1– D_MAX
Ripple Current I_L and the ^c Factor
The constant ^c 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 ^c = 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
LTC3872-1, 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 (I_L) 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 mode gain
and avoid subharmonic oscillation, it is recommended that
the ripple current in the inductor fall in the range of 20%
to 40% of the maximum average current. For example, if
the maximum average input current is 1A, choose an I_L
between 0.2A and 0.4A, and a value ^cbetween 0.2 and 0.4.
Inductor Selection
Given an operating input voltage range, and having chosen
the operating frequency and ripple current in the inductor,
38721f
8
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