LTC3704 Datasheet, PDF (13/28 Pages) Linear Technology – Wide Input Range, No RSENSE Positive-to-Negative DC/DC Controller

LTC3704
APPLICATIO S I FOR ATIO
Applications Circuits
A simple positive-to-negative application circuit for the
LTC3704 is shown in Figure 1. The basic operation of this
circuit is shown in Figure 9. During the on-time the
inductor currents flow through the switch, and during the
off-time these currents flow through the output diode. The
use of inductors in series with both the input and output
results in continuous currents in these capacitors, result-
ing in low input and output noise. Discontinuous currents
flow in the switch, the coupling capacitor, and the diode.
V_IN
+
L1
L2 +
V_OUT
R_L
+–
ON
a) Current Flow During The Switch On-Time
V_IN
+
L1
L2
+
V_OUT
R_L
+–
OFF
3704 F09
b) Current Flow During The Switch Off-Time
Figure 9. Positive-to-Negative Converter Operation
Duty Cycle Considerations
For the positive-to-negative converter shown in Figure 1,
the duty cycle of the main switch in CCM is:
D = ^VO
V_O – V_IN
where V_O is a negative number. The maximum output
voltage for this converter (in CCM) is:
V_O(MAX)
=
V_IN(MIN)
•
D_MAX
1– D_MAX
The maximum duty cycle capability of the LTC3704 is
typically 92%.
Peak and Average Input and Switch Currents
The control loop in the LTC3704 is measuring the peak
switch 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 switch in order to dimension the power MOSFET and
inductors properly. Based on the fact that, ideally, the
input power is equal to the output power, the maximum
average input current is:
I_IN(MAX)
=
– I_O(MAX)
•
D_MAX
1– D_MAX
where I_O(MAX) is a negative number. The peak input
current is:
I_IN(PEAK)
=
−1+
χ
2

• I_O(MAX)
•
D_MAX
1– D_MAX
In a positive-to-negative converter, however, the switch
current is equal to I_IN + I_O, so the maximum average switch
current is:
I_SW(MAX)
=
−I_O(MAX)
•
1−
1
D_MAX
and the peak switch current is:
I_SW(PEAK)
=
−1+
χ
2

• I_O(MAX)
•
1–
1
D_MAX
The maximum duty cycle, D_MAX, should be calculated at
minimum V_IN.
Ripple Current ∆I_L and the ‘^χ’ Factor
The constant ‘^χ’ in the equation above represents the
percentage peak-to-peak total ripple current in the induc-
tor, 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 converter operating in CCM, slope
compensation must be added for duty cycles above 50%
in order to avoid subharmonic oscillation. For the LTC3704,
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
sn3704 3704fs
13