R1280D002X Datasheet, PDF (10/26 Pages) RICOH electronics devices division – 2CH PWM DC/DC Controller

Discontinuous Mode
<Current through L>
IL
IL
ILxmax
Continuous Mode
ILxmax
ILxmin
ILxmin
Tf
Iconst
t
t
Ton
Toff
T=1/fosc
Ton
Toff
T=1/fosc
Step 1. Lx Tr. turns on, current, IL=i1 flows, energy is charged in L. In proportion to the on time, Ton, of Lx Tr. IL=i1
increases from IL=ILxmin=0 and reaches ILxmax.
Step 2. When the Lx Tr. turns off, L turns on Shottky diode (SD) and flow IL=i2 to maintain IL = ILxmax.
Step 3. IL=i2 decreases gradually, after Tf passes, IL=ILxmin=0 is true, then SD turns off. Note that in the case of
continuous mode, before IL=ILxmin=0 is true, Toff passes and next cycle starts, then Lx Tr. turns on. In this case,
ILxmin>0, therefore IL increases from IL=ILxmin>0.
With the PWM controller, switching time (fosc) in the time unit is fixed, and by controlling Ton, output voltage is
maintained.
s Output Current and Selection of External Components
There are also two modes, or discontinuous mode and continuous mode for the PWM inverting switching regulator
depending on the continuous characteristic of inductor current.
During on time of the transistor, when the voltage added on to the inductor is described as VIN, the current is VIN ×t/L.
Therefore, the electric power, P, which is supplied with input side, can be described as in next formula.
TON
P=∫VIN2×t/L dt
0
Formula 9
Thus average electric power in one cycle, PAV is described as in the next formula.
TON
PAV=1/(Ton +Toff)×∫VIN2×t/L dt =VIN2×Ton2/(2×L×(Ton + Toff))
0
Formula 10
This electric power PAV equals to output electric power VOUT×IOUT, thus,
IOUT = fOSC × VIN²Ã—TON²/(2×L ×VOUT)
Formula 11
When IOUT becomes more than formula 11, the current flows through the inductor continuously, then the mode
becomes continuous. In the continuous mode, the deviation of the current equals between Ton and Toff, therefore,
VIN×Ton/L=VOUT×Toff/L
Formula 12
In this moment, the current flowing continuously through L, is assumed as Iconst, IOUT is described as in the next
formula:
IOUT = fOSC ×VIN²Ã—TON²/(2×L×VOUT)+Ton/(Ton + Toff)×VIN× Iconst /VOUT
Formula 13
In this moment, the peak current, ILxmax flowing through the inductor and the driver Tr. is described as follows:
ILxmax = Iconst +VIN×Ton/L
Formula 14
With the formula 12,13, ILxmax is,
ILxmax = (Ton+Toff)/Toff×IOUT+VIN×Ton/(2×L)
Formula 15
Therefore, peak current is more than IOUT. Considering the value of ILxmax, the condition of input and output, and
external components should be selected.
In the formula 14, peak current ILxmax at discontinuous mode can be calculated. Put Iconst=0 in the formula.
The explanation above is based on the ideal calculation, and the loss caused by Lx switch and external components
is not included. The actual maximum output current is between 50% and 80% of the calculation. Especially, when the
ILx is large, or VIN is low, the loss of VIN is generated with the on resistance of the switch. As for VOUT, Vf (as much as
0.3V) of the diode should be considered.
Rev.1.10
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