R1282D002A Datasheet, PDF (9/18 Pages) RICOH electronics devices division – 2CH PWM DC/DC CONTROLLER

R1282D002A
Output Current and Selection of External Components
There are also two modes, or discontinuous mode and continuous mode for the PWM step-down 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− VOUT the
current is (VIN− VOUT ) ×t/L.
Therefore, the electric power, P, which is supplied from the input side, can be described as in next formula.
Ton
∫ P= VIN ･(VIN−VOUT)･t/ L dt ........................................................................................ Formula 9
0
Thus average electric power in one cycle, PAV is described as in the next formula.
∫ ^{PAV = 1/(Ton+Toff)}
Ton
VIN
･(VIN−VOUT)･t/
L
dt
=
VINï½¥(VIN−VOUT)ï½¥Ton²
/
(2ï½¥L
(Ton+Toff))....
Formula
10
0
This electric power PAV equals to output electric power VOUT × IOUT, thus,
IOUT = VIN / VOUT× (VIN − VOUT )´Ton²/(2×L× (Ton+Toff)) ................................................. Formula 11
When IOUT increases and 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− VOUT ) ×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=ICONST+VOUT×Toff /(2×L)......................................................................................... Formula 13
In this moment, the peak current, ILXmax flowing through the inductor and the driver Tr. is described as
follows:
ILXmax= IOUT +VOUT×Toff/(2×L) ..................................................................................... Formula 14
With the formula 12,13, ILxmax is,
Toff=(1−VOUT/VIN)/fosc.................................................................................................. 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.
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