R1282D002A Datasheet, PDF (6/18 Pages) RICOH electronics devices division – 2CH PWM DC/DC CONTROLLER

R1282D002A
Output Current and Selection of External Components
Output Current of Step-up Circuit and External Components
There are two modes, or discontinuous mode and continuous mode for the PWM step-up 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, PON, which is supplied with input side, can be described as in next formula.
Ton
∫ PON = VIN2 × t/L dt ...................................................................................................Formula 1
0
With the step-up circuit, electric power is supplied from power source also during off time. In this case, input
current is described as (VOUT−VIN)×t/L, therefore electric power, POFF is described as in next formula.
Tf
∫ POFF = VIN × (VOUT − VIN)t/L dt ...................................................................................Formula 2
0
In this formula, Tf means the time of which the energy saved in the inductance is being emitted. Thus average
electric power, PAV is described as in the next formula.
Ton
Tf
∫ ∫ ^{PAV = 1/(Ton + Toff) × { VIN2 × t/L dt + VIN × (VOUT − VIN)t/L dt} ............................Formula 3}
0
0
In PWM control, when Tf=Toff is true, the inductor current becomes continuos, then the operation of switching
regulator becomes continuous mode.
In the continuous mode, the deviation of the current is equal between on time and off time.
VIN×Ton/L=(VOUT−VIN)×Toff/L ..........................................................................................Formula 4
Further, the electric power, PAV is equal to output electric power, VOUT×IOUT, thus,
IOUT = fOSC × VIN²Ã—Ton²/{2×L ×(VOUT−VIN)}=VIN²Ã—Ton/(2×L×VOUT)......................................Formula 5
When IOUT becomes more than VIN×Ton×Toff/(2×L×(Ton+Toff)), the current flows through the inductor, then the
mode becomes continuous. The continuous current through the inductor is described as
Iconst, then,
IOUT = fOSC×VIN² ×Ton²/(2×L×(VOUT−VIN))+VIN×Iconst/VOUT ...............................................Formula 6
6