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.
ON
T
Tf
2
PAV=1/(Ton+Toff)×{∫VIN ×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,
2
2
2
IOUT = fOSC × VIN ×TON /{2×L ×(VOUT-VIN)}=VIN ×TON/(2×L×VOUT)
Formula 5
When IOUT becomes more than formula 5, the current flows through the inductor, then the mode becomes
continuous. The continuous current through the inductor is described as Iconst, then,
2
2
IOUT = fOSC ×VIN ×tON /(2×L×(VOUT-VIN))+VIN×Iconst/VOUT
Formula 6
In this moment, the peak current, ILxmax flowing through the inductor and the driver Tr. is described as follows:
ILxmax = Iconst +VIN×Ton/L
With the formula 4,6, and ILxmax is,
ILxmax = VOUT/VIN×IOUT+VIN×Ton/(2×L)
Formula 7
Formula 8
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 7, 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.
■ Operation of Inverting DC/DC converter and Output Current
Inverting DC/DC converter saves energy during on time of Lx transistor, and supplies the energy to output during off
time, output voltage opposed to input voltage is obtained.
Lx Tr
OUT
I
Diode
VOUT
IN
V
i1
i2
CL
Inductor
GND
Rev. 1.10
- 9 -
RICOH [ RICOH ELECTRONICS DEVICES DIVISION ]
