Ricoh RH5RH13B - Manual (Page 15)

11
RH5RH
When the output current (I OUT ) is relatively small, topen
the energy charged in the inductor during the time period of ton is discharged in its entirely during the time peri-
od of toff, so that ILmin becomes zero (ILmin=0). When I OUT is gradually increased, topen eventually becomes
equal to toff (topen=toff), and when I OUT is further increased. ILmin becomes larger than zero (ILmin >0). The
former mode is referred to as the discontinuous mode and the latter mode is referred to as the continuous mode.
In the continuous mode, when Equation 1 is solved for ton and the solution is tonc,
tonc =T · (1–V IN /V OUT ) ................................................................................................Equation 2
When ton
• Output Current in Discontinuous Mode
In the discontinuous mode, when LxTr is on, the energy P ON charged in the inductor is provided by Equation 3
as follows :
P ON =
∫
0
ton V IN · IL (t) dt =
∫
0
ton
(V IN
2 · t/L) dt
=V IN
2 · ton 2 /(2 · L).................................................................................................Equation 3
In the case of the step-up DC/DC converter, the energy is also supplied from the input power source at the time
of OFF.
Thus, P OFF =
∫
0
topen V IN · IL (t) dt =
∫
0
topen ((V OUT –V IN ) · t/L)dt
=V IN · (V OUT –V IN ) · topen 2 /(2 · L)
Here, topen=V IN · ton/(V OUT –V IN ) from Equation 1, and when this is substituted into the above equation.
=V IN
3 · ton 2 /(2 · L · (V OUT –V IN )..........................................................................Equation 4
Input power is (P ON +P OFF )/T. When this is converted in its entirely to the output.
P IN =(P ON +P OFF )/T=V OUT · I OUT =P OUT
.....................................................................Equation 5
Equation 6 can be obtained as follows by solving Equation 5 for I OUT by substituting Equations 3 and 4 into
Equation 5 :
I OUT =V IN
2 · ton 2 /(2 · L · T · (V OUT –V IN )).....................................................................Equation 6
The peak current which flows through L · LxTr · SD is
ILmax=V IN · ton/L ...................................................................................................... Equation 7