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Rev. 1.10 - 11 -
I
Output Current and Selection of External Components
<Basic Circuit>
Inductor
Diode
C
L
Lx Tr
V
IN
V
OUT
I
OUT
ILxmax
ILxmin
Ton
Toff
T=1/fosc
Tf
IL
Discontinuous Mode
t
ILxmax
ILxmin
Ton
Toff
T=1/fosc
t
IL
Iconst
Continuous Mode
<Current through L>
GND
i1
i2
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 V
IN
, the current is V
IN
×
t/L.
Therefore, the electric power, P
ON
, which is supplied with input side, can be described as in next formula.
T
ON
ON
∫
V
IN
2
×
t/L dt
0
Formula 1
With the step-up circuit, electric power is supplied from power source also during off time. In this case, input current is
described as (V
OUT
-V
IN
)
×
t/L, therefore electric power, P
OFF
is described as in next formula.
Tf
P
OFF
=
∫
V
IN
×
(V
OUT
-V
IN
)
×
t/L dt
0
Formula 2
In this formula, Tf means the time of which the energy saved in the inductance is being emitted. Thus average
electric power, P
AV
is described as in the next formula.
T
ON
Tf
AV
IN
V
IN
×
(V
OUT
-V
IN
)
×
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.
V
IN
×
Ton/L=(V
OUT
-V
IN
)
×
Toff/L
Formula 4
Further, the electric power, P
AV
is equal to output electric power, V
OUT
×
I
OUT
, thus,
I
OUT
= f
OSC
×
V
IN
2
×
T
ON
2
/{2
×
L
×
(V
OUT
-V
IN
)}=V
IN
2
×
T
ON
/(2
×
L
×
V
OUT
)
When I
OUT
becomes more than formula 5, the current flows through the inductor, then the mode becomes
Formula 5