FAN8048 データシートの表示（PDF） - Fairchild Semiconductor
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FAN8048 Datasheet PDF : 34 Pages
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FAN8048
3-10. Boost (Step-up) converter mode (VIN < VSYS)
The step-up converter keeps the average output voltage VSYS higher than DC input voltage VIN, and its circuit diagram is
shown in Figure 15-a. Figure 15-b shows an operational waveform in case inductor current is steady-state. Since in steady-
state, the integral of the inductor voltage over one time period to zero, this can be expressed by the following formula:
(VIN
×t
ON
) + ((VIN
− VSYS ) × tOFF
)
=
0
From the above formula, a redefined formula is as follows after dividing by cycle Ts:
VSYS = TS = 1
VIN tOFF 1 − D
VSYS
=
1
1
−D
×
VIN
[V
]
Assuming a lossless circuit, input and output power are the same (Pin=Po) and the above formula can be redefined as follows:
VIN I IN = VSYS IO
This can be expressed as follows using input/output current and duty ratio:
IO = (1− D)
I IN
In the boundary condition of continuous mode and discontinuous mode, the inductor's average current is defined as follows:
iLB
=
1
2 iL, peak
=
1
2
VIN
L
TON
= TSVSYS D(1 − D)2
2L
From the above formula, since inductor current and input current are the same (iIN=iL), the average output current at the edge
of continuous conduction mode can be redefined as below:
I OB
=
TS
×VSYS
2L
D(1− D)2
In a practical synchronous step-up converter, the parasitic elements are due to the loss associated with the inductor, the capaci-
tor and the switches; however, in this formula we assume that all components are at ideal conditions.In the continuous mode,
as the output current and peak-peak voltage ripple are considered to be constant, this formula can be redefined as below:
∆VSYS
=
∆Q
C
=
IO DTS
C
= VSYS
R
DTS
C
∆VSYS = DTS
VSYS RC
Where,
R = VSYS [Ω]
IO
21
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