EE462L, Power Electronics, DC-DC Boost Converter Version ... - ECS

EE462L, Power Electronics, DC-DC Boost Converter
Version Oct. 3, 2011
diL
dt
vL
Vin
−Vout
= = , DT < t < T , (3)
L L
and the inductor is “discharging.” The inductor voltage is shown in Figure 3.
V in
0
Vin − V out
Figure 3. Inductor Voltage in Continuous Conduction
Because of the steady-state inductor principle, the average voltage v L across L is zero. Since v L
has two states, both having constant voltage, the average value is
( V )
in DT + ( Vin
−Vout
T
)(1 − D)
T
= 0 ,
so that
Vin D + Vin
−Vout
−VinD
+ Vout
D = 0 .
Simplifying the above yields the final input-output voltage expression
Vout
Vin
= . (4)
1 − D
The graph of i L is shown in Figure 4.
Inductor Current in Continuous Conduction
Δ I
T
i
L max
i Lavg
i
L min
= i
= i
Lavg
Lavg
ΔI
+
2
ΔI
−
2
DT
(1–D)T
Figure 4. Inductor Current Waveform for Continuous Conduction
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