Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz %3D Let the input voltage be V, =10.0V and the duty cycle be D=0.75 . Call v.(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for v.(t),i, (1), and also the expected ripples Av (t), Ai, (1)
Consider a Unidirectional DC/DC Boost Converter with the following parameters: R = 50.02 C =100.0µF L = 100.0mH f, = 10.0kHz %3D Let the input voltage be V, =10.0V and the duty cycle be D=0.75 . Call v.(t), i, (t) the voltage across the capacitor and the current through the inductor respectively. Q1: determine the expected steady state values for v.(t),i, (1), and also the expected ripples Av (t), Ai, (1)
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Please help with Question 2. I also attached the notes that question 2 referred to.

Transcribed Image Text:Unidirectional Boost Converter
di, (t)
L
dt
-9(1)v(t)
ee
+ v(t) -
v(t)
= q(t)i¿(t)-
R
dt
C
R
V.
- DT,
q(t)
I- VIR
DT, -
D'T, -
- V/R
ee
i(t) +v,() -
+
+ v,(0) -
R
Switch in 1 (q(t)= 0) :
Switch in 2 (g(t) =1) :
di,
L
= v, (1) = V,
dt
di,
= v, (t) = V, -vc(1)
dt
cdvc
dve
= ic(t) = i,(1)
dt
dt
R
See the solution on any of the intervals. Assume
RC
«1 and use simple Taylor's series as
solution of LDES.
1
2
DT,
T
f.
Switch in 1:
V.
i,(DT.) = i_(0) + DT,
di,
dt L
0st< DT,
vc(0)
DT, = v(0)
RC
dve -vc(t)
v(DT,) =v(0) –-
dt
RC
Switch in 2:
V,-vc(0)
di, V -v.(t)
i,(T,) =| i,(0)+
|(1- D)T,
L
DT, <t<T,
dt
L
V,-(1-D)vc(0)
i, (1) vc(t)
dvc =
=i, (0) +
L
dt
C
RC
(i,(DT,) v (0)
ve(T,) = vc(0) +
C
RC (1-D)T
Ev(0) +
¿(DT,)
-(1– D)T,
C
Therefore:
i, (T.) > i,(0)
vc(T,) > vc(0)
ve(0)(1– D)<V½
if
See the transient response:
Smaller slope since the Inductor current is
charging the capacitor
i,(DT,) = i,(0) + 4 DT,
i,(1)
i, (T.) = i,(0) +
V-(1-D)v (0),
T,

Transcribed Image Text:Problem 2. (Unidirectional DC/DC Boost Converter).
Consider a Unidirectional DC/DC Boost Converter with the following parameters:
R = 50.02
C =100.0µF
L = 100.0mH
f, = 10.0kHz
Let the input voltage be V, = 10.0V and the duty cycle be D = 0.75 . Call vc(t), i, (t) the
voltage across the capacitor and the current through the inductor respectively.
Q1: determine the expected steady state values for ve(t),i, (t), and also the expected ripples
Av (1), Ai,(1)
Q2: assuming zero initial conditions v.(0) = 0, i,(0) =0 sketch v.(t),i, (t) in the first three
periods 0<tS 3T, . In particular use the Taylor series approximation in the notes and show
the values for t = 0, DT,, T,, T,+DT, ,2T,, 2T,+DT,,
3T,.
in
Q3: using the same state equations in the notes, compute the steady state values for
Vc(0), vc(DT,),i¿ (0),i¿(DT,), where time t = 0 denotes the beginning of "switch on" and
time t = DT, denotes the beginning of "switch off" (Hint: in steady state v.(0) = v.(T,) and
i.(0) = i.(T,) ). Verify that the ripples are close to what you expect.
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