
38-36 Power Electronics and Motor Drives
By replacing cos z and sin z in the relation (38.35), one obtains
v V
m
t
V
k
k
j t
c dc
dc
k
j
j
1
3
3
1
2 3
0
4
2
2= +
= =
∑ ∑
ˆ
sin sin cos
β
ω
π
π
λ ω
+
+
+
=
∑
cos
cos sin( )
( )
k t
k
j t
sw
j
j
ω
π
δ ω
2
2 1
2 1 3
0
= +
=
∑
cos
ˆ
sin cos
k t
v V
m
t
V
k
k
sw
c dc
dc
k
ω
β
ω
π
π
δ
2
3
3
1
4
2
(( )
sin( ) cos
2 1 3
0
2 1
j
j
sw
j t k t
+
=
+
∑
ω ω
(38.37)
Taking into account the parity of k (k = 2i or k = 2i + 1), relation (38.37) becomes
v V
m
t
V
i
j t
c dc
dc
i
i
j
j
1
3
3
0
2 3
0
4
2 1
1 2= +
+
−
= =
∑ ∑
ˆ
sin
( )
( ) cos
β
ω
π
λ ω
+
+ − +
=
+
∑
cos( )
( ) sin( )
( )
2 1
2
1 2 1
1
2 1
i t
V
i
j
sw
dc
i
i
j
ω
π
δ ω
33
0
2
3
3
2
2
t i t
v V
m
t
V
i
j
sw
c dc
dc
=
∑