σηματα και συστηματα-i

D1: Ιδανική δίοδος
V () t = Acos( ω t), u () t > 0
L
2
0 2
V () t = 0, u () t ≤ 0
L
T
2
1
−inω0t
cn
= Acosω0te dt
T
∫
T
−
2
e
cos( ω t)
=
0
+ e
2
iω0t −iω0t
T T T
2 4 4
−i( n−1) ω0t T
− i( n+
1) ω0t
T
A iω0t −inω0t −iω0t inω0t A −i( n−1) ω 1
0t − i( n+
1) ω0t
A e A e
4 4
n
[ ] [ ]
T
[ ]
T
2T ∫
T 2T ∫
T 2T ∫
T
2 T −j( n−1) ω −
0 4
2 T − j( n+
1) ω −
0 4
− − −
2 4 4
c = e e + e e dt = e dt + e dt = + =
T T T T
T T
−i( n−1) ω0 i( n−1) ω0 − i( n+ 1) ω0 i( n+ 1) ω0
4 4 4 4 sin[( n− 1) ω0 ] sin[( n+
1) ω0
]
A e −e A e −e A
= [ ] [ ]
4 A
+ = +
4
2 T −j( n−1) ω 2 T − j( n+ 1) ω T ( n− 1) ω T ( n+
1) ω
2π
ω0T
= T = 2π
T
0 0 0 0
εποµένως:
c
n
π π
sin( n− 1) sin( n+
1)
A
= [ 2 + 2]
2π
n− 1 n+
1
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