funzioni di rete rlc
2
Circuito RLC serie, uscita su C: RC j LC j H ω ω ω + − = 2 1 1 ) ( & ; 2 2 2 ) ( ) 1 ( 1 ) ( RC LC j H ω ω ω + − = & 2 2 2 2 2 2 2 2 ) ( ) 1 ( ) ( ) 1 ( ) ( 2 ) 2 )( 1 ( 2 2 1 ) ( RC LC RC LC RC LC LC j H d d ω ω ω ω ω ω ω ω ω + − + − + − − − = & = 2 2 2 2 2 2 2 2 2 ) ( ) 1 ( ) ( ) 1 ( ) ( ) ( 2 2 RC LC RC LC RC LC LC ω ω ω ω ω ω + − + − + + − − = [ ] 2 / 3 2 2 2 2 2 2 ) ( ) 1 ( ] ) ( ) ( 2 2 [ RC LC RC LC LC ω ω ω ω + − + + − − = 0 ) ( = ω ω j H d d & , per 0 = e per 2 0 2 2 2 2 2 2 1 1 ) 2 1 ( 1 2 1 ) ( 2 ) ( 2 s Q L C R LC L R LC LC RC LC − ± = − ± = − ± = − ± = ω ω ; tali pulsazioni esistono se e solo se 2 1 ≥ s Q ; in tal caso esse risultano minori in modulo di 0 ω . Circuito RLC serie, uscita su L: RC j LC LC j H ω ω ω ω + − − = 2 2 1 ) ( & ; 2 2 2 2 ) ( ) 1 ( ) ( RC LC LC j H ω ω ω ω + − = & 2 2 2 2 2 2 2 2 2 2 2 2 ) ( ) 1 ( ) ( ) 1 ( ) ( 2 ) 2 )( 1 ( 2 2 1 ) ( ) 1 ( 2 ) ( RC LC RC LC RC LC LC LC RC LC LC j H d d ω ω ω ω ω ω ω ω ω ω ω ω ω + − + − + − − − + − = & = = + − + − − − + − = 2 / 3 2 2 2 2 2 2 2 2 2 ] ) ( ) 1 [( ] ) ( ) 2 )( 1 [( ] ) ( ) 1 [( 2 RC LC RC LC LC RC LC LC ω ω ω ω ω ω ω = + − − + + − + = 2 / 3 2 2 2 2 4 2 2 2 2 4 ] ) ( ) 1 [( ] ) ( 2 2 ) ( 4 ) ( 2 2 [ RC LC LC LC RC LC LC LC ω ω ω ω ω ω ω ω 2 / 3 2 2 2 2 2 ] ) ( ) 1 [( ] ) ( 2 2 [ RC LC RC LC LC ω ω ω ω ω + − + − = 0 ) ( = ω ω j H d d & , per 0 = e per , cioè 0 ) ( 2 2 2 2 = + − RC LC ω ω ) 2 1 1 ( ) 2 1 1 ( ) 2 1 ( 1 2 ) ( 1 ) ( 2 2 2 0 2 2 0 2 2 2 s s Q Q L C R LC RC LC RC LC − ± = − ± = − ± = − ± = − ± = ω ω ω ; tali pulsazioni esistono s e e solo se 2 1 ≥ s Q ; in tal caso esse risultano maggiori in modulo di 0 ω .
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calcolo della risposta in frequenza per i circuiti rlc, varie uscite
Transcript of funzioni di rete rlc
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Circuito RLC serie, uscita su C:
RCjLCjH += 21
1)(& ; 222 )()1(
1)(RCLC
jH
+
=&
222
222
22
)()1()()1(
)(2)2)(1(221
)(RCLCRCLC
RCLCLC
jHdd
+
++
=& = 222222
222
)()1()()1(
)()(22
RCLCRCLC
RCLCLC
++
++=
[ ] 2/3222222
)()1(
])()(22[
RCLC
RCLCLC
+++=
0)( = jHdd & , per 0= e per
20
2
2
2
2
2
211)
21(1
21
)(2)(2
sQLCR
LCLR
LCLCRCLC ==== ; tali pulsazioni
esistono se e solo se 2
1sQ ; in tal caso esse risultano minori in modulo di 0 . Circuito RLC serie, uscita su L:
RCjLCLCjH
+= 2
2
1)(& ;
222
2
)()1()(
RCLC
LCjH
+
=&
222
222
222222
)()1()()1(
)(2)2)(1(221)()1(2
)(RCLC
RCLC
RCLCLCLCRCLCLC
jHdd
+
+++
=& =
=+++= 2/3222
222222
])()1[(])()2)(1[(])()1[(2
RCLCRCLCLCRCLCLC
=++++= 2/3222
2422224
])()1[(])(22)(4)(22[
RCLCLCLCRCLCLCLC
2/3222
22
])()1[(])(22[
RCLCRCLCLC
++=
0)( = jHdd & , per 0= e per , cio 0)(22 22 =+ RCLC
)2
11()2
11()2
1(
1
2)(
1)(2
2
2
0
2
20
222
ss QQLCRLCRCLCRCLC
=
=
=
== ; tali
pulsazioni esistono se e solo se 2
1sQ ; in tal caso esse risultano maggiori in modulo di 0 .
