§ 10-1 Parallel resonance(谐振）
Let us now define resonance,In a two-terminal
electrical network containing at least one inductor and
one capacitor,resonance is the condition which exists
when the input impedance of the network is purely
resistive.
)1(1 LCjR ?? ???
CjLjRY ?? ??? 11
f r eq u en cer es o n a n tLCr ??? 1?
LCorLCat rrrrr ??????
101,????
LR
Let us examine the magnitude of the response.
)
1
(
1
L
Cj
R
I
Y
I
V
?
? ??
??
??
?
22 11 )
L
C()
R
(
|I|
|V|
?
? ??
?
?
?
)i m u m( m a xRIVor
IRV,LC/at r
?
??? 1??
0,0 ?? Vat ?
0,??? Vat ?
V
?
r?
IR
2/IR
2?1?
At resonance the parallel RLC combination acts simply as R,
the parallel LC combination behaves as an open circuit.
21,??
--two half power frequencies.
12 ?? ??B
--band width（ 带宽）
The quality(品质 ) factor:
p er i o dainl o s ten er g yt o t a l
s t o r eden er g yi m u mm a xQ ?2?
TP
)]t(w)t(w[Qor
R
m a xLc ?? ?2
tItiL et r?co s2)( ? tRIt r?? co s2)( ?
22 )c o s2(
2
1
2
1)( tRICCtw rc ?? ??
?
?
?
??? 9090
0 ???
?
??? ??
L
RI
L
RI
Lj
VI
rrr
L
t
L
IRLitw
r
r
L ??
2
2
222
s i n21)( ??
tt a nc o n sICR)t(w)t(w Lc ???? 22
RTI
ICRQ
2
222 ??
)90co s (2)( ?? ??? tRIti r
rL
L
CR
L
RRC
/
CR
T
CR
r
r
r
????? ?????? 222
tICR r?222 c o s?
tICR r?222 s in?
)1(1 LCjRY ?? ???
)(11 QQRjR r
r ?
?
?
? ??? )](1[1
?
?
?
? r
r
jQR ???
)1(1 RRLRRCjR
r
r
r
r
?
?
??
?? ???
At the half power frequencies
21 ?? and
RYY
IRIV 2
2 ????
RjQR
r
r
2)](1[1 ???
?
?
?
? 1)( ???
?
?
?
? r
r
Q
)()(Q rr
r
?????? ???? 2
2
2 1
)()(Q rr
r
?????? ???? 1
1
1 1 221)2
1( 2
1
B
QQ r
r
r ????? ?
???
221)2
1( 2
2
B
QQ r
r
r ????? ?
???
BQorRCRCQB
r
r
rr ?
?
???? ?????? 1
12
.atVan dB,Q,F i n d:E xa m pl e rr ??? ??2
Solution:
4
63 10102105
11 ?
????? ??LCr?
810240010 64 ?????? ?RCQ r?
1250?? QB r?
V
IRV s
?
?
04
01010400 3
??
????? ?
??
mAjIjQLj IRLj VI s
r
s
r
L 80??????
?
??
?
??
mAjIjQICRjVCjI ssrrC 80???? ???? ??
Q>>1,parallel resonance--current resonance