§ 10-2 Series resonance
CjLjRZ ??
1??? )1(
CLjR ?? ???
The resonant frequency:
CLorCL rrrr ????
101 ???
tRVtia n dtVtIf rr ??? c o s2)(c o s2)( ??
tRLVtLitw rL ?22
2
2 co s)(
2
1)( ?? ?
??
?
???????? 90CR VCj R/VCj IV
rrr
C
tCR VtCR Vt r
r
r
r
C ?????
? s i n2)90c os (2)( ???
tRLVtCR VCCtw rr
r
CC ????
2
2
2
2
222
2
2 s i ns i n2
2
1
2
1)( ???
LCLC rr
112 ??? ??So that
）（ rR
Lc
/)(R/V
R/LV
TP
)]t(w)t(w[Q
???? 222 2
22
????
L
R
QB
r ???? ???
12
?
?
??
??? VRVRIRV R
?
?
??
??? VjQRVLjILjV rrL ??
?
?
??
?????? VjQRVCjICjV
rr
C ??
11
?I?V
?
CV
?
LV
C
L
RCRR
L
r
r 11 ???
?
?
Q>>1 series resonance--voltage resonance.
Frequency characteristics(XL,XC,X,z,y,),?? vs
??? ?????????? zCLjRXXjRjXRZ CL )1()(
LX
CX
X
R
r?
?
z
r? ?
y
?
r?
2/?
2/??
?
z
Resonant curves ),,,( ?vsIVVV
RCL
22 )/1(
)(
CLR
LVV
L ??
??
??
?
22 )/1(
)(
CLRC
VV
C ???? ???
22 )/1(
)(
CLR
VI
??
?
??
?
)()( ?? RIV R ?
V
?
LVCV
I
r?0
)(
0
DC
I
VVC
?
?
)(
m ax
r
CL VV
I
?
?
??
VV
V
I
L
C
?
?
?
??
0
0
?
Frequency
300Hz 1.0KHz 3.0KHz 10KHz 30KHz 100KHz
V(V1:+,V1:-) V(C1:2,C1:1) V(R1:2,R1:1) V(L1:1,L1:2)
0V
5V
10V
15V
R1
2,2 k
V-
V1
3
0 V d c
C1
2 4 0 0 p
V-
V+
V-
V+
V+V+
0
L1
2 0 0 m
1 2
V-