3E
3E 2003.6.2
C, R
1.
C, R
( )
2. CR
2.1 ( )
CR ( 1)
` L, C, R C, R
`
VR
CR j CRV j
C R j VR RV
ω ωω
= +
−
=
1
(1)
CR = τ
V VR
ωCR << 1 1
CRV j
VR ≈ ω (2)
V
)
0exp(j t V
V= ω (3)
(2)
dt CRdV
VR≈ (4)
ωCR << 1 τ << 1/ω
GR
×
= V
GR 20 log10 VR (5)
(5) VR (1) V (3)
(5)
× +
=
× +
=
−
×
−
−
×−
× +
=
× +
=
10 2
0 2 0
10
0 0
0 0
10 0
0
10
) ( 1 log 20
) ( log 1
20
) exp(
) exp(
1
) exp(
1
) exp(
log 20
) exp(
1
) exp(
log 20
CR CR V
CR CRV
t j V t j V
CR j
t j CRV j CR
j t j CRV j
t j V
CR j
t j CRV j GR
ω ω
ω ω
ω ω
ω ω ω
ω ω ω
ω ω
ω ω
(6)
θR
(1) (3) (3) (1)
) exp(
) ( 1
) ( 1 ) ( 1 ) ( 1
) ( 1
) ( 1
2
2 2
2 2
2
ω α ω
ω ω
ω ω
ω ω
ω ω
ω ω
j V CR CR
CR V j CR
CR CR
CR CR V
CR CR j
CR j CRV VR j
= +
+ + +
= + +
= +
= +
(7)
α
=
ωCR
α arctan 1 (8)
arctan (z) = tan-1(z) (8) V
VR θR α (8)
=
R ωCR
θ arctan 1 (9)
(7)
2.2 ( )
VC
CR j V
C R j
CV j VC
ω ω ω
= +
−
−
=
1
(10)
CR = τ
ωCR >> 1
1 >> 1/ ωCR (10)
CR j CRV j
CR j VC V
ω ω
ω
1 1 1 1
+
=
= +
(11)
(1) 1 CRV VC j
ω
≈ 1 (12)
V (3) (12)
∫
≈ Vdt
VC CR1 (13)
(10)
CR V CR j
CR j VC V
)2
( 1
1 1
ω ω ω +
= −
= +
(14)
(7) VR (14) VC V
) ) exp(
( 1
1
) ( 1 ) ( 1
1 )
( 1
1
2
2 2
2
ω β
ω ω ω
ω
j CR V
V CR CR j CR
CR VC
+ −
=
− + +
= +
(15)
(ωCR)
β=arctan (16)
V VR θC
β (16)
( CR)
C ω
θ =arctan (17)
(5) (15) (3)
(6) Gc ,
× +
=
+ −
×
=
10 2
0 2 0
10
) ( 1 log 1 20
) exp(
) exp(
) ) exp(
( 1
1 log
20
CR
t j V
j t j CR V
GC
ω
ω
β ω ω
(18)
V
R
C I
VRVC
1 CR
3. ( )
3.1
7 7 ( )
OK OK
1, 2
1, 2 1
GR
GR
θR
θR
GC
GC
θC
θC
3.2
1 2
1 f [Hz] (V [V] VR) [V] X [mm] x [mm] θR [deg] GR [dB]
100 1.0 0.0075 X = x 200 1.0 0.0143 X = x 400 1.0 0.0302 X = x 600 1.0 0.0456 X = x 800 1.0 0.0605 X = x 1000 1.0 0.0752 X = x 1500 1.0 0.108 X = x 2000 1.0 0.143 0.42 0.41 3000 1.0 0.223 0.70 0.66 4000 1.0 0.291 0.88 0.80 5000 1.0 0.344 1.09 0.97 6000 1.0 0.400 1.24 1.09 7000 1.0 0.450 1.40 1.20 8000 1.0 0.498 1.55 1.30 9000 1.0 0.542 1.66 1.32 10k 1.0 0.576 1.80 1.36 20k 1.0 0.788 2.39 1.27 40k 1.0 0.890 2.69 1.11 60k 1.0 0.920 2.76 0.60 80k 1.0 0.925 2.78 0.46 100k 1.0 0.934 2.78 0.40 200k 1.0 0.940 2.80 0.25
2 f [Hz] (V [V] VC [V] X [mm] ) x [mm] θC [deg] GC [dB]
100 1.0 0.905 27.2 0.1 200 1.0 0.905 27.4 0.5 400 1.0 0.904 27.4 1.2 600 1.0 0.904 27.4 1.5 800 1.0 0.904 27.4 2.0 1000 1.0 0.903 27.4 2.5 1500 1.0 0.900 27.3 3.4 2000 1.0 0.898 27.3 4.5 4000 1.0 0.860 26.2 8.4 6000 1.0 0.807 25.0 11.0 8000 1.0 0.755 23.5 12.5 10k 1.0 0.700 21.4 13.4 12k 1.0 0.645 20.2 13.4 14k 1.0 0.597 18.3 13.4 16k 1.0 0.552 17.0 13.3 18k 1.0 0.510 15.8 13.0 20k 1.0 0.477 14.7 12.6 40k 1.0 0.268 8.2 7.7 60k 1.0 0.182 5.7 5.5 80k 1.0 0.138 4.3 4.2 100k 1.0 0.112 3.6 3.6 200k 1.0 0.058 2.0 2.0
