1 7 ω ω ω 7.1 0, ( ) Q, 7.2 ( Q ) 7.1 ω Z = R +jx Z 1/ Z 7.2 ω 7.2 Abs. admittance (x10-3 S) RLC Series Circuit Y R = 20 Ω L = 100

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1 7 7., ) Q, 7. Q ) 7. Z = R +jx Z / Z Abs. admittance x -3 S) R Series ircuit Y R = Ω = mh = uf Q = V) Z = R + jx 7. Z 7. ) R = Ω = mh = µf )

2 7 V) R Z s = R + j ) 7.3 R =. 7.4) ) f = π. 7.5) V ) Z s I = V Z s 7.) Y s = /Z s * Z s Z s Y s Y s Z s Z s = R + j ) 7.) Z s j ) Z s Z s =R) Z s =. 7.3) * 7.3. = / Z s Z s R Y s /R I V /R R,, = mh = µf R = = 7.6) 3 6 = rad/s 7.7) R R Ω Ω Ω 5 Ω R = rad/s Y s R

3 Abs. admittance x -3 S) R Series ircuit Y = mh = uf R = Ω R = Ω R = Ω R = 5 Ω 5 5 I) R Y p = R + j ) 7.6 R Z p 7.4 R ) Abs. impedance Ω) 5 5 R Series ircuit Z = mh = uf R = 5 Ω R = 3 Ω R = Ω R = Ω R ) Q I ) V = Z p I 7.8) Y p = /Z p Y p Y p Y p Y p = R + j ) 7.9) Y p j ) Y p Y p =/R) Y p = 7.) =. 7.) ) f = π. 7.)

4 4 7 Abs. admittance x -3 S) 5 5 R Parallel ircuit Y = mh = uf R = Ω R = 5 Ω R = Ω R = Ω R ) Abs. impedance ) R Parallel ircuit Z = mh = uf R = Ω R = Ω R = 5 Ω R = Ω 5 5 = = 7.3) 3 6 = rad/s 7.4) R R Ω 5 Ω Ω Ω R = rad/s Z p R Q 7.8 R ) = / Y p /R Z p R V R I R,, = mh = µf R I = Y s V V = Z p I 7.9 * *

5 7.7. R Q R 5 Input Good filter Output / Q = Input Poor filter Output 7. Q 7.9 ), Q Quality Factor) 7.6 Q Quality Factor) 7. Q Q =. 7.5) / 7.7 R Q R 7. = mh = µf R = Ω Ω 5 Ω R R R R Q R = Ω Ω 5 Ω Q =, Q = 5, Q = 7.8 R Q R 7. = mh = µf R = Ω 5 Ω Ω R R R R Q R = Ω 5 Ω Ω Q = Q = 5 Q = 7.9 Q R Q R

6 6 7 a) Abs. admittance x -3 S) R Series ircuit Y R = Ω = mh = uf Q = a) Abs. impedance ) R Parallel ircuit Z R = k = mh = uf Q = b) Abs. admittance x -3 S) R Series ircuit Y R = Ω = mh = uf Q = 5 b) Abs. impedance ) R Parallel ircuit Z R = 5 = mh = uf Q = c) Abs. admittance x -3 S) 5 5 R Series ircuit Y R = 5 Ω = mh = uf Q = c) Abs. impedance ) R Parallel ircuit Z R = = mh = uf Q = = mh) = µf) R = Ω Ω 5 Ω) 7. = mh) = µf) R = Ω 5 Ω Ω) R Q Q = R = R = R. 7.6) R Q Q = R = R = R. 7.7) R 7.4 R Q Q

7 7.. 7 R V) R = Q = R a) ideal b) real 7.3 R Q 7.5 I) R R = Q = R a) ideal b) real R Q R R = Ω R R = Ω Q *3 * TDK [] mh Ω

8 8 7 eakage current =.5 V R = MΩ 7.7 TDK) [] 7.8 ) [] [] V.5 ma MΩ 7. R 7.9 R 7. R 7.. Q X Q Q X 7.5 Q X

9 7.. R 9 V) a) Ideal series circuit R R V) b) Real series circuit R s V) c) Equivalent circuit for real series circuit 7.9 a) b) c) Q R Q X Q X 3 ) ) *4 Q X Q = R, 7.) Q = G. 7.) I) I) I) a) Ideal series circuit b) Real series circuit R p R R c) Equivalent circuit for real series circuit 7. a) b) c) Q = = R. 7.8) 7.6 Q X Q = = G. 7.9) G = /R a) 7.a) 7.9b) 7.b) R R 7.9b) 7.b) 7.9c) 7.c) R 7. R 7. *4 x.xx y 4 5 )

10 7 R R s) 7. R R R p) 7. R 7.3 b) 7.3 a) 7.3 b) jx Z = jx + = + j X Q X X Q X X 7.) Q X *5 /Q X/ X w w Z jx j + w) w 7.3) X Q X X ) = X Q X + jx 7.4) 7.3 a) X /Q X jx Q X X jx a) b) 7.3 Q X 7.3 ) Q X 7.3 a), b) 7..3 R R s) R s) = R Q. 7.5) 7. R p) R p) = Q R. 7.6) R ) R s R p *5 /

11 7.. R a) Abs. admittance S) Series circuit 55 6 = mh R = Frequency khz) = pf R = M 65 7 a) Abs. impedance 6 ) Parallel circuit 55 6 = mh R = Frequency khz) = pf R = M 65 7 b) Abs. admittance S) Series circuit equivalent) 55 6 = mh R = Frequency khz) = pf R s) = R /Q 65 7 b) Abs. impedance 6 ) Parallel circuit equivalent) 55 6 Frequency khz) = mh R p) = R Q = pf R = M a) b) R 7.5 a) b) R R s = R + R s) = R + R Q, 7.7) = + = + R p R R p) R Q R. 7.8) R = mh R = Ω = pf R = MΩ = / = 6 rad/s f = /π) = 59 khz 6 khz 7.4 a) b) 7.9 c) 7.5 a) b) 7. c)

12 7 R Q R ) / ) Q 7.5) R Z s = R + ) 7.9) Y s = Z s = R + ). 7.3) = 7.3) Y s Y s = R Q = 7.3) Y s Y s = 7.33) < ) Q Y s / Y s Y s Y s = R R + ) = + R ) 7.34) R R = ±. 7.35) R R = ) R R = 7.37) = ) R R ± ) ± + = ) R R ) Q 7.4) = / 4/ 4 / = R + ) R + 7.4) = / Q = ) R R ) R = 7.4) R ) + R =. 7.43) = R ) R ± )

13 3 ± + = R ) R ) > ) < ) = R + ) R ) / Q = R ) R ) = R 7.48) Q 7.5) Q = = R = 7.49) 7.5) Q = R = R. 7.5) 7.4) = / Q = R = R. 7.5) R Q R R Y p = R + ) 7.53) Z p = Y p = R + ). 7.54) = 7.55) Z p Z p = R 7.56) Q = Z p Z p = 7.57) < ) Q Z p / Z p Z p Z p = R R + ) = + ) 7.58) R R ) = ±. 7.59) R ) = + 7.6) R R = 7.6)

14 4 7 = R { } ± + 4R 7.6) > ) < ) ± + = R { } + + 4R. 7.63) Q 7.) = / 4/ 4 / = ) R + + R 7.64) = / Q = R { } + + 4R 7.65) R ) = 7.66) ) = ) R + + R 7.7) = / Q = R { } + + 4R 7.7) = R 7.7) Q 7.5) Q = = R 7.73) = 7.74) Q = R = R. 7.75) 7.) = / Q = R = R. 7.76) R + R =. 7.67) = R { } ± + 4R. 7.68) ± + = R { } + + 4R. 7.69)

15 5 ) d f = 5.33 [mh] [pf] [MHz] 7.77) 7.3 ) d d = Q X 7.78) d 7.3 a) cosθ = R R + X 7.79) R = X /Q X cosθ = = + X R +Q X = +Q X X X ) 7.8) Q X cosθ = 7.8) Q Q X X / / / full width at half maximum: FWHM) / / FWHM / / / *6 FWHM / / f t) = a + { a n cosn t) + b n sinn t) }. 7.8) n= f t) = a + A n cosn t + ϕ n ). 7.83) n= A n = a n + b n, 7.84) ). 7.85) ϕ n = tan bn a n *6

16 6 7 ft) n = n = n = ~ t t t 3 t n = ~3 n = ~4 n = ~5 7.6 t t t 7.8 n = n = n = 5 sin n = ~ t 7.7 sin f t) = n= c n e jn t. 7.86) c n = a n jb n = c n ϕ n, 7.87) c n = A n = a n + b n, 7.88) ) ϕ n = tan bn. 7.89) a n 7.6 f t) = + π sin[n )πt] n n= = + π sinπt) + 3π sin3πt) + sin5πt) + 7.9) 5π 7.9 n = n = sin 7.9 f t) = + sin[n )πt] π n= n = a + A n cosn t + ϕ n ) 7.9) n= 7.7 n =,,,3,4,5 7.8 n = n = A n = a n + b n = b n { /nπ) n = odd) = n = even) 7.9)

7 A n.5 π ft) 3π 5π 3 t A n.5 π 3π 5π π π 3π 4π 5π 6π φ n π π 3π 4π 5π 6π n π π 3π 4π 5π 6π 9 π π 3π 4π 5π 6π 9 7.3 [3] 7.3 ) ϕ n = tan bn = a n { 9 n = odd) n = even) 7.93) = n ) A n ϕ n A n ϕ n 7.

17 7 A n.5 π ft) 3π 5π 3 t A n.5 π 3π 5π π π 3π 4π 5π 6π φ n π π 3π 4π 5π 6π n π π 3π 4π 5π 6π 9 π π 3π 4π 5π 6π [3] 7.3 ) ϕ n = tan bn = a n { 9 n = odd) n = even) 7.93) = n ) A n ϕ n A n ϕ n 7.3 *7 spectrum) 7.3 [3] spectrum analyzer) Band-pass filter = Select desired-frequency components) Noise Reduc on or Signal Detec on Original Signal ) Noise < Noise 3 > Another Signal < Signal +Noises Noise 4 > Transmi ance High-Q Band-Pass Filter 3 4 Noise Reduc on 7.3 * rad/s, rad/s, 5 rad/s rad/s *7 *8

18 I = 5 rad/s) V = 5 rad/s) I = rad/s).5 V = rad/s). -.5 I) R V) I3 3 = 5 rad/s) Abs. impedance ) R Parallel ircuit Z R = k = mh = uf Q = V3 3 = 5 rad/s) I = I + I + I3 V = V + V + V Time x -3 s) Time x -3 s) 7.33 ) rad/s) rad/s Q rad/s AM *9 *9 rad/s rad/s )

19 9 [] R,, Z ), Z = R + j + j = R + j ). =. = ) R [] R,, Y ), Y = R + j + j = R + j ) +. =. = ) /R

20 7 A. R. R R Z s Z s = R + j ). B. R. R R Y p Y p = R + j ).. R R. R R Z s =. 3. R Q R Q Q R, / Z s Q / Z s / < ) Q Q =. R Q = R. Y p =. 3. R Q R Q Q R, / Y p Q / Y p / < ) Q Q =. R Q = R. R R

21 [] [] [3]

吸収分光.PDF

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