0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db( ) v 2 20 log 0 [db] (3) v R v C v 2 (a) ω (b) : v o v o =

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1 RC LC RC 5 2 RC 2 2. /sc sl ( ) s = jω j j ω [rad/s] : C L R sc sl R 2.2 T (s) ( T (s) = = /CR ) + scr s + /CR ()

2 0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db( ) v 2 20 log 0 [db] (3) v R v C v 2 (a) ω (b) : v o v o = A(v + v ) (4) 3 v 2 v = R v 2 + R 2 v R + R 2 (5) v + = 0 (5) (4) v 2 AR 2 v 2 = v (6) (R + R 2 ) + AR 2

3 A A v 2 = R 2 R v (7) (v 2 /v ) A A ( [3] ) + v + = v (5) v + = 0 0 = R v 2 + R 2 v R + R 2 (8) (7) 4(a) v +, v v + = v v = R R + R 2 v 2 (9) v + = v v 2 ( v 2 = + R ) 2 v (0) R 4(b) R =, R 2 = 0 v 2 /v = v + v - v v + v o v - (a) v A v (b) 2: R 2 R v - v 2 v + v o 3: v v 2 R 2 R (a) v v 2 (b) 4: 3

4 ( 0) 5 5(a) T T T T 0 0 ω 0 ω 0 0 ω 0 ω 0 0 ω ω ω ω ω ω 2 5: 6 ω ω p 0 α max ω ω s α min ω p ω p, ω s, α max, α min 7 α, db α min α max 0 0 ω p ω 6: α, db O ω s ω s ω 7: 4

5 2 y 2 (x) = y 2 min[ + (α 2 )F 2 (x)] () α max α F (x) x F (x) x y(x) αy min (2) x F (x) F (x) 3.2 F (x) = x n (3) n n y 2 (x) = y 2 min[ + (α 2 )x 2n ] (4) T (s) T (jω) 2 = y 2 (ω) = H 2 + ε 2 F 2 (ω) T (s) s=jω 2 = T (s)t ( s) H = /y min ε 2 = α 2 = H 2 + ε 2 F 2 (js) = H 2 + ε 2 ( s 2 ) n (5) (6) n = 2 T (s) 5

6 (a)n = T (s)t ( s) = H 2 ( εs)( + εs) T (s) (T (s) ) s (7) T (s) = H εs + (8) H =, ε = CR = () n = () (b)n = 2 T (s)t ( s) = = H 2 + ε 2 s 4 = H 2 (εs 2 + ) 2 2εs 2 H 2 (εs 2 + 2εs + )(εs 2 2εs + ) (9) T (s) = H εs 2 + 2εs + (20) (6) =0 s p nk ( p nk = r sin 2k + 2n ) 2k + π + j cos 2n π (2) π / 2n ω k = 0,,..., n r = ε /n p nk = r 8 r T (s) π / n O r σ T (s) = H (s p nk ) n ε (22) 8: k=0 6

7 3.3 x n F (x) T n (x) T n (x) T n (x) = { cos(n cos x) x cosh(n cosh x) x (23) - T T 2 T 0 (x) = T (x) = x T 2 (x) = 2x 2 T 3 (x) = 4x 3 3x T 4 (x) = 8x 4 8x 2 + T 5 (x) = 6x 6 20x 3 + 5x (24) T (23) (6) T (s) 0 H T (s) = n 2 n ε (s + p nk ) k=0 - - T p nk = ν nk + jµ nk µ nk = a n 2 ν nk = b n 2 2k + cos 2n π 2k + sin 2n π (25) - - T a n = ( ) /2n α + + α ( ) /2n α α b n = ( ) /2n α + α ( ) /2n α α k = 0,, 2,..., n : 7

8 Σ Π ε 2 = α 2 α 6 α max α α max E π 2n ν nk C 2 ω µ nk b n 2 a n 2 C σ 0 α max[db]/20 (26) 0: 4 L L LC R C ( ) RC RC LC 4. RC T (s) 2 T T 2 T N : T (s) = N T i (s) (27) i= R R 2 C T i (s) T (s) () C 2 V V 2 R a R b 2: Sallen-Key 2 2 (Sallen-Key) T (s) = Hω 2 0 s 2 + (ω 0 /Q)s + ω 2 0 (28) 8

9 H = + R b R a ω 2 0 = C C 2 R R 2 (29) Q = R2 C 2 R C 2 + R b R C R C R 2 C R a R 2 C 2 2 (i)r a = R b = 0 R = R 2 = R C = 2Q ω 0 R (30) C 2 = 2Qω 0 R (ii)r = R 2 = R, C = C 2 = C ω 0 = CR R b = 2 R a Q (28) T (jω) = (3) H ((ω/ω0 ) 2 ) 2 + ((ω/ω 0 )/Q) 2 (32) 4.2 LC 5 LC 4 LC LC L RC L GIC (Generallized Immittance Converter) 5 GIC V V 2 I I 2 V = V 2 I = Z 2Z 4 Z Z 3 I 2 (33) R S C C 2 L L 2 C 3 R L 4: 5 LC 9

10 2 Z Z Z 2 Z 3 Z 4 Z 5 ' 2' 5: GIC R R CRR CRR 2 GIC GIC GIC (a) (b) 6: GIC Z Z = Z Z 3 Z 5 Z 2 Z 4 (34) Z = Z 3 = Z 4 = R Z 5 = R 5 Z 2 = /sc Z = scrr 5 (35) L 6(a) (33) (b) LC 5 LC 7 LC 7 a a Z I a a 0

11 R S a V LC R L V 2 a' 7: LC P IN Z I P IN = Re R S + Z I V 2 (36) 2 LC R L Z I Re R S + Z I V 2 = V 2 2 (37) 2 R L V 2 2 V 2 = T (jω) 2 = R LReZ I R S + Z I 2 = R L 2R S (Z I + Z I ) 4R S RS 2 + R S(Z I + Z I ) + Z I 2 = R L [ R ] S Z I 2 4R S R S + Z I 2 (38) Z I Z I ρ(s) = Z I R S Z I + R S (39) ρ(s)ρ( s) = 4R S R L T (s)t ( s) (40) T (s)t ( s) s=jω (39) ρ(s) s (Hurwitz ) ρ(s) ρ(s) T (s) Z I (39) Z I = + ρ(s) ρ(s) R S (4)

12 [ ] α = 2 (3dB) 3 LC (6) T (s)t ( s) = H2 s 6 () (42) 2 ± j 3 2 T (s) = H s 3 + 2s 2 + 2s + (ω = 0) L C R S R L R S = R L = (Ω) H = /2 (40) (42) (43) ρ(s)ρ( s) = 4H2 s = s6 6 s 6 s 3 = s 3 + 2s 2 + 2s + s 3 s 3 + 2s 2 2s + ρ(s) ( ) s (44) ρ(s) = ±s 3 s 3 + 2s 2 + 2s + ρ(s) T (s) + (4) Z I Z I = 2s3 + 2s 2 + 2s + 2s 2 + 2s + = s + 2s + s + 8(a) (b) 2 (45) (46) 2 Z I (a) (b) 8: LC Z I 2

13 6 /2π[Hz] f c [Hz] K old new L new = KL old 2πf c C new = C old 2πf c K (47) R new = KR old (47) 3 RC R 8(a) khz kω K = 0 3 f c = 0 3 R S = R L = kω L = 59mH C = 0.38µF 7 0 n 0 n 2 2: 0 n (exa) E 0 8 (deci) d 0 (peta) P 0 5 (centi) c 0 2 (tera) T 0 2 (milli) m 0 3 (giga) G 0 9 (micro) µ 0 6 (mega) M 0 6 (nano) n 0 9 (kilo) k 0 3 (pico) p 0 2 (hecto) h 0 2 (femto) f 0 5 (deca) da 0 (atto) a 0 8 3

14 8 CR LCR CD AC (DC2V 500mA ) /4W 5% 5% 9 V CC ±5V V V V 2 V 2 /V (600Ω) ( =) 9: ( ) 4

15 V, V 2 dbv T (jω) ( [V]) T (jω) [db] = V 2 [dbv] V [dbv] (48) V V 2 V 2 V 3 C TA ( 3: ( ) [Hz] V [dbv] V 2 [dbv] [db] [db] ( ) l f (log 0 f) l 20: A4 (i) (ii) (iii) p.24 5

16 () 2 T (jω) = V 2 /V R TA (R = 0k 500kΩ ) LCR R, R 2, R 3 R R = R + R 2 + R 3 R LCR R 2 LCR R 3 TA (a) 22 (b) p.4 9 (c) ( ) (d) (0Hz 20kHz ) ( 23) RC V V 0dBV 0dBV -0dBV V (e) 0Hz 20kHz T (jω) = V 2 /V 3 RC 0Hz, 20Hz, 30Hz,...,00Hz,0Hz,... (d) dbv V ( Vrms)=0 x[dbv]/20 0dBV 3.6Vrms, 0dBV Vrms, -0dBV 0.36Vrms Vrms 2.4V 6

17 (2) p.2 (2) -(e) V 2 /V 3dB 0 20 (3) 9 (4) CD CD 3.5mmϕ R v v 2 0nF :2 R : 0k - 500kΩ :22 (a) (b) 23: ( ) ( ) 7

18 Sallen-Key () 24 Sallen-Key K = H = + R b /R a T (jω) = V 2 /V (a) p.4 9 (b) K K (0 30Hz) V 2 /V K = 2.0, 2.3, 2.6, p.8 (28) K V 2 /V K V 2 K 3 ( ) (c) -(d) (0Hz 20kHz ) V (d) -(e) V 2 /V K = 2.3, 2.6, 2.9 (2) p.9 (32) () K Q = /(3 K), H = K (3) (4) CD CD 0nF v 0k 0k 0nF R a R b v 2 5k 2.4k 24: 2 8

19 5 α = 2dB (0 /0 ) 5 p nk (rad/s) (8 0 ) (25) p nk sin cos H p nk TA Sallen-Key khz 20nF LCR 4 (2 ) () 5 p nk H T (s) = H 2 n ε = H 2 n ε s + p 52 s + p 52 (s + p 50 )(s + p 54 ) s 2 + s(p 50 + p 54 ) + p 50 p 54 (s + p 5 )(s + p 53 ) s 2 + s(p 5 + p 53 ) + p 5 p 53 (49) (2) () CR = /p 52 C = R (3) 2 (i) (R, R a, R b ) C = C 2, R = R 2 (3) ω 0 Q ω 0 (49) ω 0 = /CR = p 50 p C = R Q Q = p 50 p 54 /(p 50 + p 54 ) R b /R a R a R b 9

20 (4) (3) 2 (ii) (R 2, R a2 /R b2 ) (5) p.3 (47) f c = khz C = 20nF C new = 20nF, C old = K R, R, R 2 (R a, R b, R a2, R b2 ) kω 0kΩ (6) TA (7) (8) (a) -(d) (0Hz 20kHz ) V (b) -(e) V 2 /V (9) (p.2 (2)) 2 2 (p.9 (32)) 3 (0) () CD CD R R R R 2 R 2 R a R b R a2 R b2 25: 5 ( rad/s) R R R 20nF R 2 R 2 20nF 20nF 20nF 20nF R a R b R a2 R b2 26: [ 3] 5 ( khz) 20

21 LC R S = R L = (Ω) LC 8(b) ( ) ( ) Z I, Z I 6 8 p. (4) Z I ρ(s) (40) ρ(s)ρ( s) T (s)t ( s) F (x) = T 5 (s) (6) () R S = R L = ω = 0 T (0) = /2 H /2 (6) H /2 (2) (6) (24) H = /2 T (s)t ( s) = 4 + ε 2 T5 2 (js) = 4 (50) ε 2 s 2 (6s s 2 + 5) 2 R S = R L = (40) ρ(s)ρ( s) = ε 2 s 2 (6s s 2 + 5) 2 = ε2 s 2 (6s s 2 + 5) 2 ε 2 s 2 (6s s 2 + 5) 2 = s(6s4 + 20s 2 + 5) k=0 (s + p 5k) s(6s4 + 20s2 + 5) k=0 ( s + p 5k) (5) ρ(s) s ρ(s) = ± s(6s4 + 20s 2 + 5) k=0 (s + p 5k) ρ(s) 8(b) ( ) (52) ρ(s) ρ(s) (3) ρ(s) (4) Z I (4) p.2 (46) Z I (5) 27 (46) 8(a) TA 2 (52)

22 R S L L 2 C C 2 C 3 R L LC 27: 5 LC GIC LC khz GIC 0kΩ 20nF R S R L 0kΩ 3 L 2 LC khz, R S = R L = 0kΩ (35) 6 R L, R L2 GIC L () LC (47) f c = khz, R S = R L = 0kΩ K (2) 28 R S, R L, C, C 2, C 3 () R, R 2 (35) L = CRR 5 R = 0kΩ, C = 20nF 28 R, R 2 (3) TA (4) (a) ( ) (b) C, C 2, C 3 C C = C + C 2 + C 3 (c) (0Hz 20kHz ) V (d) -(e) V 2 /V (5) p.2 (50) 22

23 ω = rad/s f = khz ε T (jω) = T (jω)t ( jω) = 2 + ε2 ω 2 (6ω 4 20ω 2 + 5) 2 (53) (6) (7) CD CD R R 2 R R R R R R 5.MΩ C C C R R R R = 0kΩ C = 20nF v v 2 R S C C 2 C 3 R L 28: LC 5 ( khz) 9 [ ] (23) T 6 (x) [ ] Sallen-Key R b /R a = 0 Q( 0.5) R = R 2 [ ] (34) [ ] R S = R L [ ] 28 (, ) 23

24 0 2 (Hz, db ) 3dB (e) (3) (4) (3) 2 (4) (0) 3 () 24

25 3 4 ρ(s), Z I (s) (6) 4 (7) 4 3 [] [2] 973 [3] 990 A LF : LF356(Top View) 25

26 B JIS : (%) ± ±5 0.0 ±0 ±20 30: (47 0) 470Ω ± 5% (0 00) kω ± 5% 26

27 C mmϕ kω 2 +2V µf LM µF V VR 0kA µf 0.µF 2.7Ω SPEAKER 2.5W GPP20J +2V DC IN 2V 2DC0005D00 2A 470µF LM380 TOP VIEW 3: kω kω L R GND 3.5mmφ 32: c

A9RF112.tmp.pdf

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