L L L L C C C C (a) (b) (c) 4.4 (a) (b) (a) RG59/U 6.2mm ( ) 73Ω web page (c) 4 4 dx 4 J V dx dj Ydx Zdx dv Z,Y dv = JZdx, dj = VYdx (4.8) d 2 J dx 2

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1 8 ( ) OP h g m r d 4 ( ) (lumped constant circuit) (Poynting ) (strip line) (waveguide) (coaxial cable) GHz 4.4(a) dj dx dv Zdx Ydx ( ) (distributed constatn circuit) *1 4.4(c) 4 L C C L Biot-Savart *1 Oliver Heaviside ( ) [1] 8-1

2 L L L L C C C C (a) (b) (c) 4.4 (a) (b) (a) RG59/U 6.2mm ( ) 73Ω web page (c) 4 4 dx 4 J V dx dj Ydx Zdx dv Z,Y dv = JZdx, dj = VYdx (4.8) d 2 J dx 2 = YZJ, (4.9a) d 2 V = YZV (4.9b) dx2 (telegraphic equation) (lineman s equation) κ YZ (4.10) (κ ) x =0 J,V J(0,t),V (0,t) J = J(0,t)exp(±κx), V = V (0,t)exp(±κx) (4.11) (4.11) (4.9a) V J = Z Z κ = Y (4.12) (characteristic impedance) J(0,t)=J 0 exp iωt, V (0,t)= V 0 exp iωt ω exp( κx) x exp(κx) x Maxwll ɛ (= ɛ r ɛ 0 )(ɛ r ) μ (= μ r μ 0 )(μ r 1) z E = E 0 (x, y)e iωt γz, H = H 0 (x, y)e iωt γz (4.13) [2] Maxwell ( ) ( )( ) (ω 2 ɛμ + γ 2 Ex γ x iωμ ) = y Ez, E y γ y iωμ x H z ( ) ( )( ) (ω 2 ɛμ + γ 2 Hx iωμ y γ ) = x Ez. H y iωμ x γ y H z (4.14) 8-2

3 TEM (transverse electric and magnetic) E z = H z =0(4.14) ω 2 ɛμ + γ 2 =0 γ = ±iω ɛμ (4.15) v = ω ω ɛμ = 1 (4.16) ɛμ Maxwell rot xy H =0 rot xy E =0 U V E = xy U/ ɛ, H = xy V/ μ (4.17) E x = μ ɛ H y, μ E y = ɛ H x U x = V y, U y = V x (4.18) f(w) =U + iv w = x + iy Cauchy-Riemann z z J U( ) U a U b (U a U b )/ ɛ Z 0 Z 0 = U a U b J ɛ (4.19) Maxwell a b Z 0 q C r Gauss q/(2πɛr) V = q ɛ b a dr 2πr = C = q 2πɛ log b a = q C 2πɛ log(b/a) (4.20) J ( ) J r J Φ H(r) = J 2πr, μj B(r) = 2πr Φ= b L a drb(r) = μj 2π log b a L = μ log(b/a) (4.21) 2π 8-3

4 (4.12) L C L/C Z 0 = L C = 1 ( ) μ b 2π ɛ log a (4.22) TEM 2 *2 (4.9) Z 0 = μ0 ɛ 0 376Ω (4.23) μ/ɛ ( ) 2 ( Lecher line) ( ) VHF ( ) 4.5(a) ɛ μ a q ( ) r q/2πɛr 0 φ(r) =(q/2πɛ) log(r/a) 4.5(a) d a J φ 2 φ 1 φ 1 = φ 2 = J μ 2π log d a (4.24) d 2a (a) (b) (с) 4.5 (a) 2 (b) (c) 300Ω web *2 [3] 8-4

5 Z 0 = μ 1 ɛ π log d a (4.25) 4.5(c) μ = μ 0 ɛ = ɛ 0 d/a =10 Z 0 = 277Ω 300Ω (microstrip line) 4.6(a) 4.6(a) (a) 4.6(b) 4.6(a) PC GHz 3 ( 2.5 ) ( ) 4.6(a) [4] (W/h > 3.3) Z(W, h, ɛ r )= Z { F 0 W 2 ɛ r 2h + 1 π log 4 + ɛ [ ( )] } 1 r +1 πe W log 2πɛ r 2 2h ɛr 1 2πɛ 2 log eπ2, (4.26a) r 16 W t h r h r (a) (b) (c) 4.6 (a) ( ) (b) (c) 8-5

6 (W/h 3.3) Z F 0 Z(W, h, ɛ r )= π 2(ɛ r +1) log 4h W + ( ) 2 4h +2 W 1 ɛ r 1 2 ɛ r +1 ( log π log 4 ) ɛ r π (4.26b) Z F 0 ɛ r (ɛ = ɛ r ɛ 0 ) [5] (4.16) TEM *3 () (4.10) κ Z = R + iωl ω κ(ω) =iω ( LC 1 i R ) 1/2 i ω + 1 ωl ω 0 2 R (4.27) Z 0 ω ω R/L ω 0 1/ LC Z 0 L/C exp( κx + iωt) exp( Rx/2Z 0 ) 2Z 0 /R Z 0 Z l Z 0 Z 1 x x =0 + Z 0 Z 1 (4.12) V = V + + V = Z 0 (J + J ) J = J + + J } (4.28) l 0 x + exp κx Z 1 = V J = J + J J + + J Z 0 (x = 0) (4.29) x =0 ( ) r r = V = J = Z 1 Z 0 (4.30) V + J + Z 1 + Z 0 Z 1 = Z 0 0 *3 TE () TM () 8-6

7 (voltage-standing wave ratio, VSWR) VSWR = 1+ r (4.31) 1 r MHz x = l } V = V + exp (κl)+v exp ( κl) =Z 0 (J + exp (κl) J exp ( κl)) J = J + exp (κl)+j exp ( κl) (4.32) Z l Z l = V J = J + exp (κl) J exp ( κl) J + exp (κl)+j exp ( κl) Z 0 (4.33) r l r l = r exp ( 2κl) (4.34) κ = iω LC iβ (4.33) l tanh (κl) =i tan (βl) v/(2πω) λ Z l λ/2 l = λ/4 Z l = Z0 2 /Z 1 (4.35) λ/4 Z 1 = ( ) 0 (Z 1 =0) Z 0 Z 0 Z 0 Z 0 r = Z 0 Z 0 Z 0 + Z 0 (4.36) Z 1 r (Smith chart) Z 1 Z 0 Z n Z n = x + iy r = u + iw (x, y, u, w ) u + iw = r = Z n 1 (x 1) + iy = Z n +1 (x +1)+iy (4.37) x 1=(x +1)u yw y = yu + w(x +1) } (4.38) x (4.38) y ( u x ) 2 + w 2 = x +1 1 (x +1) 2 (4.39) 8-7

8 y =1 y = 2 y = 0.5 y = 4 y = 0.2 y = 0 y = 0.2 y = 0.5 x=0.5 x=1 x=2 x=4 y = 4 x=0.1 x=0 y = y = 2 (a) (b) 4.7 (a) (b) y ( (u 1) 2 + w 1 ) 2 = 1 y y 2 (4.40) x x 0 r (4.37) (4.37) Y 1/Z r = 1 Y (4.41) 1+Y (4.37) 180 (immitance chart)?? LCR r ω =0, r =1 r =1 S 1) [1] Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age (Johns Hopkins Univ. Press, 2002). [2] ( 1959) 8-8

9 [3] (2002). [4] H. A. Wheeler, IEEE Trans. Microwave Theory and Tech. 13, (1965). [5] D. B. Davidson, Computational electromagnetics for RF and microwave engineering (Cambridge Univ. Press, 2005). C ( ) ( ) C Ω 75Ω 50Ω (4.16) 75Ω 4.8(a) 4.4 GHz 4.8(b) ( ) 4.8(c) (flexible tube corrugate tube) JIS C3501 3D-2V 3 3 ( ) mm 3D-2V φ2.9 5D-2V φ4.8 10D-2V φ9.7 (a) (b) (c) (a) 2 (b) (c) 8-9

10 D D 50Ω C 75Ω 2 2 JIS JIS V V V, W 50Ω 75Ω C2. BNC 7 mm 2 4 GHz N 7mm GHz 7mm 7mm 18 GHz SMA 4.15 mm 18 GHz 3.5 mm 3. 5mm 40 GHz K 2.92 mm 40 GHz 2.4mm 2.4 mm 50 GHz V 1.85 mm 65 GHz W 1.1 mm 110 GHz 1.0 mm 1.0 mm 110 GHZ 4.9 Special No BNC BNC GHz 50Ω 75Ω N BNC 18GHz 20mm N 50Ω SMA N BNC 50Ω 8-10

11 () T 50Ω ( ) C3. LEMO LEMO NIM (Nuclear Instrumentation Module) LEMO / LEMO / / 8-11

120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2

120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2 9 E B 9.1 9.1.1 Ampère Ampère Ampère s law B S µ 0 B ds = µ 0 j ds (9.1) S rot B = µ 0 j (9.2) S Ampère Biot-Savart oulomb Gauss Ampère rot B 0 Ampère µ 0 9.1 (a) (b) I B ds = µ 0 I. I 1 I 2 B ds = µ 0

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