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M171L_1_5_Coax_F_10

# M171L_1_5_Coax_F_10 - LAB 5(10/28 Transmission Line...

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1 LAB 5 (10/28) Transmission Line Characteristics 1. Introduction 2. Properties of Coaxial Cable 3. Telegraph Equations 4. Characteristic Impedance of Coaxial Cable 5. Reflection and Termination 6. Transfer Functions of a Transmission Line 7. Coaxial Cable Without Frequency Distortion 8. Bode Plots 9. Properties of Twisted Pair Cable 10. Impedance Matching 11. Conclusion

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3 Center Wire Braided Outer Conductor (b) Structure of coaxial cable Outer Insulation Polyethylene Insulation (a) Structure of typical UTP cable 24 gauge copper wire with insulation Outer Insulation Four twisted pairs

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4 Coaxial cable with length l . It is composed of a number of intermediate segments with properties: R , L , G and C of a unit length of cable x l S ( t ) out S ( t ) in e ( x ) Inner Wire Outer Conductor x+ x e ( x+ x ) meter); per (Henrys ln 10 2 1 2 7 m H R R L = - R 1 : radius of inner wire R 2 : radius of braided outer conductor 2·10 -7 : derived from properties of dielectric material
5 Telegraph Equations x GΔx CΔx e ( x ) e ( x+ x ) LΔx RΔx x+ x t i x L i x R x e x x e ) ( ) ( ) ( ) ( - - = + t i x L i x R e x e x x e ) ( ) ( ) ( ) ( - - = - + x 0: t i L Ri x e - - = t x x e x C x x e x G x i x x i ) ( ) ( ) ( ) ( ) ( ) ( + - + - = + t x x e x C x x e x G x i x x i ) ( ) ( ) ( ) ( ) ( ) ( + - + - = - + t e C Ge x i - - = (1) (2) Equations (1) and (2) are called the telegraph equations.

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6 They determine e ( x, t ) and i ( x, t ) from the initial and the boundary conditions. (If we set R and L to zero in these equations, the simplified equations are telephonic equations). I Lj R I Lj I R dx U d ) ( ϖ ϖ + - = - - = U Cj G U Cj U G dx I d ) ( ϖ ϖ + - = - - = (3) (4) [ ] U Cj dt de C F x j U t x e F ϖ ϖ = = ; ) , ( ) , ( [ ] I Lj dt di L F x j I t x i F ϖ ϖ = = ; ) , ( ) , ( Solution of equations (3,4) by differentiating of equation (3) with respect to x , and combine with equation (4):
7 U Cj G Lj R dx I d Lj R dx U d ) ( ) ( ) ( 2 2 ϖ ϖ ϖ + + = + - = Define the value as 2 γ ) ( ) ( C j G L j R ϖ ϖ + + U dx U d 2 2 2 γ = x x A A U γ γ + - + = e e 2 1 A 1 and A 2 are independent of x , and can be calculated from the boundary

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