# 1 Lecture 2 Transmission Line Characteristics 1. Introduction 2. Properties of Coaxial Cable 3. Telegraph Equations 4. Characteristic Impedance of Coaxial.

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1 Lecture 2 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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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 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 0: (1) (2) Equations (1) and (2) are called the telegraph equations.

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 (we assume no series impedance), the simplified equations are telephonic equations). (3) (4) Solution of equations (3,4) by differentiating of equation (3) with respect to x, and combine with equation (4):

7 Define the value as A 1 and A 2 are independent of x, and can be calculated from the boundary conditions at x = 0 and x = l. The value of is derived from the properties of the coaxial cable and the frequency : (7) (6) ( ) is the attenuation coefficient. ( ) is the phase shift coefficient. (5)

8 Characteristic Impedance of Coaxial Cable For the Fourier-transformed current insert (6) into equation (3) from equation (7) above:

9 Reflection and Termination reflected voltage / incident voltage; To express this signal in the time domain, we must divide (6) into its magnitude and phase components. We express =F(, ):

10 We can find the relationship between the magnitudes of A 1 and A 2 if we know that Z rec is pure resistance (a real value of impedance) and we know the value of Z:

11 Z = 50, R tot = 50, and = 2 V Z rec = 0, Z rec = 50 Z rec =

12 Ethernet Technologies: 10Base2 10: 10Mbps; 2: under 200 meters max cable length thin coaxial cable in a bus topology repeaters used to connect up to multiple segments repeater repeats bits it hears on one interface to its other interfaces: physical layer device only!

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14 Ethernet Cabling The most common kinds of Ethernet cabling.

15 Transfer Functions of Coaxial Cable For f<100 kHz

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17 Bode Plots

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20 Appendix Error analysis The goal of the lab experiment is to determination the transmission line bandwidth of a coaxial cable. We will use the experimental data to construct an amplitude Bode plot, and find the frequency for which the signal is attenuated by less than 3 dB. This is the bandwidth for which half or more of the input signal power is delivered to the output. the absolute error in 20·log 10 | H( j ) | due to the errors U out and U in :

21 transfer from decimal to natural logarithms with the correction factor 0.434 [ log 10 (e) ]: The worst case will occur when V out = - V in. If we set V out = 0.025:

22 Amplitude bode plot with error bars on amplitude axis.

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