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

2. Introduction
A communication network is a collection of network elements integrated and managed to support the transfer of information.
Data Transmission: links and switches.
Optical fiber
Copper coaxial cable
Unshielded twisted wire pair
Microwave or radio “wireless” links.
Optical fiber and copper links are usually point-to-point links, whereas radio links are usually broadcast links.
  Guided media:
twisted pair (unshielded and shielded)
coaxial cable
optical fiber
Unguided media:
radio waves
microwaves (high frequency radio waves)

4. Coaxial cable with length l
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
R1: radius of inner wire
R2: radius of braided outer conductor
2·10-7: derived from properties of dielectric material

5. Telegraph Equations x  0: (2) (1)
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
(5)
(6)
A1 and A2 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)
() is the attenuation coefficient. () is the phase shift coefficient.

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 A1 and A2 if we know that Zrec is pure resistance (a real value of impedance) and we know the value of Z:

11. Z = 50, Rtot= 50, and = 2 V
Zrec = 0,
Zrec = 50
Zrec = 

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!

14. The most common kinds of Ethernet cabling.

15. Transfer Functions of Coaxial Cable
For f<100 kHz

17. Bode Plots

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·log10 | H( j ) | due to the errors Uout and Uin :

21. transfer from decimal to natural logarithms with the correction factor 0.434 [ log10(e) ]:
The worst case will occur when Vout = -Vin . If we set Vout = 0.025:

22. Amplitude bode plot with error bars on amplitude axis.