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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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

Telegraph Equations

"They determine e("

	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).

Slide 7

Characteristic Impedance of Coaxial Cable

	For the Fourier-transformed current insert (6)  into equation (3)

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
	g =F(a,b):

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      Bode Plots

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Slide 19

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( jw ) | due to the errors DUout and DUin :

"transfer from decimal to natural..."

	transfer from decimal to natural logarithms with the correction factor 0.434 [ log10(e) ]:

Amplitude bode plot with error bars on amplitude axis.