Notes

Outline

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

Slide 2

Slide 3

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):

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Bode Plots

Slide 18

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 DU_out and DU_in:

"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.