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PROGRAMMING PROJECT #1
Computing Capacitance and Inductance of a Coaxial Transmission Line
A coaxial transmission line is not merely a piece of wire, as you have no doubt realized by now.
It is capable of supporting the propagation of guided electromagnetic waves, which enables the
transmission of information between points.
As we have learned in our study of electromagnetic fields so far, particularly through many
examples using the coaxial transmission line, there exists an inductance, capacitance and hence a
characteristic impedance for the transmission line.
For the transmission line above, the relative dielectric constant Ɛ and the relative permeability µ
represents media present in the coaxial line.
We have shown in previous lectures that the capacitance of the coaxial line can be derived from
the charge (hence the E-field) using Gauss’s Law for the formulation shown below.
We have also show that the inductance can be similarly derived from the current (hence the
magnetic field) using Ampere’s Law for the dual formulation show below.
The characteristic impedance of the coaxial line (characterized by the ratio of the outside
diameter of the inner conductor d and the inside diameter of the shield D, the dielectric constant
of the insulator Ɛ and the permeability µ can be calculated according to the equation:
Knowing the capacitance and inductance of the transmission line, it is then possible to construct
an equivalent model of the coaxial line (shown below), which enables faster and accurate circuit
design for transmission applications.
You will learn more about this in subsequent lectures and more advanced courses, should you
choose to pursue studies in high speed communications. A few types of coaxial lines as well as
their respective typical applications are shown in the table immediately below.
For this assignment you will use the coaxial cable LMR-100A (same as Project #1). More details
can be found at http://www.timesmicrowave.com. A copper inner conductor is of diameter d =
0.92 mm. The polyethylene (PE), used as a dielectric insulator, has the relative permittivity Ɛr =
2.30 and the loss factor tan δ = 0.001. The inner diameter of the shield is D = 3.04 mm. The outer
conductor consists of aluminum foil which is covered with the copper braid and a layer of
plastic. Note that the permeability for this is simply µr=1.
Write one or more short Python program(s) to compute and plot the following:
Capacitance versus length
Inductance versus length
Characteristic Impedance versus permittivity(Ɛr)
All Python code used
Concise write-up/summary (3 pages maximum) of the programming project including
brief background theory, diagrams, code, plots and conclusion
In-class demonstration of your code being executed