Statistics-lab™可以为您提供washington.edu PHYS322 electrodynamics电动力学的代写代考和辅导服务！
PHYS322 electrodynamics课程简介
This course provides a deeper look into the theory of electricity and magnetism.
We shall study:
– magnetostatics
– magnetic fields in matter
– Maxwell’s equations
– electromagnetic waves
PREREQUISITES
Upon successful completion of this course you will be able to:
- Understand the implications of Ampère’s and Biot-Savart’s laws
- Understand the nature of the vector potential
- Understand the behaviour of magnetic fields in medium
- Be perfectly familiar with Maxwell’s equations
- Know the nature of momentum and angular moment in Electrodynamics
- Understand the details of propagation of electromagnetic waves
PHYS322 electrodynamics HELP（EXAM HELP， ONLINE TUTOR）
Coaxial waveguides are often used in particle accelerators. There are several reasons for this;
- The waveguide can receive, transport and transmit electromagnetic waves.
- There is no leakage of waves.
- The fundamental mode is the TEM mode, which propagates for all frequencies.
- Both the phase speed and group speed of the fundamental mode are equal to the speed of light for all frequencies.
The losses in coaxial waveguides comes from the currents running along the outer and inner conductor. The losses decrease with increasing radii of the conductors. If the radii increase they eventually reach values where higher order modes start to propagate.
a) Consider a coaxial waveguide with vacuum between the conductors. Let the inner conductor have radius $a=1 \mathrm{~cm}$ and the outer conductor an inner radius of $b=2.3 \mathrm{~cm}$. Find the frequency where the second mode can start to propagate.
b) Determine if the second mode is a TE- or TM-mode.
Hints: 2D. Electromagnetic waves. Eigenfrequency. Booleans and Partitions. Difference. The fundamental mode does not show up as a resonance in Comsol so you should look for the lowest resonance frequency that is larger than zero.
a) To find the frequency where the second mode can start to propagate, we need to determine the cutoff frequency for the second mode. The cutoff frequency is the frequency below which a mode cannot propagate.
In a coaxial waveguide with vacuum between the conductors, the cutoff frequency for the $n$-th mode is given by:
f_{c,n}=\frac{1}{2\pi\sqrt{\epsilon_r}}\frac{c}{\sqrt{\left(\frac{m\pi}{b}\right)^2+\left(\frac{n\pi}{a}\right)^2}}fc,n=2πϵr1(bmπ)2+(anπ)2c
where $\epsilon_r$ is the relative permittivity of the dielectric material between the conductors (in this case, vacuum), $c$ is the speed of light, $a$ is the radius of the inner conductor, $b$ is the inner radius of the outer conductor, $m$ and $n$ are integers that determine the mode.
For the second mode, we have $m=1$ and $n=2$. Plugging in the values, we get:
f_{c,2}=\frac{1}{2\pi\sqrt{1}}\frac{c}{\sqrt{\left(\frac{\pi}{2.3 \mathrm{~cm}}\right)^2+\left(\frac{2\pi}{1 \mathrm{~cm}}\right)^2}}\approx 1.04 \mathrm{~GHz}fc,2=2π11(2.3 cmπ)2+(1 cm2π)2c≈1.04 GHz
Therefore, the frequency where the second mode can start to propagate is approximately $1.04 \mathrm{~GHz}$.
b) To determine whether the second mode is a TE- or TM-mode, we need to look at the electric and magnetic fields of the mode.
Consider that you like to use the coaxial waveguide in problem 1 for transmitting signals with frequencies between $100 \mathrm{MHz}$ and $2.2 \mathrm{GHz}$. Close to the transmitter there is a source that generates a signal with frequency $1.6 \mathrm{GHz}$. Also this signal is transmitted and you have to get rid of it. To do this you build a bandstop filter. You cut the coaxial waveguide in two pieces and put a short coaxial waveguide between the two pieces, as in the figure. The extra waveguide also has the radius $1 \mathrm{~cm}$ of the inner conductor. To find the proper radius $c$ of the outer conductor and the height $h$ you use Comsol. The flat surfaces between the outer conductors, marked in the figure, are also made of metal.
Determine $a$ and $h$ such that all frequencies except $1.6 \mathrm{GHz}$ pass. The width of the stop band should be less than $50 \mathrm{MHz}$ at the $3 \mathrm{~dB}$ level.
Hints: Axial symmetry. Type of port: Coaxial. S-parameters. What affects the frequency and what affects the bandwidth?
To design the bandstop filter for the coaxial waveguide, we need to determine the appropriate dimensions of the added short coaxial waveguide. We can use simulation software like Comsol to model the waveguide structure and simulate its response to different frequencies.
To start, we can define the geometry of the coaxial waveguide and the added short waveguide in Comsol, with axial symmetry as indicated in the problem statement. We can then define the material properties of the waveguide, such as the conductivity and permittivity of the metal, and set up a port boundary condition at the input and output of the waveguide.
We can then use the S-parameters of the waveguide to analyze its frequency response. The S-parameters are a set of parameters that describe the relationship between the incident and reflected signals at the input and output of the waveguide. By analyzing the S-parameters, we can determine the frequency and bandwidth of the filter.
To design a bandstop filter, we need to find the dimensions of the added short waveguide that will create a resonant structure at the frequency of the unwanted signal (1.6 GHz), which will cause the signal to be reflected and attenuated. The dimensions of the added waveguide will affect the frequency of the reson
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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