Determine the minimum frequency components

Assignment Help Other Engineering

Reference no: EM132181604

Assignment - Waveguides

Waveguides are very long metallic tubes to guide the propagation of electromagnetic waves. The Maxwell's equations inside these waveguides can be written as:

These equations lead to the wave equations (taking the time dependence to be harmonic e^±iωt):

What you need to do:

Assume that z-axis along the length (the direction of wave propagation) of the wave-guide.

Rectangular waveguides:

E_x, E_y, B_x, B_y → Transverse components

E_z, B_z → Longitudinal components

To get all these six components, we need to solve Helmhotz equation six times (for each component) with their boundary conditions. But boundary conditions for all the transverse components are not usually readily known. So in practice, we solve for E_z and B_z and try to find the other 4 components in terms of E_z, B_z and their partial derivatives.

(1) You are required to derive expression for E_x, E_y, B_x and B_y in terms of E_z and B_z and their partial derivatives.

(2) Determine E_z(x, y, z) by solving the Helmhotz equation.

(3) The Transverse Electric (TE) mode:

In this mode, E_z = 0.

(a) Determine the 4 transverse components.

(b) Determine the minimum frequency that can be transmitted through a waveguide of width a.

(4) The Transverse Magnetic (TM) mode:

In this mode B_z = 0.

(a) Determine the minimum frequency components.

(b) Determine the minimum frequency that can be transmitted through a waveguide of width a.

(5) The Transverse Electromagnetic (TEM) mode:

In this mode, E_z = B_z = 0.

Show that, this mode is not possible in a waveguide with one surface. However, if the waveguide consists of two co-axial tubes, one inside the other, then, in principle, it is possible to have such a mode.

Derive expressions E_ρ, B_ρ, E_φ and B_φ.

And find the minimum frequency that can be propagated through this waveguide.

Attachment:- Assignment File.rar

Reference no: EM132181604

Questions Cloud

Financial crisis that occurred in 2008 : Discuss at least two economic reasons/factors that contributed to the financial crisis that occurred in 2008.

Production costs of computer chips are also at all-time low : The cost of laptops has also dropped. Come to think of it, production costs of computer chips are also at their all-time low.

Discuss a preferred approach you can use : For each of the strategies, provide an example where you can apply them in a personal or work situation.

Effect an increase in default-risk premium : Graphically (i.e., using the IS-LM model) illustrate and explain what effect an increase in default-risk premium

Determine the minimum frequency components : The Transverse Magnetic (TM) mode: In this mode Bz = 0. Determine the minimum frequency components. Determine the minimum frequency

Role-play to consult in the strategic planning process : BSBMGT616 — Develop and implement strategic plans - confirm organisational vision and mission, consider strategic opportunities, analyse the internal

Variable costs be considered less risky than fixed costs : Why might variable costs be considered less risky than fixed costs?

What is the total impact on spending : If the marginal propensity to consume (MPC) equals 0.75 and the government increases spending by $200 billion, what is the total impact on spending?

Explain your decision and your reasoning : The "You Decide" assignment presents a difficult and painful dilemma, with you in an imagined professional role. Go through the You Decide presentation.

User Account

All Pages