Determine the minimum frequency components

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

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