Microwave radiation passing through a slab of material

A comprehensive theoretical account of the interaction of microwave radiation with a slab of material has been given by Luoma of Emerson and Cummins Inc (1977). The information is now contained in one of Laird’s technical Notes as given below –

“Energy propagation in dielectric and magnetic materials”

If one considers the voltage transmission, T, one can write a simplified formula:

where L is the thickness of the sample

e is the permittivity (a complex number)

l is the wavelength of the radiation

An EXCEL worksheet gives the calculated result:

The experimental details are given in the article above, Am, J, Phys. 54. 1986, p712 and in this case the sample thickness is varied for a constant frequency of radiation.

However, if the material has a region of frequencies over which the permittivity can be assumed to be constant then the frequency can be varied and the sample thickness is then held constant.

Typical result from the calculations

As can be seen, a series of peaks occur due to standing waves being trapped on the 90 cm coaxial line.

A later publication can be found in Am. J. Phys. 73(8) 2005 p787 and this describes measurements being taken in a waveguide cell. In this case the program can be used with only a slight modification:

If one has access to the Advanced System Design (ADS) software from Agilent Inc then

Simulations for either coaxial lines or waveguide cells can be carried out

AND FOR A COAXIAL LINE

PERMITTIVITY VALUES ARE ENTERED AT THE ARROW