--Previous Message--

: hi,

: i have problem regarding calculating the dielectric loss. i have a

: ceramic disc of 3mm and 45mm dia having dielectric constant 10 and loss

: tangent 0.0003. Microwave power of 24kw is passing through it at a

: frequency of 2.856 GHz. Please inform me the mathematics to calculate the

: dielectric loss in the ceramic.

: raju

: Hello Raju,

I have comparatively little experience with microwave engineering, but I'll try to provide some starting points.

The estimated power (in watts/cubic cm) that will be converted to heat within the dielectric due to losses can be estimated as:

Pd = (55.61*10^-14*)*(Ed^2)*f*Er*tan(d)

where:

Pd = watts/cm^3

Ed = field strength in volts/cm within the dielectric

f = frequency (in hertz) = 2.856*10^9

Er = relative dielectric constant = 10

tan(d) = 0.0003

A simple plane, sinusoidal, TEM wave in free space (Zo = 377 ohms) will have an average E field (Eo) of:

Eo = Sqrt(P*377)

where P = watts/meter^2.

The E field within the dielectric (Ed) will be about 1/10 of Eo because of the ceramic material's relatively high dielectric constant.

However, it's quite unlikely that you have this simple of a case in reality.

Finally, the total power in watts absorbed by your dielectric slab will be:

W = Pd*V

where:

V = the volume of your particular dielectric slab

= 0.3*Pi*(4.5/2)^2

= 4.77 cm^3

IN reality, the actual distribution of the electric field within the dielectric is most likely quite non-uniform and, as a result, you'll develop a number of "hot spots" wherever the E-field is more intense. A more exact solution will require using field solver/modelling software.

Here are some sources of information you may find helpful:

http://www.pueschner.com/engl/pdfs/basics_adv_en.pdf

http://www.pueschner.com/engl/pdfs/MicrowaveHeating.pdf

http://rpaulsingh.com/teaching/LectureHandouts/microwave_handout.pdf

Hope this helped and best regards,

Bert