Page - 19 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

2.1. ElectromagneticHeating 0.1 1 10 ε' ε' ≈ εs ε' ≈ ε∞ log(ωτ) log(ωτ) ε'' Figure2.3. Amplitudesofε′ andε′′ atdifferent frequencies [Met96]. According to above equations, the varying curves of ε′ and ε′′ are showninfigure 2.3. Intuitively, the real amplitudeε′ can be considered as the in-phase re- sponse with the external electric field −→ E, which defines the amount of energy that can be stored within the dielectric and does not cause energy loss. The imaginary amplitude ε′′ can be considered as the response that has 90◦ phase shift with −→ E, which determines the amount of energy dissipation from the external electric field and the heat generation within the dielectric. Correspondingly, the density of power dissipated into the dielectric due to the dipole relaxation is [Mer98] pd= 1 2 ωε0ε ′′(ω) ∥∥∥−→E∥∥∥2 , (2.4) whereε0= 8.85×10−12F/m isthepermittivityofvacuum. Itisevident from above equations as well as figure 2.3 thatf0= 1/τ is the critical pointwherethedipolepolarizationfailstofollowthedirectionchange of −→ E. Thereforeit ismoreefficienttousemicrowaveswithfrequencies 19