Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Complex permittivi

As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field. The response must always be causal (arising after the applied field) which can be represented by a phase difference. For this reason permittivity is often treated as a complex function (since complex numbers allow specification of magnitude and phase) of the (angular) frequency of the applied field ω, varepsilon 
ightarrow widehat{varepsilon}(omega). The definition of permittivity therefore becomes

D_0 e^{-i omega t} = widehat{varepsilon}(omega) E_0 e^{-i omega t},

where

D0 and E0 are the amplitudes of the displacement and electrical fields, respectively,
i is the imaginary unit, i 2 = −1.

The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity εs (also εDC ):

varepsilon_{	ext{s}} = lim_{omega 
ightarrow 0} widehat{varepsilon}(omega).

At the high-frequency limit, the complex permittivity is commonly referred to as ε. At the plasma frequency and above, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for alternating fields of low frequencies, and as the frequency increases a measurable phase difference δ emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength (E0), D and E remain proportional, and

widehat{varepsilon} = frac{D_0}{E_0} = |varepsilon|e^{idelta}.

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:

widehat{varepsilon}(omega) = varepsilon'(omega) + ivarepsilon''(omega) = frac{D_0}{E_0} left( cosdelta + isindelta 
ight).

where

ε′ is the real part of the permittivity, which is related to the stored energy within the medium;
ε″ is the imaginary part of the permittivity, which is related to the dissipation (or loss) of energy within the medium.

Office Hours

Monday 10 -2

Tuesday 10-12

Thursday 11-1

My Timetable

Contacts


email: a.abokhalil@mu.edu.sa

a_galal@yahoo.com

Phone: 2570

Welcome

Welcome To Faculty of Engineering

Almajmaah University

IEEE

Institute of Electrical and Electronics Engineers

http://www.ieee.org/

http://ieeexplore.ieee.org/Xplore/guesthome.jsp

http://ieee-ies.org/

http://www.ieee-pes.org/

http://www.pels.org/

Links of Interest

http://www.utk.edu/research/

http://science.doe.gov/grants/index.asp

http://www1.eere.energy.gov/vehiclesandfuels/

http://www.eere.energy.gov/


القران الكريم

http://quran.muslim-web.com/

Travel Web Sites

http://www.hotels.com/

http://www.orbitz.com/

http://www.hotwire.com/us/index.jsp

http://www.kayak.com/

Photovoltaic Operation


Wave Power

World's Simplest Electric Train



PeltierModule-JouleThief-Fridge

homemade Aircondition

Salt water battery


إحصائية الموقع

عدد الصفحات: 2879

البحوث والمحاضرات: 1292

الزيارات: 41519