We often see two relation for calculation the dielectric permittivity:
(1) E= C/C0 where E = dielectric permittivity, C = capacitnace and C0 is the geometric capacitance.
(2) E = Z"/wC0(Z'2+Z"2), where Z' and Z" are the real and imaginary part of complex impedance.W = angular frequency
What is the difference between these two relations? Why the values of dielectric permittivity are found different when one calculates using (1) and (2) ?
The first formula comes from definition of capacitance for an ideal capacitor
without fringing fields an with negligible losses. It does nott say how to measure
capacitane.
The second formula comes from the relationship between the complex impeance of
lossy capacitor and the complex permittivity.
Note that generally Z=Z'- jZ" =1/[jwC0(E'-jE")] where j denotes imaginary unit.
You can easily find by separation of the real and the imaginary parts
of this expression that E = Z"/wC0(Z'^2+Z"^2)
which means that you can determine permittivity at the angular frequency w from measurements the complex impedance of capacitor at this frequency.
If losses of the capacitor are small than Z"^2 in formulae (2) can be neglected and the first formula and the second formula are formally equivalent
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetism