By André Moliton
This ebook offers functional and proper technological information regarding electromagnetic houses of fabrics and their functions. it truly is aimed toward senior undergraduate and graduate scholars in fabrics technological know-how and is the made from a long time of training uncomplicated and utilized electromagnetism. issues diversity from the spectroscopy and characterization of dielectrics, to non-linear results, to ion-beam functions in fabrics.
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Extra resources for Applied Electromagnetism and Materials
48 Applied electromagnetism and materials Hcr H''r Hf Hs H f 1 Z2 W2 1 ZC0 R1 R 2 (17) (H Hf )ZW + s . 1 Z2 W2 The evolution of the plot Hr’= f(Z) is identical to that of a Debye lot. In H’’r the second term is identical to that of the Debye type, while the first term appears as a 1 supplementary term that caries with . Therefore, when Z o 0, Hr’’ o f. 5b. 6. 5. Impedance spectroscopy Given the discussion above, it is now possible to graphically summarize the representations of İ' and İ" as a function of the angular frequency, H’’ = f(H’), and also |Im(Z)| = f[Re(Z)] or Im(Y) = f[Re(Y)].
3a it is possible to state that: 1 1 Z ZS 1 1 , where Zp = Zp jZCp and ZS = RS + 1 jZCS . From this we can determine that: 1 Z = Z²CS2 R S ª º CS + jZ « Cp ». 1 Z²CS2 R S2 1 Z²CS2 R S2 »¼ «¬ (6) By making WS = RSCS, identification with Eq. (1) leads to: Hr’ = Hr’’ = Cp C0 CS 1 C0 1 Z² WS2 ZR SCS2 C0 ª1 Z²CS2 R S2 º ¬ ¼ (7) = CS ZWS C0 1 Z² WS2 . Chapter 2. 3. (a) Scheme of equivalent series parallel circuit and (b) plots of H’ =(logZ) and H’’ = f(logZ). Following these equations, it is possible to say that: x if Z = 0, Hr’’ = 0, then Hr’ is at a maximum (the derivative wH ' wZ 2ZWS2 CS C0 1 Z² W2 S 2 cancels out when Z = 0) and is equal to (Hr’)max = x Cp CS C0 (8) if Z o f, Hr’’ o 0, and Hr’ tends towards a minimal, as in (Hr’)min = x = HS .
3b. The dipole used (series and parallel combined) thus can be a good equivalent to a dielectric exhibiting a Debye type relaxation phenomenon, as the two plots have the same form. In fact, if we take the preceding values from Eqs. (8) and (9) for HS and Hf into the Eqs. , H Hf Hf s and Hccr 1 Z2 W2 Hcr (Hs Hf )ZW . 1 Z2 W2 Comment. The angular frequency ( Zmax ) for which tan G Hc ' ( Hs H f )ZW is a maximum can be calculated using Hs Hf Z2 W2 H' ª w tan G º « » ¬ wZ ¼ Zmax 0 , which leads to Z2max 1 CS / CP HS2 , from which: 1/ 2 1 CS / Cp = 2 1 Cp / CS (tgG)max .
Applied Electromagnetism and Materials by André Moliton