Permeability imaginary

Figure 1 Isolated system consisting of two sections separated by an imaginary permeable membrane. At equilibrium, the temperatures (T), pressures (P), and chemical potentials of each species i (p,) are equal in the two sections. 

The real part is the magnetic permeability whereas the imaginary part is the magnetic loss. These losses are quite different from hysteresis or eddy current losses, because they are induced by domain wall and electron-spin resonance. These materials should be placed at position of magnetic field maxima for optimum absorption of microwave energy. For transition metal oxides such as iron, nickel, and cobalt magnetic losses are high. These powders can, therefore, be used as lossy impurities or additives to induce losses within solids for which dielectric loss is too small. 

Major source of errors in LIvtv evaluation are the incomplete data of the frequency dependence of the dielectric permeability. Donners [263] has shown that Ylvw values derived from e(i ) where is the dielectric permeability of the imaginary axis of frequency [221,256], are not very reliable at thicknesses smaller than 10 nm. Since the Il(/ ) isotherms of thicker films exhibit such a disagreement as well, the inaccurate calculation of IW cannot be considered to be as an important reason. This is confirmed by the fact that Ylvw calculations employing another method for estimation of the dielectric permeability [259] does not show considerable differences. 

The values of the dielectric permeability of the imaginary axis of frequencies (/ ) were determined according to the method of Ninham and Parsegian [255] with non-linear... 

Complex permeability at 20-200 MHz was measured at room temperature. The real (p ) and imaginary (p") parts of the magnetic permeability p were recorded by a resonance method [3] at 25-200 MHz, with the alternating probing field oriented in the film plane and parallel to the sample axis. The relative error for the measured p was about 8 %. 

Figure 1. Real jj. (curves 1) and imaginary n" (curves 2) parts of permeability for/= 25 MHz vs concentration x for nanocomposiles deposited in Ar.

Figure 2. Real p (curves 1) and imaginary p" (curves 2) parts of complex permeability for /= 25 MHz vs metallic-to-dielectric phases ratio x in the nanocomposiles of set 2 deposited in argon-nitrogen gas mixture with p = 1.31 10 Pa (a) and p = 2.13-10 Pa (b).

Fig. 5.8. Effect of a gap on the frequency dependence of the real and imaginary permeabilities of a Zno.64Nio.36Fe204 ferrite (Verweel, 1971).

The imaginary part e" is a measure for the dielectric losses of the material Similarly, fi and fi" sse defined in relation to the permeability fi and fi" are defined in relation to the permeability /r ... 

The two vital EM attributes of shielding material are complex permittivity [e = (e + je")] and complex permeability = j/+ j ")]> which consists of real (polarization or storage) and imaginary (relaxation or loss) parts as shown in Figure 9.6 [1]. 

The imaginary part of the complex permittivity is a function of the conductivity of the medium and is given by e" = cr/m, where cr is the electrical conductivity of the material and co is the angular frequency of the wave. The permeability of the medium is similarly defined for magnetic fields and dipoles. In a microwave spectrum, materials are usually classified as insulators or conductors. If e 3> c , the material behaves as an insulator, and if e 3> e", the material behaves as a conductor. 

The Helmholtz equation results in a wave that propagates with a speed of 1 / y/ps. The real parts of the permittivity and permeability, s and p, affect the relation between the amplitudes of the E field and H field. The imaginary parts cause the power loss of the wave as it propagates within the medium. A more commonly used parameter for describing the power loss in an insulating medium is called the loss tangent ... 

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