Theory Of Skin Effect Research Articles

Frequency and Power Dependence of Passive Intermodulation in Connectors With Contact-Material Nonlinear Modeling

Passive intermodulation (PIM) is generally regarded as an unavoidable interference in radio frequency (RF) circuit and system, which exhibits dynamic characteristics with the change of signal frequencies and powers. In this letter, a prediction model of frequency and power dependence of PIM is theoretically proposed and experimentally verified. Physical nonlinearities of truncated distortion and tunneling effect are introduced to provide explanations for the contact surface-induced PIM. Considering nickel is the nonlinear material source in connector coating, the impact of signal frequency on PIM is investigated by calculating the current density in the magnetic area coupled with skin effect theory. Through the combination of two PIM generation mechanisms, a novel equation-based equivalent circuit model is provided to simulate the third-order intermodulation (IM3) powers in connector resulting from different signal frequencies and powers. The frequency and power dependence characteristics are observed from both the theoretical predictions and measurements.

DETERMINATION OF EQUIVALENT QUANTITIES OF ELECTROMAGNETIC FIELD IN MASSIVE FERROUS DETAILS OF ELECTRIC EQUIPMENT UNDER STRONGLY VARYING LOADS

Purpose. To derive the relationships for calculating determination of equivalent quantities for electromagnetic field in massive ferrous bodies at strongly varying loads.Methodology. We have applied methodological fundamentals of skin-effect theory for massive ferrous bodies combined with methods of mathematical physics as well as physical and computer simulation.Findings. We have found the mathematical expressions for the equivalence ratios allowing calculate basic electromagnetic field quantities, such as magnetic flux and losses, in massive ferrous bodies under strongly varying loads. Their adequacy is confirmed by research on physical and computer models, as well as existing computational procedures of the additional losses in the massive units of energy-intensive electrical equipment for special purposes.Originality. For the first time, we have established mathematical dependencies between skin losses and magnetic flux in massive ferrous body and total and individual harmonic distortion of periodically varying magnetic and electric fields. Found dependences are the basis for the development of refined computational procedures for determining the parameters of the electromagnetic field in massive ferromagnetic elements of electrical equipment under strongly-varying loads.Practical value. The use of derived expressions for the equivalence ratios enable successfully solve the problems aimed to optimize constructive components when designing electrical equipment for supplying consumers with strongly-varying behavior of the load.

Skin Effects of Induced Eddy in Lossy Layered Stratum

The study of induced eddy skin effects plays an important role to determine the reservoir distribution. This paper calculated the apparent conductivity of loss stratum by the use of geometrical factor theory and skin effects theory. The numerical results show that the skin effect theory has higher accuracy due to the consideration of the interaction between the induced eddy currents. And it is also easy to spread in use of inhomogeneous media. These conclusions provide a theoretical basis for the analysis of electromagnetic response characteristics in lossy multilayered stratum.

Superconducting surface impedance under radiofrequency field

Based on BCS theory with moving Cooper pairs, the electron states distribution at 0K and the probability of electron occupation with finite temperature have been derived and applied to anomalous skin effect theory to obtain the surface impedance of a superconductor under radiofrequency (RF) field. We present the numerical results for Nb and compare these with representative RF field-dependent effective surface resistance measurements from a 1.5GHz resonant structure.

Performance Analysis of Three Phase Squirrel Cage Induction Motor with Deep Rotor Bars in Transient Behavior

The rotor parameters, the resistance and the leakage inductance, vary with the currents frequency of rotor bars due to skin effect, and for small frequencies can be negligible (under 10 15 Hz); but for higher frequencies this variation of the parameters cannot be negligible. In this paper, for higher frequencies some analytic expressions are proposed, that result from the skin effect theory, for the rotor resistance and for the leakage inductance. The simulations were done by SYMNAP - SYmbolic Modified Nodal Analysis Program, a program that can determine, in a full-symbolic form the voltages and the currents for the equivalent scheme for one phase of the asynchronous motor. Symbolic expressions for the characteristics quantities of the general regime of the induction motor allow graphic representation for different parameters. These analytic expressions allows a more accurate analysis of asynchronous motor performance for different drive systems. To simulate the dynamic (transient) behavior of the induction motor, Park-Blondel equations have been used; these equations have a nonlinear form due to both their structure and frequency variation of the rotor parameters. The integration of these equations is performed with the help of the integration routines for ordinary differential equations in Matlab programming environment. It was found that the nominal values of the quantities that characterize the induction motor operation, obtained by simulation, practically coincide with the values from the catalogue.

Magnetic properties of micro- and nanowires in the superhigh-frequency range

The skin-effect theory is presented using the example of an amorphous ferromagnetic material taking into account the ferromagnetic resonance. The theoretical dependence of the impedance of a microwire on its magnetic permeability is determined. The results allow analyzing experiments on studying the high-frequency properties of amorphous microwires.

A physics-based VLSI interconnect model including substrate and conductor skin effects

The goal of this work was to model the influence of the substrate and conductor skin effects on the RL line characteristics of on-chip interconnects. The proposed modelling approach is based on the skin-effect theory results for rectangular wires and the complex integration technique for perturbation series per unit length impedance of silicon substrate. It is shown that the calculated frequency-dependent distributed inductance and the associated resistance are in good agreement with the results obtained from rigorous full-wave solutions and CAD-oriented analytic modelling technique.

On the theory of skin effect: inclusion of arriving term in collision integral

An algorithm for calculating the surface impedance of a normal isotropic metal is constructed by taking into account the arriving term in the collision integral (in the case of specular reflection). Analytic expressions are obtained for scattering probability describing the s-, p-, and d-scattering.

Superconductor–insulator–superconductor tunnel strip line: Features and applications

The superconductor–insulator–superconductor (SIS) tunnel junction based on Nb material has been investigated theoretically at frequencies of 200–1400 GHz by modeling it as a segment of a superconducting microstrip transmission line and using the Mattis–Bardeen theory of anomalous skin effect. The modeling was used to predict the performance of a flux-flow oscillator (FFO) and a SIS frequency down-converter (mixer). It is shown that in a FFO the internal loss (quasiparticle and surface) limits flux flow to the frequency band of 260–770 GHz. A SIS junction of micron size employed as a mixer for frequency down-conversion demonstrates distributed behavior at frequencies above 550 GHz. We suggest that electrically long SIS junctions of resonant size can be used as self-compensating mixing elements with attractive performance in Nb as well as NbN mixers.

The optical properties of manganese thin films

The optical constants n and k of thin manganese films of different thicknesses ranging from 20 up to 50 nm were determined in the spectral range 3.5–20 μm. The results were compared with the predictions of the Drude free electron theory and anomalous skin effect theory. The previous theories were used to evaluate some micro characteristics of Mn thin films such as the free charge concentration N, the relaxation time τ, the static conductivity σ s, and the electron velocity at Fermi surface V F and the value of the effective area of Fermi surface A F. Using the optical constants, the optical conductivity ( σ = σ 1 + i σ 2) was also estimated. It was found that the contribution of the effective absorption A eff equals 69%, i.e. the absorption due to bound electrons may be 31%.

Interpretation of attenuated total reflection changes induced by a submonolayer of caesium adatoms on silver films

The attenuated total reflection changes induced by a submonolayer of caesium on silver are precisely analysed in the framework of the semiclassical anomalous skin effect theory. It is shown that the variations observed in the clean film reflectance may be attributed partially to a decrease in the Fuchs specularity parameter at the perturbed surface. The superficial dipolar layer absorption contribution is, however, predominant, and is about three times greater than that from the Fuchs specularity parameter.This work confirms that the anomalous skin effect and surface polarization corrections cannot be ignored when an accurate determination of the bulk optical constants is desired.

The near-IR surface impedance of thin metallic films with unlike surfaces

A simple formula is proposed for the near-IR surface impedance of thin metallic films with unlike surfaces. It is derived from a previous N-dimensional model based on the Reuter and Sondheimer anomalous skin effect theory. The relative precision on the surface resistance thus calculated is found to be a few times 0.1% at wavelengths smaller than or about 2 μm. Anisotropy may easily be introduced into the electron relaxation time to treat the polycrystalline case or (and) into the Fuchs electron-surface scattering parameters.

Thermal radiative properties of some cryogenic materials

The normal reflectivities of Al and Al alloys which are important as cryogenic materials are measured mainly in the infrared region below room temperature down to 16 K. A new model is proposed which assumes that in the Drude equation, additional scattering of conduction electrons occur at the surface layer which explains the temperature dependence of the radiative properties. This model can predict the radiative properties of metals at low temperatures better than the anomalous skin effect theory.

Thermal Radiative Properties of the Noble Metals at Cryogenic Temperatures

Experimental values of the monochromatic, near normal emittance, ελN, of gold at cryogenic temperatures are presented and compared with values predicted by existing theoretical models. From this comparison recommendations are made regarding the engineering suitability of these models. Data obtained by the present authors for ελN of gold in the wavelength range 1 to 30μ and at temperatures of 300, 79, and 6.0 K are compared with the Drude free electron model, the anomalous skin effect theory for both specular and diffuse electron reflections, and the Holstein quantum mechanical model. Results show that the anomalous skin effect model with diffuse electron reflections predicts ελN most accurately. At room temperature and at liquid nitrogen temperature the agreement between this model and the data is within 5 percent. At liquid helium temperatures the agreement is somewhat poorer, i.e., within 30 percent.

On the normal skin-effect theory for inhomogeneous conductors

On the normal skin-effect theory for inhomogeneous conductors

Modal Theory of Skin Effect in Single and Multiple Turn Coils

The skin effect in circularly symmetric structures is formulated in terms of an integral equation, which may be solved in terms of the normal modes of the corresponding integral equation eigenvalue problem. The necessary modal functions are computed numerically, using a simple discrete model of the coil. The modal series solution easily accounts for electrical excitation of the coil as for external magnetic fields. A comparison with so-called direct calculation methods, as well as with published experimental results, shows that the method is capable of good accuracy, while effecting substantial economies in computation.

Thick Film Analysis of Radiative Transfer Between Parallel Metallic Surfaces

The radiative transfer between two infinite parallel metallic surfaces separated by a nonconducting ideal dielectric is calculated on the basis of electromagnetic wave theory. The solution is restricted to the case of large spacing (thick film) wherein the effects of interference and radiation tunneling can be neglected. The optical properties of the metals are predicted via the anomalous skin effect theory, the Drude single electron theory and the Hagen-Rubens relation. A comparison of the predicted radiative fluxes indicates the large disparities which result from the three different specifications of the optical properties of metals. For practical applications at cryogenic temperatures, approximations are obtained for the thick film solution using the anomalous skin effect theory of the optical properties.

Zur Mikrowellendiagnostik stromstarker Entladungen mit Skineffekt. Teil II: Bestimmung der Plasmaparameter eines angeströmten Stickstoffbogens bei Atmosphärendruck

AbstractMicrowave diagnostics of an inhomogeneous, dense, cylindrical plasma column may be used to determine the complex impedance and a mean noise temperature in the range of strong skin effect (theory see part I). This case is realized if the specific d.c. impedance E/I falls below a critical value, e.g. 20 Ω/cm for ω = 1010. It is shown, that for any radial conductivity profile the complex impedance is a function of E/I only.A formula is derived for calculating the noise temperature of the column as a weighted mean value due to the local plasma temperature and conductivity. In the case of strong skin effect this mean value equals the electron temperature of plasma regions near the boundary of the conducting diameter.These results in connection with spectroscopical diagnostics are use to determine some plasma parameters of an arc discharge in a streaming nitrogen atmosphere at 760 Torr. The temperature profil was obtained from the intensity of the 3371 Å molecular band and then the conductivity profile was calculated using an energy balance equation.The results show that even in the 10 A‐case the arc plasma is not in thermal equilibrium, the difference Te—Tg being about 1,500 ºK. This large difference is due to the flow of neutral gas streaming downward the discharge chamber. The length of the discharge (1·3 cm) is not sufficient for the neutral atoms to reach their equilibrium temperature.

Far-Infrared Absorption Spectra of Thick Superconducting Films

We have examined the absorption spectra of thick evaporated films of Pb, Sn, In, V, Ta, and Nb in the superconductive energy-gap region by a calorimetric detection technique. The intensity available from our far-infrared monochromator, together with the improved sensitivity of the detection system, made it possible to employ modulation techniques to obtain the derivatives of the absorption spectra of our samples. Multiple energy gaps were found for a Sn film and two thick Pb films, while a thinner Pb film and the other samples had single gaps. We suggest that these are the first far-infrared measurements to reveal multiple absorption edges in films. The energy gaps found for the two thick Pb films were $(4.18\ifmmode\pm\else\textpm\fi{}0.04)k{T}_{c}$ and $(4.46\ifmmode\pm\else\textpm\fi{}0.04)k{T}_{c}$ for one, and $(4.28\ifmmode\pm\else\textpm\fi{}0.04)k{T}_{c}$ and $(4.65\ifmmode\pm\else\textpm\fi{}0.04)k{T}_{c}$ for the other. For the Sn film, the gaps were $(3.58\ifmmode\pm\else\textpm\fi{}0.02)k{T}_{c}$ and $(3.86\ifmmode\pm\else\textpm\fi{}0.04)k{T}_{c}$. The gaps found for the other samples, in units of $k{T}_{c}$, were: for the thin Pb film, 4.34\ifmmode\pm\else\textpm\fi{}0.02; for In, 3.69\ifmmode\pm\else\textpm\fi{}0.04; for V, 3.4\ifmmode\pm\else\textpm\fi{}0.1; for Ta, 3.5\ifmmode\pm\else\textpm\fi{}0.2; and for Nb, 3.6\ifmmode\pm\else\textpm\fi{}0.2. These values are more precise than the earlier far-infrared results; in addition, the anomalously low values of $\ensuremath{\sim}3k{T}_{c}$ obtained in previous far-infrared experiments for the Ta and Nb gaps are not reproduced in this work. The observed absorption edges are steeper than those predicted by either the extreme local or extreme anomalous limits of skin-effect theory. The energy gap of a thick Pb sample was measured as a function of magnetic field, this being the first such measurement by far-infrared calorimetric techniques. The gap was found to decrease by approximately 7% in going from zero field to the critical field for the bulk material (${H}_{\mathrm{cb}}$), in fair agreement with the Ginzburg-Landau theory. No gap was observed above ${H}_{\mathrm{cb}}$, in agreement with previous observations on the superconducting surface sheath.

Verification of the Anomalous-Skin-Effect Theory for Silver in the Infrared

The measured infrared reflectance of silver films prepared by rapid evaporation in ultrahigh vacuum was found to be in excellent agreement (0.1%) with values predicted by the anomalous skin effect theory in the wavelength region from 4-24 \ensuremath{\mu} (values of $\ensuremath{\omega}\ensuremath{\tau}$ between 15 and 2, where $\ensuremath{\tau}$ is the relaxation time). If a small correction term was included for electron-electron collisions, the agreement could be extended to 1 \ensuremath{\mu} ($\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\simeq}50$). The theoretical curves were determined from values of dc conductivity and Hall constant measured on silver films prepared in the same evaporation as the optical samples. No optical data were used to fit the calculated curves to the experimental data. Silver films of varying degrees of roughness were prepared by evaporating silver onto supersmooth fused-quartz optical flats which had been roughened with calcium fluoride films. It was found that there was no difference between the infrared reflectance of rough and smooth silver samples for roughnesses up to 45 \AA{} rms. Thus $p\ensuremath{\simeq}1$, a condition usually interpreted as specular reflection of the conduction electrons, for surfaces about an order of magnitude rougher than the value predicted by simple diffraction theory. For rougher surfaces, $p$ dropped rapidly to 0 and, for the roughest surfaces studied (\ensuremath{\sim}100 \AA{} rms), the reflectance was somewhat lower than that predicted theoretically.