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The purpose of this paper is to present a method for calculating frequency-dependent resistance when multiple current-carrying conductors are present.

Analytical and numerical formulations are presented. Both skin- and proximity-effects are considered in the numerical approach, whereas only skin-effect can be taken into account in analytical equations. The calculation is done using a self-developed integral equation-based field solver. The results are benchmarked using professional software based on the finite element method (FEM).

Results from the numerical approach are in agreement with FEM-based software throughout the whole frequency range. Analytical formulations yield unsatisfactory results in higher frequency range. When multiple conductors are mutually relatively close, the proximity-effect has an impact on effective resistance and has to be taken into account.

The methodology is presented using axially symmetrical conductors. However, the same procedure can be developed for straight conductors as well.

Presented fast and stable procedure can be used in most electromagnetic devices when frequency-dependent resistance needs to be precisely determined.

The value of the presented numerical methodology lies in its ability to take both skin- and proximity-effects into account. As conductors are densely packed in most electromagnetic devices, both effects influence the effective resistance. The method can be easily implemented using a self-developed solver and yields satisfactory results.

Platinum gold conductors, used as solderable terminations, contain a glass frit which reacts with the minority constituents in debased alumina substrates forming an adhesive bond. Some conductor inks also contain copper and cadmium, in addition to the glass frit, which react directly with the alumina to form a chemical bond. Dielectric inks contain a crystalline filler, such as alumina or zirconia, in a glass matrix. The effect on the physical and electrical properties of platinum golds on various dielectrics was examined in comparison with the behaviour on alumina. Composition and surface structure of the dielectric affects the adhesion strength, solderability and solder leach resistance of the conductor inks. Interaction between the glasses in the dielectrics and conductors was determined by analysis in the SEM. Interdiffusion between the conductor and solder metals occurs and brittle intermetallic compounds are formed. The effects of the intermetallic formation on the adhesion strength and modes of failure, especially after thermal ageing at 150°C, have been examined. Thick film resistors printed and fired onto dielectrics rather than onto alumina substrates generally have different electrical properties. Chosen resistor systems, terminated with a gold conductor, were evaluated on different dielectrics. The values of electrical parameters such as resistance, TCR and noise index were compared with those on alumina. Interactions between the glasses in the resistors and dielectrics were examined as for the conductors. Thermal ageing on various resistor/dielectric combinations was carried out in order to determine the long‐term stability. The activation energies and time dependences of the ageing mechanisms for each combination were found. Corresponding ageing equations were calculated in order to predict the likely behaviour during life.

The paper aims to develop expressions for calculating the mutual impedance between isolated conductors buried in homogeneous earth. The conductors have finite length and arbitrary position.

The conductors are represented by the use of elementary electric dipoles. Well‐known existing expressions are employed for the electric field of these dipoles. The induced voltages are evaluated and the final expressions for the mutual impedance are derived. The resulting expressions involve infinite double integrals, evaluated by using adaptive quadratures that are, however, time consuming. Therefore, an alternative approach is followed involving Sommerfeld integrals (SI) for representing the electric field of a dipole and a recently devised method for computing the SI, in the spatial domain, by using calculation of discrete complex images.

Final expressions for parallel and perpendicular conductors were derived and numerical results for several values of frequency, conductors' length and horizontal distance between them, were produced. Comparison to results produced with the well‐known Pollaczek formula showed excellent agreement.

For future research, it is possible to use the developed expressions for earthing systems study, where the grounding grid is discretized and the moment method is invoked.

Currently, the formulas used for calculating mutual impedance are valid for parallel conductors of infinite length. With the present work, accurate expressions are given for finite length and arbitrary horizontal positioned conductors. In addition, the use of SI and the discrete complex image method results in a rapid and efficient tool for massive impedance calculations.

Establishes a quantitative evaluation method on solder bridging in microsoldering using a printed wiring board with comb pattern conductors. Bridge tests were conducted by immersing the comb pattern board into a molten solder bath. The total length of solder bridge between conductors against the total length between conductors was measured as a measure of the occurrence of solder bridging. The occurrence of bridging depended on the number of immersions, flux activity including solid content, conductor spacing, solder bath temperature and solder composition. The increase in number of immersion enhanced bridging. The rosin flux without activators showed higher bridging than the activated flux. Sn‐37Pb solder showed lower bridging than Sn‐3.5Ag‐5Bi solder. Solder bridging was found to be closely correlated with wettability, therefore, the improvement of wettability could be effective to suppress solder bridging. The proposed method is believed to be suitable for the quantitative evaluation of solder bridging.

It is proposed that reliable multilevel thick‐film conductor interconnect, having high track conductivity, can be fabricated with conventional air‐firing thick‐film materials, by combining the high conductivity of a pure silver conductor with the solderability of a palladium‐silver conductor. Thick‐film conductor interconnect fabricated in this manner was shown to meet comfortably the stringent requirements of a 20 year service life. A development in the standard technology used to obtain high conductivity interconnect, nitrogen‐firing copper thick‐film materials was also evaluated. It was found that new lower porosity dielectrics may allow copper thick‐film conductor interconnect to be as reliable as the air‐firing alternatives. The activation energy for the process of silver migration through a thick‐film dielectric in a humid environment was found to be in the region of 0.6 eV. The accelerating influence of humidity was also measured.

The purpose of this study is to evaluate and minimize the losses of alternating current (AC) in the winding of electrical machines. AC winding losses are frequently disregarded at low frequencies, but they become a significant concern at high frequencies. This is the situation where applications require a high speed. The most significant applications in this category are electrical propulsion and drive systems.

An analytical model is used to predict the AC losses in the winding of electrical machines. The process involves dividing the slot into separate layers and then calculating the AC loss factor for each layer. The model aims to calculate AC losses for two different winding arrangements involving circular conductors. This application focuses on the stator winding of a permanent magnet synchronous motor that is specifically designed for electric vehicles. The model is integrated into an optimization process that makes use of the genetic algorithm method to minimize AC losses resulting from the arrangement of conductors within the slot.

This study and its findings demonstrate that the arrangement of the conductors within the slot has a comparable effect on the AC losses in the winding as the machine's geometric and physical properties. The effectiveness of electrical machines depends heavily on optimizing the arrangement of conductors in the slot to minimize AC winding losses.

The proposed strategy seeks to minimize AC winding losses in high-speed electric machines by providing a cost-effective and precise solution to improve energy efficiency.

In this chapter, I re-frame leading in organizing as teaching and identify physical movement as a core mechanism through which leaders are sensitive and responsive to the progress of their group’s learning. To demonstrate this, I analyze interview data with choral and orchestral conductors in terms of Sheets-Johnstone’s (1999/2011) four qualities of movement: tension, linearity, amplitude, and projection. These four qualities serve as a grammar or set of basic categories to better understand how and why leaders move in certain ways in relation to their followers, for the sake of the latter’s learning and the collective ability to accomplish organizational goals. The ability to categorize conductors’ physical movements and the movement of the ensemble’s learning can help practitioners and scholars to assess the congruence between the two. With this grammar in hand, leaders can better assess and articulate what kinds of movements can be performed when, in order to guide the progress of their group’s collective learning.

Few organisations exhibit the importance of physicality in leadership as explicitly as the symphony orchestra. While usually attributed to the direction of the conductor my own experience suggests that leading in orchestral performance is grounded in physical relations between individuals and among instrumental groups across the orchestra as much as in the interaction between musicians and maestro. In order to further interrogate this experience while enhancing our understanding of onstage relations among orchestral musicians, I recently undertook research that employed an autoethnographic methodology underpinned by the phenomenology of Merleau-Ponty (2002, 2004) and the sense-making ideas of Weick (1995, 2001a). Using this method while drawing on ideas such as kinaesthetic empathy (Pallaro, 1995; Parviainen, 2002), the picture presented in what follows is one of leadership embedded in physical interaction among colleagues.

This interaction is, I suggest, based on sense-making and sense-giving activity that occurs in a ‘kinaesthetic loop’ that draws on and is generated by auditory, visual and gestural information given and received by individual musicians. This activity in turn mediates the acoustic space between musicians and thus, ultimately, determines how leadership and coordination in the orchestra are constituted. Rather than being disembodied products of dictatorial direction dispensed through the orchestra’s hierarchy, orchestral performance and leadership emerge in this more nuanced account as co-creative processes in which all the musicians on stage share responsibility.

Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors.

The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance.

The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation.

The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires.

The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

Driven by the demand for higher density in electronic packaging, each signal plane of printed wiring board must accommodate more conductors. As a result, conductor width is becoming narrower each year. This chapter reviews some of the important steps of forming finer line conductors in printed wiring boards, such as surface preparation, plating/etching, photo‐exposure, automatic optical inspection, etc.