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This paper seeks to consider the design of small, naturally cooled, and high‐frequency (in excess of 10 kHz) inductors. Its purpose is to show that the design of such inductors can be obtained from the solution of a signomial program. In its most general form, the signomial program calls for minimising the total mass (or cost) of the inductor whilst ensuring the satisfaction of the inductance value together with constraints imposed by the copper fill‐factor, the allowed temperature rise, Kirchhoff's mmf law, and the core flux density.

The signomial program is solved using a sequential geometric programming (SGP) approach specifically tailored to the inductor design problem. In essence, SGP seeks a constrained minimum mass (or cost) solution by optimally setting the inductor geometry parameters, the air‐gap length, and the relevant electrical and magnetic quantities.

Design results reveal that including the inductor geometry parameters in the set of problem variables leads to significant savings in the inductor mass (or cost).

In cases where there are restrictions on the inductor weight, the optimal solution of the signomial program can be used for manufacturing inductors having cores with non‐standard sizes. In other applications where core dimensions are chosen from the manufacturer's database, the SGP approach can be used to complete the design by either maximising the inductance value or minimising the total loss whilst enforcing a given inductance value.

This work presents a first attempt to optimise an inductor design via signomial programming. The proposed solution methodology is based on SGP, but specifically adapted to the inductor design problem.

This paper presents performance comparison of RF inductors with the same lateral geometry applying different substrate configurations. The purpose of presented research is to demonstrate and verify some advantages of low temperature co-fired ceramic (LTCC) technology in comparison to printed circuit board (PCB) technology based on the performance analysis of presented inductors in lower RF range.

The presented inductors are meander structures fabricated in LTCC and PCB technology, with same line width and outer dimensions. Performance analysis of all configurations is based on measurement results and numerical simulations. Advantage of LTCC technology is demonstrated by application of substrate pattering in order to maintain and/or improve expected inductor performances.

As expected, obtained results for the inductor with an air-gap show increase of the quality factor over 30 percent and widening of the operating frequency range by 50 percent when compared with the same LTCC structure without a gap. But what is more important the inductor with air-gap embedded inside LTCC stack maintains efficiency when compared to PCB inductor. This fact offers possibility of integration good quality components inside LTCC stack and reduction of used chip space.

Advantages of LTCC with respect to PCB design are demonstrated by efficiency increase of the proposed inductor configurations by means of design optimization relying on substrate pattering and incensement of the packaging density by embedding inductors. The presented findings are verified through consistency of measurement results and simulated data.

The paper aims to present the novel design approach for a low power LC-voltage-controlled oscillators (VCO) design with low phase noise that too targeted at the most sought band of Bluetooth applications. Owing to their crucial role in a wide variety of modern applications, VCO and phase-locked loop (PLL) frequency synthesizers have been the subject of extensive research in recent years. In fact, VCO is one of the key components being used in a modern PLL to provide local frequency signal since a few decades. The complicated synthesizer requirements imposed by cellular phone applications have been a key driver for PLL research.

This paper first opted to present the recent developments on implemented techniques of LC-VCO designs in popular RF bands. An LC-VCO with a differential (cross-coupled) MOS structure is then presented which has aimed to compensate the losses of an on-chip inductor implemented in UMC’s 130 nm RF-CMOS process. The LC-VCO is finally targeted to embed onto the synthesizer chip, to address the narrowband (S-Band) applications where Bluetooth has been the most sought one. The stacked inductor topology has been adopted to get the benefit of its on-chip compatibility and low noise. The active differential architecture, which basically is a cross-coupled NMOS structure, has been then envisaged for the gain which counters the losses completely. Three major areas of LC-VCO design are considered and worked upon for the optimum design parameters, which includes Bluetooth coverage range of 2.410 GHz to 2.490 GHz, better linearity and high sensitivity and finally the most sought phase noise performance for an LC-VCO.

The work provides the complete design aspect of a novel LC-VCO design for low phase noise narrowband applications such as Bluetooth. Using tuned MOS varactor, in 130 nm-RF CMOS process, a high gain sensitivity of 194 MHz/Volt was obtained. Thus, the entire frequency range of 2415-2500 MHz for Bluetooth applications, supporting multiple standards from 3G to 5G, was covered by voltage tuning of 0.7-1.0 V. To achieve the low power dissipation, low bias (1.2 V) cross-coupled differential structure was adopted, which completely paid for the losses occurred in the LC resonator. The power dissipation comes out to be 8.56 mW which is a remarkably small value for such a high gain and low noise VCO. For the VCO frequencies in the presented LO-plan, the tank inductor was allowed to have a moderate value of inductance (8 nH), while maintaining a very high Q factor. The LC-VCO of the proposed LO-generator achieved extremely low phase noise of −140 dBc/Hz @ 1 MHz, as compared to the contemporary designs.

Though a professional tool for inductor and circuit design (ADS-by Keysight Technologies) has been chosen, actual inductor and circuit implementation on silicon may still lead to various parasitic evolutions; therefore, one must have that margin pre-considered while finalizing the design and testing it.

The proposed LC-VCO architecture presented in this work shows low phase noise and wide tuning range with high gain sensitivity in S-Band, low power dissipation and narrowband nature of wireless applications.

The on-chip stacked inductor has uniquely been designed with the provided dimensions and other parameters. Though active design is in a conventional manner, its sizing and bias current selection are unique. The pool of results obtained completely preserves the originally to the full extent.

Present 3D electromagnetic simulators have high accuracy but they are time and memory expensive. Owing to a fast and simple expression for inductance is also necessary for initial inductor design. In this paper, new efficient methods for total inductance calculation of meander inductor, are given. By using an algorithm, it is possible to predict correctly all inductance variations introduced by varying geometry parameters such as number of turns, width of conductor or spacing between conductors.

The starting point for the derivation of the recurrent formula is Greenhouse theory. Greenhouse decomposed inductor into its constituent segments. Meander inductor is divided into straight conductive segments. Then the total inductance of the meander inductor is a sum of self‐inductances of all segments and the negative and positive mutual inductances between all combinations of straight segments. The monomial equation for the total inductance of meander inductor has been obtained by fitting procedure. The fitting technique, using the method of least squares, finds the parameters of the monomial equation that minimize the sum of squares of the error between the accurate data and fitted equation. The paper presents new expression for inductance of meander inductor, in the monomial form, which is suitable for optimization via geometric programming. The computed inductances are compared with measured data from the literature.

The first, recurrent, expression has the advantage that it indicates to the designer how the relative contributions of self, positive, and negative mutual inductance are related to the geometrical parameters. The second expression presents the inductance of the meander inductor in the monomial form, so that the optimization of the inductor can be done by procedure of the geometric programming. Simplicity and relatively good accuracy are the advantages of this expression, but on the other hand the physical sense of the expression is being lost. Thus, the effects of various geometry parameters on inductance are analyzed using two expressions and the software tool INDCAL.

Applied flexible efficient methods for inductance calculation of meander inductor are able to significantly increase the speed of RF and sensor integrated circuit design.

For the first time a simple expression for fast inductance calculation for meander inductor in monomial form is presented. It is explained how such an expression is generated, which can be directly implemented in circuit simulators.

Recognizing the need and the room for improvement in computer aided engineering (CAE), evolutionary programming and, more specifically, genetic algorithms are used together with an expert system in a hybrid approach to inductor design. The genetic algorithm is used to derive design suggestions and the expert system for the appropriate testing and evaluation of these suggestions. In addition to functional manufacturing constraints, other optimization goals can be added.

This paper aims to present an efficient method to improve quality factor of printed fractal inductors based on electromagnetic band-gap (EBG) surface.

Hilbert fractal inductor is designed and simulated using high-frequency structural simulator. To improve the quality factor, an EBG surface underneath the inductor is incorporated without any degradation in inductance value.

The proposed inductor and Q factor are measured based on well-known three-dimensional simulator, and the results are compared experimentally.

The proposed method was able to significantly decrease the noise with increase in the speed of radio frequency and sensor-integrated circuit design.

Fractal inductor is designed and simulated with and without EBG surfaces. The measurement of printed circuit board prototypes demonstrates that the inclusion of split-ring array as EBG surface increases the quality factor by 90 per cent over standard fractal inductor of the same dimensions with a small degradation in inductance value and is capable of operating up to 2.4 GHz frequency range.

This paper aims to overcome the lack of methodologies for optimizing the volume of bulky low-frequency inductors that the authors came across with when working on the design of hybrid active power filters. Sound work was published concerning this well-known technology, but it became evident that the mentioned optimization topic was left unaddressed.

Using the Lagrange multipliers optimization method combined with the electromagnetic laws of inductor design, it was possible to establish a new design method to determine the optimal solutions that fulfil any given scenario of specifications. In other words, it is now possible to obtain the inductor’s geometric and electric parameters that not only satisfy the system’s electromagnetic requirements but also lead to smaller, lighter or economical solutions.

A generalized set of equations was obtained to facilitate the calculations of all the inductor-building parameters. As expected, these equations take as inputs the inductor’s required inductance, its maximum current and the desired resistance, but also a customizable cost function. The later cost function will optimize the inductor’s volumes of copper and iron and can be settled, among other purposes, for minimizing the total weight, volume or cost.

All the mathematical expressions to obtain the general optimal solutions are given as well as practical graphics for the three above-mentioned optimization criteria. Using these charts, the reader will be able to obtain by simple inspection the optimal solutions for a large, generalized universe of intended specifications.

The purpose of this paper is to design an on-chip inductor with high inductance, high-quality factor and high self-resonance frequency for the equivalent on-chip area using fractal curves.

A novel hybrid series stacked differential fractal inductor using Hilbert and Sierpinski fractal curves is proposed with two different layers connected in series using vias. The inductor is implemented in Sonnet EM simulator using 180 nm CMOS standard process technology.

The proposed inductor reduces the parasitic capacitance and negative mutual inductance between the adjacent layers with significant improvement in overall inductance, quality factor and self-resonance frequency when compared with conventional series stacked fractal inductors.

The fractal inductor is used to create high inductance in the single-layer process, but access to multilayers is restricted owing to unusual and expensive fabrication processes.

The proposed inductor can be used in implementation of low noise amplifier, voltage controlled oscillators and power amplifiers.

This paper introduces a combination of two fractal curves to implement a hybrid fractal inductor that enhances the performance of the inductor.

The purpose of this study is to develop a high-quality factor fractal inductor for wireless applications such as satellite, WLAN, Bluetooth, microwave, radar and cellular phone.

The Hilbert fractal curve is used in the implementation of the proposed inductor. In the proposed inductor, the metal width has split into multiple paths based on the skin depth of the metal. The simulations of the proposed inductor are performed in 180 nm CMOS technology using the Advanced Design System EM simulator.

The multipath technique reduces the skin effects and proximity effects, which, in turn, decreases the series resistance of the inductor and attains high-quality factor over conventional fractal inductor for the equal on-chip area.

The width of the path has chosen higher than the skin depth of the metal for a required operating frequency. Due to cost constraints, the manufacturing of the proposed fractal inductor is limited to a single layer.

The proposed inductor will be useful for the implementation of critical building blocks of radio frequency integrated circuits and monolithic microwave integrated circuits such as low-noise amplifiers, voltage-controlled oscillators, mixers, filters and power amplifiers.

This paper presents for the first time the use of a multipath technique for the fractal inductors to enhance the quality factor.

Magnetic fluid hyperthermia experiment requires a uniform magnetic field in order to control the heating rate of a magnetic nanoparticle fluid for laboratory tests. The automated optimal design of a real-life device able to generate a uniform magnetic field suitable to heat cells in a Petri dish is presented. The paper aims to discuss these issues.

The inductor for tests has been designed using finite element analysis and evolutionary computing coupled to design of experiments technique in order to take into account sensitivity of solutions.

The geometry of the inductor has been designed and a laboratory prototype has been built. Results of preliminary tests, using a previously synthesized and characterized magneto fluid, are presented.

Design of experiment approach combined with evolutionary computing has been used to compute the solution sensitivity and approximate a 3D Pareto front. The designed inductor has been tested in an experimental set-up.