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Magnetic Ceramics
Published in Lionel M. Levinson, Electronic Ceramics, 2020
For the same reasons, it is important that the inductance (or permeability) of a material not vary significantly with changes in temperature, drive level, superimposed DC, or time. Magnetic components, such as telephone and transmission lines, can be subject to extreme temperatures. Most telephones have superimposed direct current at times for ringing purposes. Some components are expected to operate for about 20 years without great differences in properties. Figures 14 and 15 show the variations of some ferrite material with temperature and frequency. These variations are obtained by chemistry and processing control. Note that in Fig. 14 there are materials in which the permeability slopes are positive with respect to temperature and one in which it is flat. The resonant frequency of an LC circuit is obtained when the effects of inductance and capacitance cancel. At that frequency, the following condition exists: fres=12πLC
Basic ideas
Published in C.W. Evans, Engineering Mathematics, 2019
The resonant frequency of a circuit of inductance L and capacitance C with negligible resistance is given by f = 1/[2π√(LC)]. If L and C increase respectively by 1% and 2%, estimate the percentage error in f.
Silicon Carbide Oscillators for Extreme Environments
Published in Sumeet Walia, Krzysztof Iniewski, Low Power Semiconductor Devices and Processes for Emerging Applications in Communications, Computing, and Sensing, 2018
Daniel R. Brennan, Hua-Khee Chan, Nicholas G. Wright, Alton B. Horsfall
The internal losses within the tank circuit are compensated by the amplifier, which draws energy from the DC supply used in the circuit, resulting in a constant oscillation magnitude. LC oscillators are most commonly used at radio frequencies, where a tunable frequency source is required. Three commonly used circuit configurations are the Hartley, Colpitts and Clapp oscillators, as shown in Figure 10.10a–c, respectively.
Theoretical analysis of new techniques applied to applications in fluid dynamics
Published in International Journal of Modelling and Simulation, 2023
Nazek A. Obeidat, Mahmoud S. Rawashdeh
The generalized KdV equation is a crucial model for a number of physical phenomena, such as shallow-water waves close to the critical value of surface tension and waves in a nonlinear LC circuit with mutual inductance between neighboring inductors [1–4]. An LC circuit is a type of electric circuit that consists of a capacitor and an inductor coupled together. It is also known as a tuned circuit, tank circuit, or resonant circuit. Even if the precise solution of the fifth-order KdV equation was found for the special case of solitary waves, there is no universal solution for this class of models; see [5]. The Lax equation, the Sawada–Kotera equation, the Kaup–Kuperschmidt equation, the Caudrey–Dodd–Gibbon equation, and the Ito equation are just a few examples of the many KdV-type equations that make up the extended fifth-order Korteweg–de Vries (efKdV) equation, which is a crucial equation in fluid dynamics for the description of nonlinear wave processes; see [6]. The Sawada–Kotera equation is a well-known mathematical model that appears in many physical systems to explain how long waves flow in shallow water while being affected by gravity and moving through a one-dimensional nonlinear lattice [7–12].
Resonant inductive-coupling configurations with load-independent transfer-parameters for wireless power transfer – a perspective from the transformer equivalent-models
Published in EPE Journal, 2018
The models of Figure 4 can be immediately related to the double-sided double-tuned configurations of Figure 1: Figure 4(a) → PS, Figure 4(b) → SP, Figure 4(c) → SS, and Figure 4(d) → PP. In all these configurations, the capacitors make series LC circuits with the series inductors of the models, and they make parallel LC circuits with the parallel inductors. In a certain configuration, if the primary LC circuit and the secondary LC circuit resonate at the same frequency and the system is operated at that frequency, all the inductors and capacitors are eliminated from the circuit point of view, and the equivalent model is reduced to the ideal transformer or to the ideal gyrator, exposing them. This is due to the fact that, at resonance, a series LC circuit is a short-circuit and a parallel LC circuit is an open-circuit, in the frequency domain. Under such resonance conditions, several load-regulation phenomena must occur: for the PS and SP configurations, the transfer-parameters Av and Ai become load-independent; for the SS and PP configurations, the transfer-parameters Zm and Ym become load-independent, according to (5).