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Phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude and initial phase are time-invariant and whose angular frequency is fixed. It is related to a more general concept called analytic representation,Bracewell, Ron. ''The Fourier Transform and Its Applications''. McGraw-Hill, 1965. p269 which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor. A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency. Phasor representation allows the analyst to represent the amplitude and phase of the signal using a single complex number. The only difference in their analytic rep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Signal
In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analytic representation of a real-valued function is an ''analytic signal'', comprising the original function and its Hilbert transform. This representation facilitates many mathematical manipulations. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead. That makes certain attributes of the function more accessible and facilitates the derivation of modulation and demodulation techniques, such as single-sideband. As long as the manip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Analysis (electrical Circuits)
In electrical engineering and electronics, a '' network'' is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values; however, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to ''linear'' network analysis. Definitions Equivalent circuits A useful procedure in network analysis is to simplify the network by reducing the number of components. This can be done by replacing physical components with other notional components that have the same effect. A particular technique might directly reduce the number of components, for instance by combining impedances in series. On the other hand, it might merely change the form into one in which the components can be reduced in a later operation. For instance, one might transform a voltage ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronics Engineering
Electronic engineering is a sub-discipline of electrical engineering that emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors, and capacitors. It covers fields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. It is also involved in many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, photonics and robotics. The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important professional bodies for electronics engineers in the US; the equivalent body in the UK is the Institution of Engineering an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Proteus Steinmetz
Charles Proteus Steinmetz (born Karl August Rudolph Steinmetz; April 9, 1865 – October 26, 1923) was a Prussian mathematician and electrical engineer and professor at Union College. He fostered the development of alternating current that made possible the expansion of the electric power industry in the United States, formulating mathematical theories for engineers. He made ground-breaking discoveries in the understanding of hysteresis that enabled engineers to design better electromagnetic apparatus equipment, especially electric motors for use in industry. At the time of his death, Steinmetz held over 200 patents. A genius in both mathematics and electronics, he did work that earned him the nicknames "Forger of Thunderbolts" and "The Wizard of Schenectady". Steinmetz's equation, Steinmetz solids, Steinmetz curves, and Steinmetz equivalent circuit are all named after him, as are numerous honors and scholarships, including the IEEE Charles Proteus Steinmetz Award, one of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steady State (electronics)
In electronics, steady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important. Steady state is reached (attained) after transient (initial, oscillating or turbulent) state has subsided. During steady state, a system is in relative stability. The term sinusoidal steady state emphasizes that sine waves of essentially-infinite duration may exist, as long as their amplitude and frequency remain constant. Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics. Periodic steady-state solution is also a prerequisite for small signal dynamic modeling. Steady-state analysis is therefore an indispensable component of the design process. Calculation methods Steady state calculation methods can be sorted into time-domain algorithms (time domain sensitivities, shooting) and frequency-domain algorithms ( harmonic ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RLC Circuit
An RLC circuit is an electrical circuit consisting of a electrical resistance, resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC. The circuit forms a harmonic oscillator for current, and resonance, resonates in a manner similar to an LC circuit. Introducing the resistor increases the decay of these oscillations, which is also known as damping. The resistor also reduces the peak resonant frequency. Some resistance is unavoidable even if a resistor is not specifically included as a component. RLC circuits have many applications as electronic oscillator, oscillator circuits. receiver (radio), Radio receivers and television sets use them for tuner (electronics), tuning to select a narrow frequency range from ambient radio waves. In this role, the circuit is often referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0, where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x^5-3x+1=0 is an algebraic equation with integer coefficients and :y^4 + \frac - \frac + xy^2 + y^2 + \frac = 0 is a multivariate polynomial equation over the rationals. For many authors, the term ''algebraic equation'' refers only to the univariate case, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables (the ''multivariate'' case), in which case the term ''polynomial equation'' is usually preferred. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved algebraically). This can be done for all such eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Electric
General Electric Company (GE) was an American Multinational corporation, multinational Conglomerate (company), conglomerate founded in 1892, incorporated in the New York (state), state of New York and headquartered in Boston. Over the years, the company had multiple divisions, including GE Aerospace, aerospace, GE Power, energy, GE HealthCare, healthcare, lighting, locomotives, appliances, and GE Capital, finance. In 2020, GE ranked among the Fortune 500, ''Fortune'' 500 as the 33rd largest firm in the United States by gross revenue. In 2023, the company was ranked 64th in the Forbes Global 2000, ''Forbes'' Global 2000. In 2011, GE ranked among the Fortune 20 as the 14th most profitable company, but later very severely underperformed the market (by about 75%) as its profitability collapsed. Two employees of GE—Irving Langmuir (1932) and Ivar Giaever (1973)—have been awarded the Nobel Prize. From 1986 until 2013, GE was the owner of the NBC television network through its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
