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Richards' Transformation
Commensurate line circuits are electrical circuits composed of transmission lines that are all the same length; commonly one-eighth of a wavelength. Lumped element circuits can be directly converted to distributed-element circuits of this form by the use of Richards' transformation. This transformation has a particularly simple result; inductors are replaced with transmission lines terminated in short-circuits and capacitors are replaced with lines terminated in open-circuits. Commensurate line theory is particularly useful for designing distributed-element filters for use at microwave frequencies. It is usually necessary to carry out a further transformation of the circuit using Kuroda's identities. There are several reasons for applying one of the Kuroda transformations; the principal reason is usually to eliminate series connected components. In some technologies, including the widely used microstrip, series connections are difficult or impossible to implement. The freque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commensurate Line Theory
Commensurate line circuits are electrical circuits composed of transmission lines that are all the same length; commonly one-eighth of a wavelength. Lumped element circuits can be directly converted to distributed-element circuits of this form by the use of Richards' transformation. This transformation has a particularly simple result; inductors are replaced with transmission lines terminated in short-circuits and capacitors are replaced with lines terminated in open-circuits. Commensurate line theory is particularly useful for designing distributed-element filters for use at microwave frequencies. It is usually necessary to carry out a further transformation of the circuit using Kuroda's identities. There are several reasons for applying one of the Kuroda transformations; the principal reason is usually to eliminate series connected components. In some technologies, including the widely used microstrip, series connections are difficult or impossible to implement. The frequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase (waves)
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richards Transform Of Chebyshev Filter
Richards may refer to: *Richards (surname) In places: * Richards, New South Wales, Australia * Richards, Missouri, United States * Richards, Texas Richards is an unincorporated community and census-designated place (CDP) in eastern Grimes County, Texas, United States. The community is located on Farm roads 1486 and 149. The Chicago, Rock Island and Pacific Railroad line passes the east sid ..., United States In other uses: * Richards (lunar crater), on the Moon {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Admittance
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance is the siemens (symbol S); the older, synonymous unit is mho, and its symbol is ℧ (an upside-down uppercase omega Ω). Oliver Heaviside coined the term ''admittance'' in December 1887. Heaviside used ''Y'' to represent the magnitude of admittance, but it quickly became the conventional symbol for admittance itself through the publications of Charles Proteus Steinmetz. Heaviside probably chose ''Y'' simply because it is next to ''Z'' in the alphabet, the conventional symbol for impedance. Admittance is defined as :Y \equiv \frac \, where :''Y'' is the admittance, measured in siemens :''Z'' is the impedance, measured in ohms Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: ''self capacitance'' and ''mutual capacitance''. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operations of the capacitor, a device designed for this purpose as an elementary Linear circuit, linear electronic component. Capacitance is a function only of the geometry of the design of the capacitor, e.g., the opposing surface area of the plates and the distance between them, and the permittivity of the dielectric material between the plates. For many dielectric materials, the permittivity and thus the capaci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called ''back EMF''. Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. It is a proportionality factor that depends on the geometry of circuit conductors and the magnetic permeability of nearby materials. An electronic component designed to add inductance to a circuit is called an inductor. It typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stub (electronics)
In microwave and radio-frequency engineering, a stub or resonant stub is a length of transmission line or waveguide that is connected at one end only. The free end of the stub is either left open-circuit, or short-circuited (as is always the case for waveguides). Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus function as capacitors, inductors and resonant circuits at radio frequencies. The behaviour of stubs is due to standing waves along their length. Their reactive properties are determined by their physical length in relation to the wavelength of the radio waves. Therefore, stubs are most commonly used in UHF or microwave circuits in which the wavelengths are short enough that the stub is conveniently small. They are often used to replace discrete capacitors and inductors, because at UHF and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Driving Point Impedance
Driving is the controlled operation and movement of a vehicle, including cars, motorcycles, trucks, buses, and bicycles. Permission to drive on public highways is granted based on a set of conditions being met and drivers are required to follow the established road and traffic laws in the location they are driving. The word driving, has etymology dating back to the 15th century and has developed as what driving has encompassed has changed from working animals in the 15th to automobiles in the 1800s. Driving skills have also developed since the 15th century with physical, mental and safety skills being required to drive. This evolution of the skills required to drive have been accompanied by the introduction of driving laws which relate to not only the driver but the driveability of a car. Etymology The origin of the term ''driver'', as recorded from the 15th century, refers to the occupation of driving working animals, especially pack horses or draft horses. The verb ' '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Delay
In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifier, loudspeaker, telecommunications system or ethernet cable. These delays are generally frequency dependent. This means that different frequency components experience different delays, which cause distortion of the signal's waveform as it passes through the system. This distortion can cause problems such as poor fidelity in analog video and analog audio, or a high bit-error rate in a digital bit stream. For a modulation signal (passband signal), the information carried by the signal is carried exclusively in the wave envelope. Group delay therefore operates only with the frequency components derived from the envelope. Introduction The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Frequency
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the complex frequency domain, also known as ''s''-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication. For suitable functions ''f'', the Laplace transform is the integral \mathcal\(s) = \int_0^\infty f(t)e^ \, dt. History The Laplace transform is named after mathematician and astronomer Pierre-Simon, marquis de Laplace, who used a similar transform in his work on probability theory. Laplace wrote extensively about the use of generating functions in ''Essai philosophique sur les probabilités'' (1814), and the integral form of the Laplac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity.(UP1) One turn is equal to 2''π'' radians, hence \omega = \frac = , where: *''ω'' is the angular frequency (unit: radians per second), *''T'' is the period (unit: seconds), *''f'' is the ordinary frequency (unit: hertz) (sometimes ''ν''). Units In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. The unit hertz (Hz) is dimensionally equivalent, but by convention it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Analysis
A network, in the context of electrical engineering and electronics, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
