Scattering parametersScattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals. The parameters are useful for several branches of electrical engineering, including electronics, communication systems design, and especially for microwave engineering. The S-parameters are members of a family of similar parameters, other examples being: Y-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters.
ParameterA parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
Admittance parametersAdmittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal (linearized) response of non-linear networks. Y parameters are also known as short circuited admittance parameters.
SynchronizationSynchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or in time. Systems that operate with all parts in synchrony are said to be synchronous or in sync—and those that are not are asynchronous. Today, time synchronization can occur between systems around the world through satellite navigation signals and other time and frequency transfer techniques. Time-keeping and synchronization of clocks is a critical problem in long-distance ocean navigation.
Statistical parameterIn statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population.
Kuramoto modelThe Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto, is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications in areas such as neuroscience and oscillating flame dynamics. Kuramoto was quite surprised when the behavior of some physical systems, namely coupled arrays of Josephson junctions, followed his model.
Scale parameterIn probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. If a family of probability distributions is such that there is a parameter s (and other parameters θ) for which the cumulative distribution function satisfies then s is called a scale parameter, since its value determines the "scale" or statistical dispersion of the probability distribution.
Location parameterIn statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter , which determines the "location" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways: either as having a probability density function or probability mass function ; or having a cumulative distribution function ; or being defined as resulting from the random variable transformation , where is a random variable with a certain, possibly unknown, distribution (See also #Additive_noise).
Phase-locked loopA phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator's frequency and phase are controlled proportionally by an applied voltage, hence the term voltage-controlled oscillator (VCO).
Crystal oscillatorA crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. The most common type of piezoelectric resonator used is a quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators.
Impedance parametersImpedance parameters or Z-parameters (the elements of an impedance matrix or Z-matrix) are properties used in electrical engineering, electronic engineering, and communication systems engineering to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal (linearized) response of non-linear networks. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters, Y-parameters, H-parameters, T-parameters or ABCD-parameters.
Voltage-controlled oscillatorA voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input.
Exponential familyIn probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family.
Neural oscillationNeural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
Adaptive controlAdaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.
Injection lockingInjection locking and injection pulling are the frequency effects that can occur when a harmonic oscillator is disturbed by a second oscillator operating at a nearby frequency. When the coupling is strong enough and the frequencies near enough, the second oscillator can capture the first oscillator, causing it to have essentially identical frequency as the second. This is injection locking. When the second oscillator merely disturbs the first but does not capture it, the effect is called injection pulling.
Haar measureIn mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced by Alfréd Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral". Haar measures are used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theory, and ergodic theory.
Stochastic controlStochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
