Transfer Function Matrix
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Transfer Function Matrix
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially ...
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Control System
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable (PV) being controlled with the desired value or setpoint (SP), and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint. For sequential and combinational logic, software logic, such as in a programmable logic controller, is used. Open-loop and closed-loop control There are two common classes of control action: open loop and closed loop. ...
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Discrete Time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities ...
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Power (physics)
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called ''activity''. Power is a scalar quantity. Power is related to other quantities; for example, the power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through the element and of the voltage across the element. Definition Power is the rate with respect to time at which work is done; it is the time derivative of work: P =\frac where is power, is work, and is time. If a constant force F is applied throughout a distance x, t ...
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Waveguide
A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities decrease according to the inverse square law as they expand into three-dimensional space. There are different types of waveguides for different types of waves. The original and most common meaningInstitute of Electrical and Electronics Engineers, “The IEEE standard dictionary of electrical and electronics terms”; 6th ed. New York, N.Y., Institute of Electrical and Electronics Engineers, c1997. IEEE Std 100-1996. d. Standards Coordinating Committee 10, Terms and Definitions; Jane Radatz, (chair)/ref> is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves. Dielectric waveguides are used at higher radio frequencies, and transparent dielectric waveguides and optical fibers serve as waveguides ...
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Microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF (millimeter wave) bands. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz (wavelengths between 0.3 m and 3 mm). In all cases, microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations. The prefix ' in ''microwave'' is not meant to suggest a wavelength in the micrometer range. Rather, it indicates that microwaves are "small" (having shorter wavelengths), compared to the radio waves used prior to microwave ...
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Resistive Divider2
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ). The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather than inte ...
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Admittance Parameters
Admittance 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. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters. The Y-parameter matrix A Y-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports. A ''port'' in this context is a pair of electrical terminals carrying equal and opposite currents into and out of the network, and having a particular voltage between them. The Y-matrix gives n ...
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Impedance Parameters
Impedance 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. Z-parameters are also known as ''open-circuit impedance parameters'' as they are calculated under open circuit conditions. i.e., Ix=0, where x=1,2 refer to input and output currents flowing through the ports (of a two-port network in this case) respectively. The Z-parameter matrix A Z-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports. A ''port'' in this context is a p ...
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Two-port Network
A two-port network (a kind of four-terminal network or quadripole) is an electrical network ( circuit) or device with two ''pairs'' of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition: the electric current entering one terminal must equal the current emerging from the other terminal on the same port.Gray, §3.2, p. 172Jaeger, §10.5 §13.5 §13.8 The ports constitute interfaces where the network connects to other networks, the points where signals are applied or outputs are taken. In a two-port network, often port 1 is considered the input port and port 2 is considered the output port. It's used in mathematical circuit analysis. Application The two-port network model is used in mathematical circuit analysis techniques to isolate portions of larger circuits. A two-port network is regarded as a " black box" with its properties specified by a matrix of n ...
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Electric Current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons. The SI unit of electric current is the ampere, or ''amp'', which is the flow of electric charge across a surface at the rate of one coulomb per second. The ampere (symbol: A) is an SI base unit. Electric current is measured using a device called an ammeter. Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers. In ...
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Voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named '' volt''. The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and transformers). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground of the system is used as one of the points. A voltage can represent either a ...
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Port (circuit Theory)
In electrical circuit theory, a port is a pair of terminals connecting an electrical network or circuit to an external circuit, as a point of entry or exit for electrical energy. A port consists of two nodes (terminals) connected to an outside circuit which meets the ''port condition'' - the currents flowing into the two nodes must be equal and opposite. The use of ports helps to reduce the complexity of circuit analysis. Many common electronic devices and circuit blocks, such as transistors, transformers, electronic filters, and amplifiers, are analyzed in terms of ports. In multiport network analysis, the circuit is regarded as a "black box" connected to the outside world through its ports. The ports are points where input signals are applied or output signals taken. Its behavior is completely specified by a matrix of parameters relating the voltage and current at its ports, so the internal makeup or design of the circuit need not be considered, or even known, in det ...
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