Signal in the context of electrical engineering?

Signal 

A signal as referred to in communication systems, signal processing, and electrical engineering is a function that "conveys information about the behavior or attributes of some phenomenon". In the physical world, any quantity exhibiting variation in time or variation in space (such as an image) is potentially a signal that might provide information on the status of a physical system, or convey a message between observers, among other possibilities. The IEEE Transactions on Signal Processing states that the term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals.

Typically, signals are provided by a sensor, and often the original form of a signal is converted to another form of energy using a transducer. For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse.

The formal study of the information content of signals is the field of information theory. The information in a signal is usually accompanied by noise. The term noise usually means an undesirable random disturbance, but is often extended to include unwanted signals conflicting with the desired signal (such as crosstalk). The prevention of noise is covered in part under the heading of signal integrity. The separation of desired signals from a background is the field of signal recovery, one branch of which is estimation theory, a probabilistic approach to suppressing random disturbances.

Engineering disciplines such as electrical engineering have led the way in the design, study, and implementation of systems involving transmission, storage, and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines, specialising in the design and analysis of systems that manipulate physical signals; electronic engineering and computer engineering as examples; while design engineering developed to deal with functional design of man–machine interfaces.

Definitions

Definitions specific to sub-fields are common. For example, in information theory, a signal is a codified message, that is, the sequence of states in a communication channel that encodes a message.

In the context of signal processing, arbitrary binary data streams are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

In a communication system, a transmitter encodes a message to a signal, which is carried to a receiver by the communications channel. For example, the words "Mary had a little lamb" might be the message spoken into a telephone. The telephone transmitter converts the sounds into an electrical voltage signal. The signal is transmitted to the receiving telephone by wires; at the receiver it is reconverted into sounds.

In telephone networks, signalling, for example common-channel signaling, refers to phone number and other digital control information rather than the actual voice signal.

Signals can be categorized in various ways. The most common distinction is between discrete and continuous spaces that the functions are defined over, for example discrete and continuous time domains. Discrete-time signals are often referred to as time series in other fields. Continuous-time signals are often referred to as continuous signals even when the signal functions are not continuous; an example is a square-wave signal.

A second important distinction is between discrete-valued and continuous-valued. Particularly in digital signal processing a digital signal is sometimes defined as a sequence of discrete values, that may or may not be derived from an underlying continuous-valued physical process. In other contexts, digital signals are defined as the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation method is considered as converted to an analog signal, while it is considered as a digital signal in the second case.

Another important property of a signal (actually, of a statistically defined class of signals) is its entropy or information content.

Analog and digital signals

A digital signal has two or more distinguishable waveforms, in this example, high voltage and low voltages, each of which can be mapped onto a digit. Characteristically, noise can be removed from digital signals provided it is not too large.

Two main types of signals encountered in practice are analog and digital. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals are quantized, while analog signals are continuous.

analog signal

digital signal

Digital signals often arise via sampling of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by an analog-to-digital converter circuit, wherein the circuit will read the voltage level on the line, say, every 50 microseconds and represent each reading with a fixed number of bits. The resulting stream of numbers is stored as digital data on a discrete-time and quantized-amplitude signal. Computers and other digital devices are restricted to discrete time.

Time discretization

Discrete-time signal created from a continuous signal by sampling

One of the fundamental distinctions between different types of signals is between continuous and discrete time. In the mathematical abstraction, the domain of a continuous-time (CT) signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (DT) signal is the set of integers (or some interval). What these integers represent depends on the nature of the signal; most often it is time.

If for a signal, the quantities are defined only on a discrete set of times, we call it a discrete-time signal. A simple source for a discrete time signal is the sampling of a continuous signal, approximating the signal by a sequence of its values at particular time instants.

A discrete-time real (or complex) signal can be seen as a function from (a subset of) the set of integers (the index labeling time instants) to the set of real (or complex) numbers (the function values at those instants).

A continuous-time real (or complex) signal is any real-valued (or complex-valued) function which is defined at every time t in an interval, most commonly an infinite interval.

Amplitude quantization

Digital signal resulting from approximation to an analog signal, which is a continuous function of time

If a signal is to be represented as a sequence of numbers, it is impossible to maintain exact precision - each number in the sequence must have a finite number of digits. As a result, the values of such a signal belong to a finite set; in other words, it is quantized. Quantization is the process of converting a continuous analog audio signal to a digital signal with discrete numerical values.

Signal processing

Main article: Signal processing

Signal transmission using electronic signals

A typical role for signals is in signal processing. A common example is signal transmission between different locations. The embodiment of a signal in electrical form is made by a transducer that converts the signal from its original form to a waveform expressed as a current (I) or a voltage (V), or an electromagnetic waveform, for example, an optical signal or radio transmission. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as electronic amplifiers and electronic filters, and can be transmitted to a remote location by electronic transmitters and received using electronic receivers.

Signals and systems

In Electrical engineering programs, a class and field of study known as "signals and systems" (S and S) is often seen as the "cut class" for EE careers, and is dreaded by some students as such. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous linear algebra and differential equation classes they have taken.

The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: Time, Frequency, s and z. Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous time signals (t), one might transform from the time domain to a frequency or s domain; or from discrete time (n) to frequency or z domains. Systems also can be transformed between these domains like signals, with continuous to s and discrete to z.

Although S and S falls under and includes all the topics covered in this article, as well as Analog signal processing and Digital signal processing, it actually is a subset of the field of Mathematical modeling. The field goes back to RF over a century ago, when it was all analog, and generally continuous. Today, software has taken the place of much of the analog circuitry design and analysis, and even continuous signals are now generally processed digitally. Ironically, digital signals also are processed continuously in a sense, with the software doing calculations between discrete signal "rests" to prepare for the next input/transform/output event.

In past EE curricula S and S, as it is often called, involved circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with Dynamical systems tools including differential equations, and recently, Lagrangians. The difficulty of the field at that time included the fact that not only mathematical modeling, circuits, signals and complex systems were being modeled, but physics as well, and a deep knowledge of electrical (and now electronic) topics also was involved and required.

Today, the field has become even more daunting and complex with the addition of circuit, systems and signal analysis and design languages and software, from MATLAB and Simulink to NumPy, VHDL, PSpice, Verilog and even Assembly language. Students are expected to understand the tools as well as the mathematics, physics, circuit analysis, and transformations between the 8 domains.

Because mechanical engineering topics like friction, dampening etc. have very close analogies in signal science (inductance, resistance, voltage, etc.), many of the tools originally used in ME transformations (Laplace and Fourier transforms, Lagrangians, sampling theory, probability, difference equations, etc.) have now been applied to signals, circuits, systems and their components, analysis and design in EE. Dynamical systems that involve noise, filtering and other random or chaotic attractors and repellors have now placed stochastic sciences and statistics between the more deterministic discrete and continuous functions in the field. (Deterministic as used here means signals that are completely determined as functions of time).

EE taxonomists are still not decided where S&S falls within the whole field of signal processing vs. circuit analysis and mathematical modeling, but the common link of the topics that are covered in the course of study has brightened boundaries with dozens of books, journals, etc. called Signals and Systems, and used as text and test prep for the EE, as well as, recently, computer engineering exams. 

Electrical network analysis using different methods?

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A network, in the context of electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, every component in the network. There are many different techniques for calculating these values. However, for the most part, the applied technique assumes that the components of the network are all linear. The methods described in this article are only applicable to linear network analysis, except where explicitly stated.

Definitions

Component A device with two or more terminals into which, or out of which, current may flow.

Node A point at which terminals of more than two components are joined. A conductor with a substantially zero resistance is considered to be a node for the purpose of analysis.

Branch The component(s) joining two nodes.

Mesh A group of branches within a network joined so as to form a complete loop such that there is no other loop inside it .

Port Two terminals where the current into one is identical to the current out of the other.

Circuit A current from one terminal of a generator, through load component(s) and back into the other terminal. A circuit is, in this sense, a one-port network and is a trivial case to analyse. If there is any connection to any other circuits then a non-trivial network has been formed and at least two ports must exist. Often, "circuit" and "network" are used interchangeably, but many analysts reserve "network" to mean an idealised model consisting of ideal components.

Transfer function The relationship of the currents and/or voltages between two ports. Most often, an input port and an output port are discussed and the transfer function is described as gain or attenuation.

Component transfer function For a two-terminal component (i.e. one-port component), the current and voltage are taken as the input and output and the transfer function will have units of impedance or admittance (it is usually a matter of arbitrary convenience whether voltage or current is considered the input). A three (or more) terminal component effectively has two (or more) ports and the transfer function cannot be expressed as a single impedance. The usual approach is to express the transfer function as a matrix of parameters. These parameters can be impedances, but there is a large number of other approaches (see two-port network).

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 the actual 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 generator into a current generator using Norton's theorem in order to be able to later combine the internal resistance of the generator with a parallel impedance load.

equivalent circuits

A resistive circuit is a circuit containing only resistors, ideal current sources, and ideal voltage sources. If the sources are constant (DC) sources, the result is a DC circuit. Analysis of a circuit consists of solving for the voltages and currents present in the circuit. The solution principles outlined here also apply to phasor analysis of AC circuits.

Two circuits are said to be equivalent with respect to a pair of terminals if the voltage across the terminals and current through the terminals for one network have the same relationship as the voltage and current at the terminals of the other network.

Nodal analysis

1. Label all nodes in the circuit. Arbitrarily select any node as reference.

2. Define a voltage variable from every remaining node to the reference. These voltage variables must be defined as voltage rises with respect to the reference node.

3. Write a KCL equation for every node except the reference.

4. Solve the resulting system of equations.

Mesh analysis

Mesh — a loop that does not contain an inner loop.

1. Count the number of “window panes” in the circuit. Assign a mesh current to each window pane.

2. Write a KVL equation for every mesh whose current is unknown.

3. Solve the resulting equations

Superposition

In this method, the effect of each generator in turn is calculated. All the generators other than the one being considered are removed and either short-circuited in the case of voltage generators or open-circuited in the case of current generators. The total current through or the total voltage across a particular branch is then calculated by summing all the individual currents or voltages.

There is an underlying assumption to this method that the total current or voltage is a linear superposition of its parts. Therefore, the method cannot be used if non-linear components are present. Note that mesh analysis and node analysis also implicitly use superposition so these too, are only applicable to linear circuits. Superposition cannot be used to find total power consumed by elements even in linear circuits. Power varies according to the square of total voltage or current and the square of the sum is not generally equal to the sum of the squares.

Choice of method

Choice of method is to some extent a matter of taste. If the network is particularly simple or only a specific current or voltage is required then ad-hoc application of some simple equivalent circuits may yield the answer without recourse to the more systematic methods.

Nodal analysis

 The nuber of voltage variables, and hence simultaneous equations to solve, equals the number of nodes minus one. Every voltage source connected to the reference node reduces the number of unknowns and equations by one.

Mesh analysis

 The number of current variables, and hence simultaneous equations to solve, equals the number of meshes. Every current source in a mesh reduces the number of unknowns by one. Mesh analysis can only be used with networks which can be drawn as a planar network, that is, with no crossing components.

Superposition is possibly the most conceptually simple method but rapidly leads to a large number of equations and messy impedance combinations as the network becomes larger.

Transfer function

A transfer function expresses the relationship between an input and an output of a network. For resistive networks, this will always be a simple real number or an expression which boils down to a real number. Resistive networks are represented by a system of simultaneous algebraic equations. However, in the general case of linear networks, the network is represented by a system of simultaneous linear differential equations. In network analysis, rather than use the differential equations directly, it is usual practice to carry out a Laplace transform on them first and then express the result in terms of the Laplace parameter s, which in general is complex. This is described as working in the s-domain. Working with the equations directly would be described as working in the time (or t) domain because the results would be expressed as time varying quantities. The Laplace transform is the mathematical method of transforming between the s-domain and the t-domain.

This approach is standard in control theory and is useful for determining stability of a system, for instance, in an amplifier with feedback.

Ground verses neutral in a descriptive way?

Ground and neutral

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For uses of the term "grounding" or "earth" in electricity but not in the context of mains wiring, see ground (electricity).

symbols for grounding

As the neutral point of an electrical supply system is often connected to earth ground, ground and neutral are closely related. Under certain conditions, a conductor used to connect to a system neutral is also used for grounding (earthing) of equipment and structures. Current carried on a grounding conductor can result in objectionable or dangerous voltages appearing on equipment enclosures, so the installation of grounding conductors and neutral conductors is carefully defined in electrical regulations. Where a neutral conductor is used also to connect equipment enclosures to earth, care must be taken that the neutral conductor never rises to a high voltage with respect to local ground.

Definitions

Ground or earth in a mains (AC power) electrical wiring system is a conductor that provides a low-impedance path to the earth to prevent hazardous voltages from appearing on equipment. (The terms "ground" and "earth" are used synonymously here. "Ground" is more common in North American English, and "earth" is more common in British English.) Under normal conditions, a grounding conductor does not carry current.

Neutral is a circuit conductor that normally carries current back to the source, and is connected to ground (earth) at the main electrical panel.

In the electrical trade, the conductor of a 2-wire circuit connected to the supply neutral point and earth ground is referred to as the "neutral". 

In a polyphase (usually three-phase) AC system, the neutral conductor is intended to have similar voltages to each of the other circuit conductors, but may carry very little current if the phases are balanced.

The United States' National Electrical Code and Canadian electrical code only define neutral as the grounded, not the polyphase common connection. In North American use, the polyphase definition is used in less formal language but not in official specifications. In the United Kingdom the Institution of Engineering and Technology defines a neutral conductor as one connected to the supply system neutral point, which includes both these uses.

All neutral wires of the same earthed (grounded) electrical system should have the same electrical potential, because they are all connected through the system ground. Neutral conductors are usually insulated for the same voltage as the line conductors, with interesting exceptions.

Circuitry

Neutral wires are usually connected at a neutral bus within panelboards or switchboards, and are "bonded" to earth ground at either the electrical service entrance, or at transformers within the system. For electrical installations with split-phase (three-wire single-phase service), the neutral point of the system is at the center-tap on the secondary side of the service transformer. For larger electrical installations, such as those with polyphase service, the neutral point is usually at the common connection on the secondary side of delta/wye connected transformers. Other arrangements of polyphase transformers may result in no neutral point, and no neutral conductors.

Grounding systems

Main article: Grounding system

The IEC standard (IEC 60364) codifies methods of installing neutral and ground conductors in a building, where these earthing systems are designated with letter symbols. The letter symbols are common in countries using IEC standards, but North American practices rarely refer to the IEC symbols. The differences are that the conductors may be separate over their entire run from equipment to earth ground, or may be combined over all or part of their length. Different systems are used to minimize the voltage difference between neutral and local earth ground. Current flowing in a grounding conductor will produce a voltage drop along the conductor, and grounding systems seek to ensure this voltage does not reach unsafe levels.

In the TN-S system, separate neutral and protective earth conductors are installed between the equipment and the source of supply (generator or electric utility transformer). Normal circuit currents flow only in the neutral, and the protective earth conductor bonds all equipment cases to earth to intercept any leakage current due to insulation failure. The neutral conductor is connected to earth at the building point of supply, but no common path to ground exists for circuit current and the protective conductor.

In the TN-C system, a common conductor provides both the neutral and protective grounding. The neutral conductor is connected to earth ground at the point of supply, and equipment cases are connected to the neutral. The danger exists that a broken neutral connection will allow all the equipment cases to rise to a dangerous voltage if any leakage or insulation fault exists in any equipment. This can be mitigated with special cables but the cost is then higher.

In the TN-C-S system, each piece of electrical equipment has both a protective ground connection to its case, and a neutral connection. These are all brought back to some common point in the building system, and a common connection is then made from that point back to the source of supply and to the earth.

In a TT system, no lengthy common protective ground conductor is used, instead each article of electrical equipment (or building distribution system) has its own connection to earth ground.

Combining neutral with ground

Stray voltages created in grounding (earthing) conductors by currents flowing in the supply utility neutral conductors can be troublesome. For example, special measures may be required in barns used for milking dairy cattle. Very small voltages, not usually perceptible to humans, may cause low milk yield, or even mastitis (inflammation of the udder). So-called "tingle voltage filters" may be required in the electrical distribution system for a milking parlour.

Connecting the neutral to the equipment case provides some protection against faults, but may produce a dangerous voltage on the case if the neutral connection is broken.

Combined neutral and ground conductors are commonly used in electricity supply companies' wiring and occasionally for fixed wiring in buildings and for some specialist applications where there is little alternative, such as railways and trams. Since normal circuit currents in the neutral conductor can lead to objectionable or dangerous differences between local earth potential and the neutral, and to protect against neutral breakages, special precautions such as frequent rodding down to earth (multiple ground rod connections), use of cables where the combined neutral and earth completely surrounds the phase conductor(s), and thicker than normal equipotential bonding must be considered to ensure the system is safe.

Fixed appliances on three-wire circuits

In North America, the cases of some kitchen stoves (ranges, ovens), cook tops, clothes dryers and other specifically listed appliances were grounded through their neutral wires as a measure to conserve copper from copper cables during World War II. This practice was removed from the NEC in the 1996 edition, but existing installations (called "old work") may still allow the cases of such listed appliances to be connected to the neutral conductor for grounding.

This practice arose from the three-wire system used to supply both 120 volt and 240 volt loads. Because these listed appliances often have components that use either 120, or both 120 and 240 volts, there is often some current on the neutral wire. This differs from the protective grounding wire, which only carries current under fault conditions. Using the neutral conductor for grounding the equipment enclosure was considered safe since the devices were permanently wired to the supply and so the neutral was unlikely to be broken without also breaking both supply conductors. Also, the unbalanced current due to lamps and small motors in the appliances was small compared to the rating of the conductors and therefore unlikely to cause a large voltage drop in the neutral conductor.

Portable appliances

In North American and European practice, small portable equipment connected by a cord set is permitted under certain conditions to have merely two conductors in the attachment plug. A polarized plug can be used to maintain the identity of the neutral conductor into the appliance but neutral is never used as a chassis/case ground. The small cords to lamps, etc., often have one or more molded ridges or embedded strings to identify the neutral conductor, or may be identified by colour. Portable appliances never use the neutral conductor for case grounding, and often feature "double-insulated" construction.

In places where the design of the plug and socket cannot ensure that a system neutral conductor is connected to particular terminals of the device ("unpolarized" plugs), portable appliances must be designed on the assumption that either pole of each circuit may reach full voltage with respect to ground.

Technical equipment

In North American practice, equipment connected by a cord set must have three wires, if supplied exclusively by 240 volts, or must have four wires (including neutral and ground), if supplied by 120/240 volts.

There are special provisions in the NEC for so-called technical equipment, mainly professional grade audio and video equipment supplied by so-called "balanced" 120 volt circuits. The center tap of a transformer is connected to ground, and the equipment is supplied by two line wires each 60 volts to ground (and 120 volts between line conductors). The center tap is not distributed to the equipment and no neutral conductor is used. These cases generally use a grounding conductor which is separated from the safety grounding conductor specifically for the purposes of noise and "hum" reduction.

Another specialized distribution system was formerly specified in patient care areas of hospitals. An isolated power system was furnished, from a special isolation transformer, with the intention of minimizing any leakage current that could pass through equipment directly connected to a patient (for example, an electrocardiograph for monitoring the heart). The neutral of the circuit was not connected to ground. The leakage current was due to the distributed capacitance of the wiring and capacitance of the supply transformer.  Such distribution systems were monitored by permanently installed instruments to give an alarm when high leakage current was detected.

Shared neutral

A shared neutral is a connection in which a plurality of circuits use the same neutral connection. This is also known as a common neutral, and the circuits and neutral together are sometimes referred to as an Edison circuit.

Three-phase circuits

In a three-phase circuit, a neutral is shared between all three phases. Commonly the system neutral is connected to the star point on the feeding transformer. This is the reason that the secondary side of most three-phase distribution transformers is wye or star wound. Three-phase transformers and their associated neutrals are usually found in industrial distribution environments.

A system could be made entirely ungrounded. In this case a fault between one phase and ground would not cause any significant current. In fact, this is not a good scheme. Commonly the neutral is grounded (earthed) through a bond between the neutral bar and the earth bar. It is common on larger systems to monitor any current flowing through the neutral-to-earth link and use this as the basis for neutral fault protection.

The connection between neutral and earth allows any phase-to-earth fault to develop enough current flow to "trip" the circuit overcurrent protection device. In some jurisdictions, calculations are required to ensure the fault loop impedance is low enough so that fault current will trip the protection (In Australia, this is referred to in AS3000:2007 Fault loop impedance calculation). This may limit the length of a branch circuit.

In the case of two phases sharing one neutral, the worst-case current draw is one side has zero load and the other has full load, or when both sides have full load. The latter case results in 1 + 1@120deg = 1@60deg, i.e. the magnitude of the current in the neutral equals that of the other two wires.

In a three-phase linear circuit with three identical resistive or reactive loads, the neutral carries no current. The neutral carries current if the loads on each phase are not identical. In some jurisdictions, the neutral is allowed to be reduced in size if no unbalanced current flow is expected. If the neutral is smaller than the phase conductors, it can be overloaded if a large unbalanced load occurs.

The current drawn by non-linear loads, such as fluorescent & HID lighting and electronic equipment containing switching power supplies, often contains harmonics. Triplen harmonic currents (odd multiples of the third harmonic) are additive, resulting in more current in the shared neutral conductor than in any of the phase conductors. In the absolute worst case, the current in the shared neutral conductor can be triple that in each phase conductor. Some jurisdictions prohibit the use of shared neutral conductors when feeding single-phase loads from a three-phase source; others require that the neutral conductor be substantially larger than the phase conductors. It is good practice to use four-pole circuit breakers (as opposed to the standard three-pole) where the fourth pole is the neutral phase, and is hence protected against overcurrent on the neutral conductor.

Split phase

Main article: Split-phase electric power

In split-phase wiring, for example a duplex receptacle in a North American kitchen, devices may be connected with a cable that has three conductors, in addition to ground. The three conductors are usually coloured red, black, and white. The white serves as a common neutral, while the red and black each feed, separately, the top and bottom hot sides of the receptacle. Typically such receptacles are supplied from two circuit breakers in which the handles of two poles are tied together for a common trip. If two large appliances are used at once, current passes through both and the neutral only carries the difference in current. The advantage is that only three wires are required to serve these loads, instead of four. If one kitchen appliance overloads the circuit, the other side of the duplex receptacle will be shut off as well. This is called a multiwire branch circuit. Common trip is required when the connected load uses more than one phase simultaneously. The common trip prevents overloading of the shared neutral if one device draws more than rated current.