# Port (circuit theory)

Last updated Network N has a port connecting it to an external circuit. The port meets the port condition because the current I entering one terminal of the port is equal to the current exiting the other.

In electrical circuit theory, a port is a pair of terminals connecting an electrical network or circuit to an external circuit, a point of entry or exit for electrical energy. A port consists of two nodes (terminals) connected to an outside circuit, that meets the port condition; the currents flowing into the two nodes must be equal and opposite. An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response. In electrical engineering, a node is any point on a circuit where the terminals of two or more circuit elements meet. In circuit diagrams, connections are ideal wires with zero resistance, so a node may consist of the entire section of wire between elements, not just a single point. A terminal is the point at which a conductor from an electrical component, device or network comes to an end and provides a point of connection to external circuits. A terminal may simply be the end of a wire or it may be fitted with a connector or fastener. In network analysis, terminal means a point at which connections can be made to a network in theory and does not necessarily refer to any real physical object. In this context, especially in older documents, it is sometimes called a pole. On circuit diagrams, terminals for external connections are denoted by empty circles. They are distinguished from nodes that are entirely internal to the circuit, which are denoted by solid circles.

## Contents

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 determining the circuit's response to applied signals. A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power. It is composed of semiconductor material usually with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits. A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core. Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil. Electronic filters are circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic filters can be:

The concept of ports can be extended to waveguides, but the definition in terms of current is not appropriate and the possible existence of multiple waveguide modes must be accounted for.

## Port condition Simple resistive network with three possible port arrangements: (a) Pole pairs (1, 2) and (3, 4) are ports; (b) pole pairs (1, 4) and (2, 3) are ports; (c) no pair of poles are ports

Any node of a circuit that is available for connection to an external circuit is called a pole (or terminal if it is a physical object). The port condition is that a pair of poles of a circuit is considered a port if and only if the current flowing into one pole from outside the circuit is equal to the current flowing out of the other pole into the external circuit. Equivalently, the algebraic sum of the currents flowing into the two poles from the external circuit must be zero. 

In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements.

It cannot be determined if a pair of nodes meets the port condition by analysing the internal properties of the circuit itself. The port condition is dependent entirely on the external connections of the circuit. What are ports under one set of external circumstances may well not be ports under another. Consider the circuit of four resistors in the figure for example. If generators are connected to the pole pairs (1, 2) and (3, 4) then those two pairs are ports and the circuit is a box attenuator. On the other hand, if generators are connected to pole pairs (1, 4) and (2, 3) then those pairs are ports, the pairs (1, 2) and (3, 4) are no longer ports, and the circuit is a bridge circuit. A generator in electrical circuit theory is one of two ideal elements: an ideal voltage source, or an ideal current source. These are two of the fundamental elements in circuit theory. Real electrical generators are most commonly modelled as a non-ideal source consisting of a combination of an ideal source and a resistor. Voltage generators are modelled as an ideal voltage source in series with a resistor. Current generators are modelled as an ideal current source in parallel with a resistor. The resistor is referred to as the internal resistance of the source. Real world equipment may not perfectly follow these models, especially at extremes of loading but for most purposes they suffice. A bridge circuit is a topology of electrical circuitry in which two circuit branches are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge was originally developed for laboratory measurement purposes and one of the intermediate bridging points is often adjustable when so used. Bridge circuits now find many applications, both linear and non-linear, including in instrumentation, filtering and power conversion.

It is even possible to arrange the inputs so that no pair of poles meets the port condition. However, it is possible to deal with such a circuit by splitting one or more poles into a number of separate poles joined to the same node. If only one external generator terminal is connected to each pole (whether a split pole or otherwise) then the circuit can again be analysed in terms of ports. The most common arrangement of this type is to designate one pole of an n-pole circuit as the common and split it into n1 poles. This latter form is especially useful for unbalanced circuit topologies and the resulting circuit has n1 ports. In electrical engineering, an unbalanced circuit is one in which the transmission properties between the ports of the circuit are different for the two poles of each port. It is usually taken to mean that one pole of each port is bonded to a common potential but more complex topologies are possible. This common point is commonly called ground or earth but it may well not actually be connected to electrical ground at all.

In the most general case, it is possible to have a generator connected to every pair of poles, that is, nC2 generators, then every pole must be split into n1 poles. For instance, in the figure example (c), if the poles 2 and 4 are each split into two poles each then the circuit can be described as a 3-port. However, it is also possible to connect generators to pole pairs (1, 3), (1, 4), and (3, 2) making 4C2 = 6 generators in all and the circuit has to be treated as a 6-port.

## One-ports

Any two-pole circuit is guaranteed to meet the port condition by virtue of Kirchhoff's current law and they are therefore one-ports unconditionally.  All of the basic electrical elements (inductance, resistance, capacitance, voltage source, current source) are one-ports, as is a general impedance.

Study of one-ports is an important part of the foundation of network synthesis, most especially in filter design. Two-element one-ports (that is RC, RL and LC circuits) are easier to synthesise than the general case. For a two-element one-port Foster's canonical form or Cauer's canonical form can be used. In particular, LC circuits are studied since these are lossless and are commonly used in filter design. 

## Two-ports

Linear two port networks have been widely studied and a large number of ways of representing them have been developed. One of these representations is the z-parameters which can be described in matrix form by;

${\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}$ where Vn and In are the voltages and currents respectively at port n. Most of the other descriptions of two-ports can likewise be described with a similar matrix but with a different arrangement of the voltage and current column vectors.

Common circuit blocks which are two-ports include amplifiers, attenuators and filters.

## Multiports

In general, a circuit can consist of any number of ports—a multiport. Some, but not all, of the two-port parameter representations can be extended to arbitrary multiports. Of the voltage and current based matrices, the ones that can be extended are z-parameters and y-parameters. Neither of these are suitable for use at microwave frequencies because voltages and currents are not convenient to measure in formats using conductors and are not relevant at all in waveguide formats. Instead, s-parameters are used at these frequencies and these too can be extended to an arbitrary number of ports. 

Circuit blocks which have more than two ports include directional couplers, power splitters, circulators, diplexers, duplexers, multiplexers, hybrids and directional filters.

## RF and microwave

RF and microwave circuit topologies are commonly unbalanced circuit topologies such as coaxial or microstrip. In these formats, one pole of each port in a circuit is connected to a common node such as a ground plane. It is assumed in the circuit analysis that all these commoned poles are at the same potential and that current is sourced to or sunk into the ground plane that is equal and opposite to that going into the other pole of any port. In this topology a port is treated as being just a single pole. The corresponding balancing pole is imagined to be incorporated into the ground plane. 

The one-pole representation of a port will start to fail if there are significant ground plane loop currents. The assumption in the model is that the ground plane is perfectly conducting and that there is no potential difference between two locations on the ground plane. In reality, the ground plane is not perfectly conducting and loop currents in it will cause potential differences. If there is a potential difference between the commoned poles of two ports then the port condition is broken and the model is invalid.

## Waveguide A Moreno coupler, a type of waveguide directional coupler. Directional couplers have four ports. This one has one port permanently terminated internally with a matched load, so only three ports are visible. The ports are the openings in the centres of the waveguide flanges

The idea of ports can be (and is) extended to waveguide devices, but a port can no longer be defined in terms of circuit poles because in waveguides the electromagnetic waves are not guided by electrical conductors. They are, instead guided by the walls of the waveguide. Thus, the concept of a circuit conductor pole does not exist in this format. Ports in waveguides consist of an aperture or break in the waveguide through which the electromagnetic waves can pass. The bounded plane through which the wave passes is the definition of the port. 

Waveguides have an additional complication in port analysis in that it is possible (and sometimes desirable) for more than one waveguide mode to exist at the same time. In such cases, for each physical port, a separate port must be added to the analysis model for each of the modes present at that physical port. 

## Other energy domains

The concept of ports can be extended into other energy domains. The generalised definition of a port is a place where energy can flow from one element or subsystem to another element or subsystem.  This generalised view of the port concept helps to explain why the port condition is so defined in electrical analysis. If the algebraic sum of the currents is not zero, such as in example diagram (c), then the energy delivered from an external generator is not equal to the energy entering the pair of circuit poles. The energy transfer at that place is thus more complex than a simple flow from one subsystem to another and does not meet the generalised definition of a port.

The port concept is particularly useful where multiple energy domains are involved in the same system and a unified, coherent analysis is required such as with mechanical-electrical analogies or bond graph analysis.  Connection between energy domains is by means of transducers. A transducer may be a one-port as viewed by the electrical domain, but with the more generalised definition of port it is a two-port. For instance, a mechanical actuator has one port in the electrical domain and one port in the mechanical domain.  Transducers can be analysed as two-port networks in the same way as electrical two-ports. That is, by means of a pair of linear algebraic equations or a 2×2 transfer function matrix. However, the variables at the two ports will be different and the two-port parameters will be a mixture of two energy domains. For instance, in the actuator example, the z-parameters will include one electrical impedance, one mechanical impedance, and two transimpedances that are ratios of one electrical and one mechanical variable. 

## Related Research Articles In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses. A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting expansion to one dimension or two. There is a similar effect in water waves constrained within a canal, or guns that have barrels which restrict hot gas expansion to maximize energy transfer to their bullets. Without the physical constraint of a waveguide, wave amplitudes decrease according to the inverse square law as they expand into three dimensional space. Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electrical elements interconnected by wires. Where the elements roughly correspond to real components the representation can be in the form of a schematic diagram or circuit diagram. This is called a lumped element circuit model. In other cases infinitesimal elements are used to model the network in a distributed element model. A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators. Gyrators do not however change the range of one-port devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op-amps using feedback.

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, 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. A Gunn diode, also known as a transferred electron device (TED), is a form of diode, a two-terminal passive semiconductor electronic component, with negative resistance, used in high-frequency electronics. It is based on the "Gunn effect" discovered in 1962 by physicist J. B. Gunn. Its largest use is in electronic oscillators to generate microwaves, in applications such as radar speed guns, microwave relay data link transmitters, and automatic door openers. A two-port network 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. 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. An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are not to be confused with electrical elements, which are conceptual abstractions representing idealized electronic components. An orthomode transducer (OMT) is a waveguide component. It is commonly referred to as a polarisation duplexer. Orthomode transducers serve either to combine or to separate two orthogonally polarized microwave signal paths. One of the paths forms the uplink, which is transmitted over the same waveguide as the received signal path, or downlink path. Such a device may be part of a VSAT antenna feed or a terrestrial microwave radio feed; for example, OMTs are often used with a feed horn to isolate orthogonal polarizations of a signal and to transfer transmit and receive signals to different ports.

This is an alphabetical list of articles pertaining specifically to electrical and electronics engineering. For a thematic list, please see List of electrical engineering topics. For a broad overview of engineering, see List of engineering topics. For biographies, see List of engineers.

An equivalent impedance is an equivalent circuit of an electrical network of impedance elements which presents the same impedance between all pairs of terminals as did the given network. This article describes mathematical transformations between some passive, linear impedance networks commonly found in electronic circuits.

An antimetric electrical network is an electrical network that exhibits anti-symmetrical electrical properties. The term is often encountered in filter theory, but it applies to general electrical network analysis. Antimetric is the diametrical opposite of symmetric; it does not merely mean "asymmetric". It is possible for networks to be symmetric or antimetric in their electrical properties without being physically or topologically symmetric or antimetric. A mechanical filter is a signal processing filter usually used in place of an electronic filter at radio frequencies. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electrical signal. At the input and output of the filter, transducers convert the electrical signal into, and then back from, these mechanical vibrations.

The impedance analogy is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. By converting to an electrical representation, these tools in the electrical domain can be directly applied to a mechanical system without modification. A further advantage occurs in electromechanical systems: Converting the mechanical part of such a system into the electrical domain allows the entire system to be analysed as a unified whole.

Mechanical–electrical analogies are the representation of mechanical systems as electrical networks. At first, such analogies were used in reverse to help explain electrical phenomena in familiar mechanical terms. James Clerk Maxwell introduced analogies of this sort in the 19th century. However, as electrical network analysis matured it was found that certain mechanical problems could more easily be solved through an electrical analogy. Theoretical developments in the electrical domain that were particularly useful where the representation of an electrical network as an abstract topological diagram using the lumped element model and the ability of network analysis to synthesise a network to meet a prescribed frequency function.

The mobility analogy, also called admittance analogy or Firestone analogy, is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. By converting to an electrical representation, these tools in the electrical domain can be directly applied to a mechanical system without modification. A further advantage occurs in electromechanical systems: Converting the mechanical part of such a system into the electrical domain allows the entire system to be analysed as a unified whole.

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.

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1. Yang & Lee, p. 401
2. Carlin & Civalleri, pp. 213-216
3. Russer, Chapter 10, "Microwave circuits: Linear multiports"
4. Gustrau, p. 162
5. Russer, pp. 237-238
6. Karnopp et al., p. 14
7. Borutzsky, p. 20
8. Beranek & Mellow, pp. 96-100