![Port condition](https://upload.wikimedia.org/wikipedia/commons/4/41/Port_condition.svg)
In electrical
circuit theory
Circuit may refer to:
Science and technology
Electrical engineering
* Electrical circuit, a complete electrical network with a closed-loop giving a return path for current
** Analog circuit, uses continuous signal levels
** Balanced circui ...
, a port is a pair of
terminals connecting an
electrical network
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...
or
circuit to an external circuit, as a point of entry or exit for
electrical energy
Electrical energy is energy related to forces on electrically charged particles and the movement of electrically charged particles (often electrons in wires, but not always). This energy is supplied by the combination of electric current and electr ...
. A port consists of two
nodes
In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two ...
(terminals) connected to an outside circuit which meets the ''port condition'' - the
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
s flowing into the two nodes must be equal and opposite.
The use of ports helps to reduce the complexity of
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 t ...
. Many common electronic devices and circuit blocks, such as
transistor
upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink).
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
s,
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
s,
electronic filter
Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
s, and
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
s, 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
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
of parameters relating the
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 m ...
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.
The concept of ports can be extended to
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 de ...
s, but the definition in terms of current is not appropriate and the possible existence of multiple
waveguide mode
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwav ...
s must be accounted for.
Port condition
![4-pole port arrangements](https://upload.wikimedia.org/wikipedia/commons/7/7f/4-pole_port_arrangements.svg)
Any node of a circuit that is available for connection to an external circuit is called a pole (or
terminal
Terminal may refer to:
Computing Hardware
* Terminal (electronics), a device for joining electrical circuits together
* Terminal (telecommunication), a device communicating over a line
* Computer terminal, a set of primary input and output devic ...
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
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false.
The connective is bicondi ...
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
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matr ...
of the currents flowing into the two poles from the external circuit must be zero.
[Yang & Lee, p. 401]
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 bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge ...
.
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
Generator may refer to:
* Signal generator, electronic devices that generate repeating or non-repeating electronic signals
* Electric generator, a device that converts mechanical energy to electrical energy.
* Generator (circuit theory), an eleme ...
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 ''n''−1 poles. This latter form is especially useful for
unbalanced circuit
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 com ...
topologies and the resulting circuit has ''n''−1 ports.
In the most general case, it is possible to have a generator connected to every pair of poles, that is,
''n''C2 generators, then every pole must be split into ''n''−1 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 , , and making 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
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhof ...
and they are therefore one-ports unconditionally.
[ All of the basic electrical elements (]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 ...
, resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
, 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 ...
, voltage source
A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply unli ...
, current source) are one-ports, as is a general impedance.
Study of one-ports is an important part of the foundation of network synthesis
Network synthesis is a design technique for linear electrical circuits. Synthesis starts from a prescribed impedance function of frequency or frequency response and then determines the possible networks that will produce the required response. ...
, most especially in filter design
Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient ...
. Two-element one-ports (that is RC, RL and LC circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...
s) 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 circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...
s are studied since these are lossless and are commonly used in filter design
Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient ...
.
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 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 electr ...
which can be described in matrix form by;
:
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 amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
s, attenuators and filters
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
.
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
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 el ...
. Neither of these are suitable for use at 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 ran ...
frequencies because voltages and currents are not convenient to measure in formats using conductors and are not relevant at all in 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 de ...
formats. Instead, s-parameters
Scattering 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 f ...
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 coupler
Power dividers (also power splitters and, when used in reverse, power combiners) and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmiss ...
s, power splitter
Power dividers (also power splitters and, when used in reverse, power combiners) and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmiss ...
s, circulator
A circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an ...
s, diplexer
A diplexer is a passive device that implements frequency-domain multiplexing. Two ports (e.g., L and H) are multiplexed onto a third port (e.g., S). The signals on ports L and H occupy disjoint frequency bands. Consequently, the signals on L and ...
s, duplexer
A duplexer is an electronic device that allows bi-directional ( duplex) communication over a single path. In radar and radio communications systems, it isolates the receiver from the transmitter while permitting them to share a common antenna. M ...
s, multiplexers
In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The sele ...
, hybrid
Hybrid may refer to:
Science
* Hybrid (biology), an offspring resulting from cross-breeding
** Hybrid grape, grape varieties produced by cross-breeding two ''Vitis'' species
** Hybridity, the property of a hybrid plant which is a union of two dif ...
s and directional filters.
RF and microwave
RF and 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 ran ...
circuit topologies are commonly unbalanced circuit topologies such as coaxial or microstrip
Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as the substrate. Microstrip lines are used to convey microwave-frequ ...
. In these formats, one pole of each port in a circuit is connected to a common node such as a ground plane
In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground.
The term has two different meanings in separate areas of electrical engineering.
*In antenna theory, a ground plane is a ...
. It is assumed in the circuit analysis that all these commoned poles are at the same potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
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.[Gustrau, p. 162]
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
The idea of ports can be (and is) extended to 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 de ...
devices, but a port can no longer be defined in terms of circuit poles because in waveguides the electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
s 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
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwav ...
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.[Karnopp ''et al.'', p. 14] 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
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 introduc ...
or bond graph analysis. Connection between energy domains is by means of transducer
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and contr ...
s. 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 algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices.
...
ic equations or a 2×2 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 (M ...
. 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
Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the for ...
, and two transimpedance Transconductance (for transfer conductance), also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciproca ...
s that are ratios of one electrical and one mechanical variable.[Beranek & Mellow, pp. 96–100]
References
Bibliography
* Won Y. Yang, Seung C. Lee, ''Circuit Systems with MATLAB and PSpice'', John Wiley & Sons, 2008 .
* Frank Gustrau, ''RF and Microwave Engineering: Fundamentals of Wireless Communications'', John Wiley & Sons, 2012 .
* Peter Russer, ''Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering'', Artech House, 2003 .
* Herbert J. Carlin, Pier Paolo Civalleri, ''Wideband Circuit Design'', CRC Press, 1997 .
* Dean Karnopp, Donald L. Margolis, Ronald C. Rosenberg, ''System Dynamics'', Wiley, 2000 .
* Wolfgang Borutzky, ''Bond Graph Methodology'', Springer 2009 .
* Leo Leroy Beranek, Tim Mellow, ''Acoustics: Sound Fields and Transducers'', Academic Press, 2012 {{ISBN, 0123914213.
Circuit theorems
Linear electronic circuits