An integrated circuit or monolithic integrated circuit is a set of electronic circuits on one small flat piece of semiconductor material, silicon. The integration of large numbers of tiny transistors into a small chip results in circuits that are orders of magnitude smaller and faster than those constructed of discrete electronic components; the IC's mass production capability and building-block approach to circuit design has ensured the rapid adoption of standardized ICs in place of designs using discrete transistors. ICs are now used in all electronic equipment and have revolutionized the world of electronics. Computers, mobile phones, other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs. Integrated circuits were made practical by mid-20th-century technology advancements in semiconductor device fabrication. Since their origins in the 1960s, the size and capacity of chips have progressed enormously, driven by technical advances that fit more and more transistors on chips of the same size – a modern chip may have many billions of transistors in an area the size of a human fingernail.
These advances following Moore's law, make computer chips of today possess millions of times the capacity and thousands of times the speed of the computer chips of the early 1970s. ICs have two main advantages over discrete circuits: performance. Cost is low because the chips, with all their components, are printed as a unit by photolithography rather than being constructed one transistor at a time. Furthermore, packaged ICs use much less material than discrete circuits. Performance is high because the IC's components switch and consume comparatively little power because of their small size and close proximity; the main disadvantage of ICs is the high cost to fabricate the required photomasks. This high initial cost means. An integrated circuit is defined as: A circuit in which all or some of the circuit elements are inseparably associated and electrically interconnected so that it is considered to be indivisible for the purposes of construction and commerce. Circuits meeting this definition can be constructed using many different technologies, including thin-film transistors, thick-film technologies, or hybrid integrated circuits.
However, in general usage integrated circuit has come to refer to the single-piece circuit construction known as a monolithic integrated circuit. Arguably, the first examples of integrated circuits would include the Loewe 3NF. Although far from a monolithic construction, it meets the definition given above. Early developments of the integrated circuit go back to 1949, when German engineer Werner Jacobi filed a patent for an integrated-circuit-like semiconductor amplifying device showing five transistors on a common substrate in a 3-stage amplifier arrangement. Jacobi disclosed cheap hearing aids as typical industrial applications of his patent. An immediate commercial use of his patent has not been reported; the idea of the integrated circuit was conceived by Geoffrey Dummer, a radar scientist working for the Royal Radar Establishment of the British Ministry of Defence. Dummer presented the idea to the public at the Symposium on Progress in Quality Electronic Components in Washington, D. C. on 7 May 1952.
He gave many symposia publicly to propagate his ideas and unsuccessfully attempted to build such a circuit in 1956. A precursor idea to the IC was to create small ceramic squares, each containing a single miniaturized component. Components could be integrated and wired into a bidimensional or tridimensional compact grid; this idea, which seemed promising in 1957, was proposed to the US Army by Jack Kilby and led to the short-lived Micromodule Program. However, as the project was gaining momentum, Kilby came up with a new, revolutionary design: the IC. Newly employed by Texas Instruments, Kilby recorded his initial ideas concerning the integrated circuit in July 1958 demonstrating the first working integrated example on 12 September 1958. In his patent application of 6 February 1959, Kilby described his new device as "a body of semiconductor material … wherein all the components of the electronic circuit are integrated." The first customer for the new invention was the US Air Force. Kilby won the 2000 Nobel Prize in Physics for his part in the invention of the integrated circuit.
His work was named an IEEE Milestone in 2009. Half a year after Kilby, Robert Noyce at Fairchild Semiconductor developed a new variety of integrated circuit, more practical than Kilby's implementation. Noyce's design was made of silicon. Noyce credited Kurt Lehovec of Sprague Electric for the principle of p–n junction isolation, a key concept behind the IC; this isolation allows each transistor to operate independently despite being part of the same piece of silicon. Fairchild Semiconductor was home of the first silicon-gate IC technology with self-aligned gates, the basis of all modern CMOS integrated circuits; the technology was developed by Italian physicist Federico Faggin in 1968. In 1970, he joined Intel in order to develop the first single-chip central processing unit microprocessor, the Intel 4004, for which he received the National Medal of Technology and Innovation in 2010; the 4004 was designed by Busicom's Masatoshi Shima and Intel's Ted Hoff in 1969, but it was Faggin's improved design in 1970 that made it a reality.
Advances in IC technology smaller features and la
In electrical engineering, ground or earth is the reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to the earth. Electrical circuits may be connected to ground for several reasons. Exposed metal parts of electrical equipment are connected to ground, so that failures of internal insulation will trigger protective mechanisms such as fuses or circuit breakers in the circuit to remove power from the device; this ensures that exposed parts can never have a dangerous voltage with respect to ground, which could cause an electric shock if a grounded person touched them. In electric power distribution systems, a protective earth conductor is an essential part of the safety provided by the earthing system. Connection to ground limits the build-up of static electricity when handling flammable products or electrostatic-sensitive devices. In some telegraph and power transmission circuits, the earth itself can be used as one conductor of the circuit, saving the cost of installing a separate return conductor.
For measurement purposes, the Earth serves as a constant potential reference against which other potentials can be measured. An electrical ground system should have an appropriate current-carrying capability to serve as an adequate zero-voltage reference level. In electronic circuit theory, a "ground" is idealized as an infinite source or sink for charge, which can absorb an unlimited amount of current without changing its potential. Where a real ground connection has a significant resistance, the approximation of zero potential is no longer valid. Stray voltages or earth potential rise effects will occur, which may create noise in signals or if large enough will produce an electric shock hazard; the use of the term ground is so common in electrical and electronics applications that circuits in portable electronic devices such as cell phones and media players as well as circuits in vehicles may be spoken of as having a "ground" connection without any actual connection to the Earth, despite "common" being a more appropriate term for such a connection.
This is a large conductor attached to one side of the power supply which serves as the common return path for current from many different components in the circuit. Long-distance electromagnetic telegraph systems from 1820 onwards used two or more wires to carry the signal and return currents, it was discovered by the German scientist Carl August Steinheil in 1836–1837, that the ground could be used as the return path to complete the circuit, making the return wire unnecessary. However, there were problems with this system, exemplified by the transcontinental telegraph line constructed in 1861 by the Western Union Company between St. Joseph and Sacramento, California. During dry weather, the ground connection developed a high resistance, requiring water to be poured on the ground rod to enable the telegraph to work or phones to ring; when telephony began to replace telegraphy, it was found that the currents in the earth induced by power systems, electrical railways, other telephone and telegraph circuits, natural sources including lightning caused unacceptable interference to the audio signals, the two-wire or'metallic circuit' system was reintroduced around 1883.
An electrical connection to earth can be used as a reference potential for radio frequency signals for certain kinds of antennas. The part directly in contact with the earth - the "earth electrode" - can be as simple as a metal rod or stake driven into the earth, or a connection to buried metal water piping; because high frequency signals can flow to earth due to capacitative effects, capacitance to ground is an important factor in effectiveness of signal grounds. Because of this, a complex system of buried rods and wires can be effective. An ideal signal ground maintains a fixed potential regardless of how much electric current flows into ground or out of ground. Low impedance at the signal frequency of the electrode-to-earth connection determines its quality, that quality is improved by increasing the surface area of the electrode in contact with the earth, increasing the depth to which it is driven, using several connected ground rods, increasing the moisture content of the soil, improving the conductive mineral content of the soil, increasing the land area covered by the ground system.
Some types of transmitting antenna systems in the VLF, LF, MF and lower SW range must have a good ground to operate efficiently. For example, a vertical monopole antenna requires a ground plane that consists of an interconnected network of wires running radially away from the base of the antenna for a distance about equal to the height of the antenna. Sometimes a counterpoise is used as a ground plane, supported above the ground. Electrical power distribution systems are connected to ground to limit the voltage that can appear on distribution circuits. A distribution system insulated from ground may attain a high potential due to transient voltages caused by arcing, static electricity, or accidental contact with higher potential circuits. A ground connection of the system dissipates such potentials and limits the rise in voltage of the grounded system. In a mains electricity wiring installation, the term ground conductor refers to three different conductors or conductor systems as listed below: Equipment earthing conductors provide an electrical connection between the physical ground and the grounding/bonding system, which connects the non-current-carrying metallic parts of equipment.
According to the U. S. National E
Power dividers and directional couplers
Power dividers and directional couplers are passive devices used in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. Power entering the output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power between two ports is called a hybrid coupler. Directional couplers are most constructed from two coupled transmission lines set close enough together such that energy passing through one is coupled to the other; this technique is favoured at the microwave frequencies where transmission line designs are used to implement many circuit elements. However, lumped component devices are possible at lower frequencies, such as the audio frequencies encountered in telephony. At microwave frequencies the higher bands, waveguide designs can be used.
Many of these waveguide couplers correspond to one of the conducting transmission line designs, but there are types that are unique to waveguide. Directional couplers and power dividers have many applications; these include providing a signal sample for measurement or monitoring, combining feeds to and from antennas, antenna beam forming, providing taps for cable distributed systems such as cable TV, separating transmitted and received signals on telephone lines. The symbols most used for directional couplers are shown in figure 1; the symbol may have the coupling factor in dB marked on it. Directional couplers have four ports. Port 1 is the input port. Port 3 is the coupled port. Port 2 is the transmitted port where the power from port 1 is outputted, less the portion that went to port 3. Directional couplers are symmetrical so there exists port 4, the isolated port. A portion of the power applied to port 2 will be coupled to port 4. However, the device is not used in this mode and port 4 is terminated with a matched load.
This termination can be internal to the device and port 4 is not accessible to the user. This results in a 3-port device, hence the utility of the second symbol for directional couplers in figure 1. Symbols of the form. A symbol for power dividers is shown in figure 2. Power dividers and directional couplers are in all essentials the same class of device. Directional coupler tends to be used for 4-port devices that are only loosely coupled – that is, only a small fraction of the input power appears at the coupled port. Power divider is used for devices with tight coupling and is considered a 3-port device. Common properties desired for all directional couplers are wide operational bandwidth, high directivity, a good impedance match at all ports when the other ports are terminated in matched loads; some of these, other, general characteristics are discussed below. The coupling factor is defined as: C 3, 1 = 10 log d B where P1 is the input power at port 1 and P3 is the output power from the coupled port.
The coupling factor represents the primary property of a directional coupler. Coupling factor is a negative quantity, it cannot exceed 0 dB for a passive device, in practice does not exceed −3 dB since more than this would result in more power output from the coupled port than power from the transmitted port – in effect their roles would be reversed. Although a negative quantity, the minus sign is dropped in running text and diagrams and a few authors go so far as to define it as a positive quantity. Coupling varies with frequency. While different designs may reduce the variance, a flat coupler theoretically cannot be built. Directional couplers are specified in terms of the coupling accuracy at the frequency band center; the main line insertion loss from port 1 to port 2 is: Insertion loss: L i 2, 1 = − 10 log d B Part of this loss is due to some power going to the coupled port and is called coupling loss and is given by: Coupling loss: L c 2, 1 = − 10 log d B The insertion loss of an ideal directional coupler will consist of the coupling loss.
In a real directional coupler, the insertion loss consists of a combination of coupling loss, dielectric
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; this article covers two-conductor transmission line such as parallel line, coaxial cable and microstrip. Some sources refer to waveguide, dielectric waveguide, optical fibre as transmission line, however these lines require different analytical techniques and so are not covered by this article. Ordinary electrical cables suffice to carry low frequency alternating current, such as mains power, which reverses direction 100 to 120 times per second, audio signals. However, they cannot be used to carry currents in the radio frequency range, above about 30 kHz, because the energy tends to radiate off the cable as radio waves, causing power losses.
Radio frequency currents tend to reflect from discontinuities in the cable such as connectors and joints, travel back down the cable toward the source. These reflections act as bottlenecks. Transmission lines use specialized construction, impedance matching, to carry electromagnetic signals with minimal reflections and power losses; the distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform impedance, called the characteristic impedance, to prevent reflections. Types of transmission line include parallel line, coaxial cable, planar transmission lines such as stripline and microstrip; the higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the transmitted frequency's wavelength is sufficiently short that the length of the cable becomes a significant part of a wavelength. At microwave frequencies and above, power losses in transmission lines become excessive, waveguides are used instead, which function as "pipes" to confine and guide the electromagnetic waves.
Some sources define waveguides as a type of transmission line. At higher frequencies, in the terahertz and visible ranges, waveguides in turn become lossy, optical methods, are used to guide electromagnetic waves; the theory of sound wave propagation is similar mathematically to that of electromagnetic waves, so techniques from transmission line theory are used to build structures to conduct acoustic waves. Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable; the model predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations. In many electric circuits, the length of the wires connecting the components can for the most part be ignored; that is, the voltage on the wire at a given time can be assumed to be the same at all points.
However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire. A common rule of thumb is that the cable or wire should be treated as a transmission line if the length is greater than 1/10 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behaviour in systems which have not been designed using transmission line theory. For the purposes of analysis, an electrical transmission line can be modelled as a two-port network, as follows: In the simplest case, the network is assumed to be linear, the two ports are assumed to be interchangeable. If the transmission line is uniform along its length its behaviour is described by a single parameter called the characteristic impedance, symbol Z0.
This is the ratio of the complex voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z0 are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, about 300 ohms for a common type of untwisted pair used in radio transmission; when sending power down a transmission line, it is desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source. This can be ensured by making the load impedance equal to Z0, in which case the transmission line is said to be matched; some of the power, fed into a transmission line is lost because of its resistance. This effect is called resistive loss. At high frequencies, another effect cal
In telecommunications, a repeater is an electronic device that receives a signal and retransmits it. Repeaters are used to extend transmissions so that the signal can cover longer distances or be received on the other side of an obstruction; some types of repeaters broadcast an identical signal, but alter its method of transmission, for example, on another frequency or baud rate. There are several different types of repeaters. A broadcast relay station is a repeater used in broadcast television; when an information-bearing signal passes through a communication channel, it is progressively degraded due to loss of power. For example, when a telephone call passes through a wire telephone line, some of the power in the electric current which represents the audio signal is dissipated as heat in the resistance of the copper wire; the longer the wire is, the more power is lost, the smaller the amplitude of the signal at the far end. So with a long enough wire the call will not be audible at the other end.
The farther from a radio station a receiver is, the weaker the radio signal, the poorer the reception. A repeater is an electronic device in a communication channel that increases the power of a signal and retransmits it, allowing it to travel further. Since it amplifies the signal, it requires a source of electric power; the term "repeater" originated with telegraphy in the 19th century, referred to an electromechanical device used to regenerate telegraph signals. Use of the term has continued in data communications. In computer networking, because repeaters work with the actual physical signal, do not attempt to interpret the data being transmitted, they operate on the physical layer, the first layer of the OSI model; this is used to increase the range of telephone signals in a telephone line. Land line repeaterThey are most used in trunklines that carry long distance calls. In an analog telephone line consisting of a pair of wires, it consists of an amplifier circuit made of transistors which use power from a DC current source to increase the power of the alternating current audio signal on the line.
Since the telephone is a duplex communication system, the wire pair carries two audio signals, one going in each direction. So telephone repeaters have to be bilateral, amplifying the signal in both directions without causing feedback, which complicates their design considerably. Telephone repeaters were the first type of repeater and were some of the first applications of amplification; the development of telephone repeaters between 1900 and 1915 made long distance phone service possible. Now, most telecommunications cables are fiber optic cables. Before the invention of electronic amplifiers, mechanically coupled carbon microphones were used as amplifiers in telephone repeaters. After the turn of the 20th century it was found that negative resistance mercury lamps could amplify, they were used; the invention of audion tube repeaters around 1916 made transcontinental telephony practical. In the 1930s vacuum tube repeaters using hybrid coils became commonplace, allowing the use of thinner wires.
In the 1950s negative impedance gain devices were more popular, a transistorized version called the E6 repeater was the final major type used in the Bell System before the low cost of digital transmission made all voiceband repeaters obsolete. Frequency frogging repeaters were commonplace in frequency-division multiplexing systems from the middle to late 20th century. Submarine cable repeaterThis is a type of telephone repeater used in underwater submarine telecommunications cables; this is used to increase the range of signals in a fiber optic cable. Digital information travels through a fiber optic cable in the form of short pulses of light; the light is made up of particles called photons, which can be scattered in the fiber. An optical communications repeater consists of a phototransistor which converts the light pulses to an electrical signal, an amplifier to increase the power of the signal, an electronic filter which reshapes the pulses, a laser which converts the electrical signal to light again and sends it out the other fiber.
However, optical amplifiers are being developed for repeaters to amplify the light itself without the need of converting it to an electric signal first. This is used to extend the range of coverage of a radio signal; the history of radio relay repeaters began in 1898 from the publication by Johann Mattausch in Austrian Journal Zeitschrift für Electrotechnik. But his proposal "Translator" was not suitable for use; the first relay system with radio repeaters, which functioned, was that invented in 1899 by Emile Guarini-Foresio. A radio repeater consists of a radio receiver connected to a radio transmitter; the received signal is amplified and retransmitted on another frequency, to provide coverage beyond the obstruction. Usage of a duplexer can allow the repeater to use one antenna for both receive and transmit at the same time. Broadcast relay station, rebroadcastor or translator: This is a repeater used to extend the coverage of a radio or television broadcasting station, it consists of a secondary television transmitter.
The signal from the main transmitter comes over leased telephone lines or by microwave relay. Microwave relay: This is a specialized point-to-point telecommunications link, consisting of a microwave receiver that receives information over a beam of microwaves from an
A telephone exchange is a telecommunications system used in the public switched telephone network or in large enterprises. An exchange consists of electronic components and in older systems human operators that interconnect telephone subscriber lines or virtual circuits of digital systems to establish telephone calls between subscribers. In historical perspective, telecommunication terms have been used with different semantics over time; the term telephone exchange is used synonymously with central office, a Bell System term. A central office is defined as a building used to house the inside plant equipment of several telephone exchanges, each serving a certain geographical area; such an area has been referred to as the exchange. Central office locations may be identified in North America as wire centers, designating a facility from which a telephone obtains dial tone. For business and billing purposes, telephony carriers define rate centers, which in larger cities may be clusters of central offices, to define specified geographical locations for determining distance measurements.
In the United States and Canada, the Bell System established in the 1940s a uniform system of identifying central offices with a three-digit central office code, used as a prefix to subscriber telephone numbers. All central offices within a larger region aggregated by state, were assigned a common numbering plan area code. With the development of international and transoceanic telephone trunks driven by direct customer dialing, similar efforts of systematic organization of the telephone networks occurred in many countries in the mid-20th century. For corporate or enterprise use, a private telephone exchange is referred to as a private branch exchange, when it has connections to the public switched telephone network. A PBX is installed in enterprise facilities collocated with large office spaces or within an organizational campus to serve the local private telephone system and any private leased line circuits. Smaller installations might deploy a PBX or key telephone system in the office of a receptionist.
In the era of the electrical telegraph, post offices, railway stations, the more important governmental centers, stock exchanges few nationally distributed newspapers, the largest internationally important corporations and wealthy individuals were the principal users of such telegraphs. Despite the fact that telephone devices existed before the invention of the telephone exchange, their success and economical operation would have been impossible on the same schema and structure of the contemporary telegraph, as prior to the invention of the telephone exchange switchboard, early telephones were hardwired to and communicated with only a single other telephone. A telephone exchange is a telephone system located at service centers responsible for a small geographic area that provided the switching or interconnection of two or more individual subscriber lines for calls made between them, rather than requiring direct lines between subscriber stations; this made it possible for subscribers to call each other at businesses, or public spaces.
These made telephony an available and comfortable communication tool for everyday use, it gave the impetus for the creation of a whole new industrial sector. As with the invention of the telephone itself, the honor of "first telephone exchange" has several claimants. One of the first to propose a telephone exchange was Hungarian Tivadar Puskás in 1877 while he was working for Thomas Edison; the first experimental telephone exchange was based on the ideas of Puskás, it was built by the Bell Telephone Company in Boston in 1877. The world's first state-administered telephone exchange opened on November 12, 1877 in Friedrichsberg close to Berlin under the direction of Heinrich von Stephan. George W. Coy designed and built the first commercial US telephone exchange which opened in New Haven, Connecticut in January, 1878; the switchboard was built from "carriage bolts, handles from teapot lids and bustle wire" and could handle two simultaneous conversations. Charles Glidden is credited with establishing an exchange in Lowell, MA. with 50 subscribers in 1878.
In Europe other early telephone exchanges were based in London and Manchester, both of which opened under Bell patents in 1879. Belgium had its first International Bell exchange a year later. In 1887 Puskás introduced the multiplex switchboard.. Exchanges consisted of one to several hundred plug boards staffed by switchboard operators; each operator sat in front of a vertical panel containing banks of ¼-inch tip-ring-sleeve jacks, each of, the local termination of a subscriber's telephone line. In front of the jack panel lay a horizontal panel containing two rows of patch cords, each pair connected to a cord circuit; when a calling party lifted the receiver, the local loop current lit a signal lamp near the jack. The operator responded by inserting the rear cord into the subscriber's jack and switched her headset into the circuit to ask, "Number, please?" For a local call, the operator inserted the front cord of the pair into the called party's local jack and started the ringing cycle. For a long distance call, she plugged into a trunk circuit to connect to another operator in another bank of boards or at a remote central office.
In 1918, the average time to complete the connection for a long-distance call was 15 minutes. Early manual switchboards required the operator to operate listening keys and ringing keys, but by the late 1910s and 1920s, advances in switchboard technology led to features which allowed the call to be automatic
Port (circuit theory)
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 connected to an outside circuit; the use of ports helps to reduce the complexity of circuit analysis. Many common electronic devices and circuit blocks, such as transistors, electronic filters, 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 output signals taken. Its behavior is 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 known, in determining the circuit's response to applied signals; 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.
Any node of a circuit, available for connection to an external circuit is called a pole. 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, 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 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 and those two pairs are ports and the circuit is a box attenuator. On the other hand, if generators are connected to pole pairs and those pairs are ports, the pairs and are no longer ports, the circuit is a bridge circuit.
It is 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 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 useful for unbalanced circuit 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, nC2 generators every pole must be split into n−1 poles. For instance, in the figure example, if the poles 2 and 4 are each split into two poles each the circuit can be described as a 3-port. However, it is possible to connect generators to pole pairs, making 4C2 = 6 generators in all and the circuit has to be treated as a 6-port.
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 are one-ports. Study of one-ports is an important part of the foundation of network synthesis, most in filter design. Two-element one-ports 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 used in filter design. Linear two port networks have been studied and a large number of ways of representing them have been developed. One of these representations is the z-parameters. Most of the other descriptions of two-ports can 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 and filters. 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 n