1.
Zobel network
–
For the wave filter invented by Zobel and sometimes named after him see m-derived filters. Zobel networks are a type of filter section based on the design principle. They are named after Otto Zobel of Bell Labs, who published a paper on image filters in 1923. The distinguishing feature of Zobel networks is that the impedance is fixed in the design independently of the transfer function. This characteristic is achieved at the expense of a higher component count compared to other types of filter sections. The impedance would normally be specified to be constant and purely resistive, for this reason, they are also known as constant resistance networks. However, any impedance achievable with discrete components is possible, however, as analogue technology has given way to digital, they are now little used. When used to out the reactive portion of loudspeaker impedance. In this case, only half the network is implemented as fixed components and this network is more akin to the power factor correction circuits used in electrical power distribution, hence the association with Boucherots name. A common circuit form of Zobel networks is in the form of a bridged T and this term is often used to mean a Zobel network, sometimes incorrectly when the circuit implementation is, in fact, something other than a bridged T. Parts of this article or section rely on the knowledge of the complex impedance representation of capacitors and inductors. The basis of a Zobel network is a bridge circuit as shown in the circuit to the right. The bridging impedance ZB is across the points and hence has no potential across it. Consequently, it will draw no current and its value makes no difference to the function of the circuit, however, its value is often chosen to be Z0 for reasons which will become clear in the discussion of bridged T circuits. If the Z0 in the right of the bridge is taken to be the output load then a transfer function of Vin/Vo can be calculated for the section. Only the rhs branch needs to be considered in this calculation, the reason for this can be seen by considering that there is no current flow through RB. None of the current flowing through the lhs branch is going to flow into the load, the lhs branch therefore, cannot possibly affect the output. It certainly affects the input impedance but not the transfer function, if we also set, Z B = Z0 then the circuit to the right results
2.
Resistor
–
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of power as heat may be used as part of motor controls, in power distribution systems. Fixed resistors have resistances that only slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds, Resistors are also implemented within integrated circuits. The electrical function of a resistor is specified by its resistance, the nominal value of the resistance falls within the manufacturing tolerance, indicated on the component. Two typical schematic diagram symbols are as follows, The notation to state a resistors value in a circuit diagram varies, one common scheme is the letter and digit code for resistance values following IEC60062. It avoids using a separator and replaces the decimal separator with a letter loosely associated with SI prefixes corresponding with the parts resistance. For example, 8K2 as part marking code, in a diagram or in a bill of materials indicates a resistor value of 8.2 kΩ. Additional zeros imply a tighter tolerance, for example 15M0 for three significant digits, when the value can be expressed without the need for a prefix, an R is used instead of the decimal separator. For example, 1R2 indicates 1.2 Ω, and 18R indicates 18 Ω, for example, if a 300 ohm resistor is attached across the terminals of a 12 volt battery, then a current of 12 /300 =0.04 amperes flows through that resistor. Practical resistors also have some inductance and capacitance which affect the relation between voltage and current in alternating current circuits, the ohm is the SI unit of electrical resistance, named after Georg Simon Ohm. An ohm is equivalent to a volt per ampere, since resistors are specified and manufactured over a very large range of values, the derived units of milliohm, kilohm, and megohm are also in common usage. The total resistance of resistors connected in series is the sum of their resistance values. R e q = R1 + R2 + ⋯ + R n, the total resistance of resistors connected in parallel is the reciprocal of the sum of the reciprocals of the individual resistors. 1 R e q =1 R1 +1 R2 + ⋯ +1 R n. For example, a 10 ohm resistor connected in parallel with a 5 ohm resistor, a resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other
3.
Capacitor
–
A capacitor is a passive two-terminal electrical component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance, a capacitor was therefore historically first known as an electric condenser. The physical form and construction of practical capacitors vary widely and many types are in common use. Most capacitors contain at least two electrical conductors often in the form of plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, the nonconducting dielectric acts to increase the capacitors charge capacity. Materials commonly used as dielectrics include glass, ceramic, plastic film, paper, mica, Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, a capacitor does not dissipate energy. No current actually flows through the dielectric, instead, the effect is a displacement of charges through the source circuit, if the condition is maintained sufficiently long, this displacement current through the battery ceases. However, if a voltage is applied across the leads of the capacitor. Capacitance is defined as the ratio of the charge on each conductor to the potential difference between them. The unit of capacitance in the International System of Units is the farad, capacitance values of typical capacitors for use in general electronics range from about 1 pF to about 1 mF. The capacitance of a capacitor is proportional to the area of the plates. In practice, the dielectric between the plates passes a small amount of leakage current and it has an electric field strength limit, known as the breakdown voltage. The conductors and leads introduce an undesired inductance and resistance, Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies, in resonant circuits they tune radios to particular frequencies. In electric power systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in digital computers. Von Kleists hand and the water acted as conductors, and the jar as a dielectric, von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine
4.
Inductor
–
An inductor, also called a coil or reactor, is a passive two-terminal electrical component that stores electrical energy in a magnetic field when electric current is flowing through it. An inductor typically consists of a conductor, such as a wire. When the current flowing through an inductor changes, the magnetic field induces a voltage in the conductor. According to Lenzs law, the direction of induced electromotive force opposes the change in current that created it, as a result, inductors oppose any changes in current through them. An inductor is characterized by its inductance, which is the ratio of the voltage to the rate of change of current, in the International System of Units, the unit of inductance is the henry. Inductors have values that range from 1 µH to 1 H. Many inductors have a core made of iron or ferrite inside the coil. Along with capacitors and resistors, inductors are one of the three passive linear circuit elements that make up electronic circuits, Inductors are widely used in alternating current electronic equipment, particularly in radio equipment. They are used to block AC while allowing DC to pass and they are also used in electronic filters to separate signals of different frequencies, and in combination with capacitors to make tuned circuits, used to tune radio and TV receivers. An electric current flowing through a conductor generates a magnetic field surrounding it, any changes of current and therefore in the magnetic flux through the cross-section of the inductor creates an opposing electromotive force in the conductor. An inductor is a component consisting of a wire or other conductor shaped to increase the flux through the circuit. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, increasing the field, the more turns, the higher the inductance. The inductance also depends on the shape of the coil, separation of the turns, by adding a magnetic core made of a ferromagnetic material like iron inside the coil, the magnetizing field from the coil will induce magnetization in the material, increasing the magnetic flux. The high permeability of a core can increase the inductance of a coil by a factor of several thousand over what it would be without it. Any change in the current through an inductor creates a changing flux, for example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. This is usually taken to be the relation of the inductor. The dual of the inductor is the capacitor, which stores energy in a field rather than a magnetic field. Its current-voltage relation is obtained by exchanging current and voltage in the inductor equations, the polarity of the induced voltage is given by Lenzs law, which states that it will be such as to oppose the change in current
5.
Voltage
–
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against an electric field to move the test charge between two points. This is measured in units of volts, voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage between two points in a system, often a reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy or lost, used, given two points in space, x A and x B, voltage is the difference in electric potential between those two points. Electric potential must be distinguished from electric energy by noting that the potential is a per-unit-charge quantity. Like mechanical potential energy, the zero of electric potential can be chosen at any point, so the difference in potential, i. e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the energy required to move a small electric charge along that path. Mathematically this is expressed as the integral of the electric field. In the general case, both an electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Historically this quantity has also called tension and pressure. Pressure is now obsolete but tension is used, for example within the phrase high tension which is commonly used in thermionic valve based electronics. Voltage is defined so that negatively charged objects are pulled towards higher voltages, therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when a source of energy is present to push it against the electric field. This is the case within any electric power source, for example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal. The electric field is not the only factor determining charge flow in a material, the electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of voltage can be found instead in the concept of Fermi level, in this case the voltage between two bodies is the thermodynamic work required to move a unit of charge between them
6.
High-pass filter
–
A high-pass filter is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design, a high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a filter or bass-cut filter. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices and they can also be used in conjunction with a low-pass filter to produce a bandpass filter. Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier and that is, high-frequency signals are inverted and amplified by R2/R1. Discrete-time high-pass filters can also be designed, discrete-time filter design is beyond the scope of this article, however, a simple example comes from the conversion of the continuous-time high-pass filter above to a discrete-time realization. That is, the behavior can be discretized. Substituting Equation into Equation and then Equation into Equation gives, V out = C ⏞ I R = R C This equation can be discretized, for simplicity, assume that samples of the input and output are taken at evenly spaced points in time separated by Δ T time. Let the samples of V in be represented by the sequence, the expression for parameter α yields the equivalent time constant R C in terms of the sampling period Δ T and α, R C = Δ T. If α =0.5, then the R C time constant equal to the sampling period, if α ≪0.5, then R C is significantly smaller than the sampling interval, and R C ≈ α Δ T. The filter recurrence relation provides a way to determine the output samples in terms of the input samples, in particular, A large α implies that the output will decay very slowly but will also be strongly influenced by even small changes in input. By the relationship between parameter α and time constant R C above, a large α corresponds to a large R C, hence, this case corresponds to a high-pass filter with a very narrow stop band. Because it is excited by changes and tends to hold its prior output values for a long time. However, a constant input will always decay to zero, as would be expected with a filter with a large R C. A small α implies that the output will decay quickly and will require changes in the input to cause the output to change much. By the relationship between parameter α and time constant R C above, a small α corresponds to a small R C, hence, this case corresponds to a high-pass filter with a very wide stop band. Because it requires large changes and tends to forget its prior output values, it can only pass relatively high frequencies. They are used as part of a crossover to direct high frequencies to a tweeter while attenuating bass signals which could interfere with, or damage
7.
Ohm
–
The ohm is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. The definition of the ohm was revised several times, today the definition of the ohm is expressed from the quantum Hall effect. In many cases the resistance of a conductor in ohms is approximately constant within a range of voltages, temperatures. In alternating current circuits, electrical impedance is also measured in ohms, the siemens is the SI derived unit of electric conductance and admittance, also known as the mho, it is the reciprocal of resistance in ohms. The power dissipated by a resistor may be calculated from its resistance, non-linear resistors have a value that may vary depending on the applied voltage. The rapid rise of electrotechnology in the last half of the 19th century created a demand for a rational, coherent, consistent, telegraphers and other early users of electricity in the 19th century needed a practical standard unit of measurement for resistance. Two different methods of establishing a system of units can be chosen. Various artifacts, such as a length of wire or a standard cell, could be specified as producing defined quantities for resistance, voltage. This latter method ensures coherence with the units of energy, defining a unit for resistance that is coherent with units of energy and time in effect also requires defining units for potential and current. Some early definitions of a unit of resistance, for example, the absolute-units system related magnetic and electrostatic quantities to metric base units of mass, time, and length. These units had the advantage of simplifying the equations used in the solution of electromagnetic problems. However, the CGS units turned out to have impractical sizes for practical measurements, various artifact standards were proposed as the definition of the unit of resistance. In 1860 Werner Siemens published a suggestion for a reproducible resistance standard in Poggendorffs Annalen der Physik und Chemie and he proposed a column of pure mercury, of one square millimetre cross section, one metre long, Siemens mercury unit. However, this unit was not coherent with other units, one proposal was to devise a unit based on a mercury column that would be coherent – in effect, adjusting the length to make the resistance one ohm. Not all users of units had the resources to carry out experiments to the required precision. The BAAS in 1861 appointed a committee including Maxwell and Thomson to report upon Standards of Electrical Resistance, in the third report of the committee,1864, the resistance unit is referred to as B. A. unit, or Ohmad. By 1867 the unit is referred to as simply Ohm, the B. A. ohm was intended to be 109 CGS units but owing to an error in calculations the definition was 1. 3% too small. The error was significant for preparation of working standards, on September 21,1881 the Congrès internationale délectriciens defined a practical unit of Ohm for the resistance, based on CGS units, using a mercury column at zero deg
8.
Farad
–
The farad is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday, one farad is defined as the capacitance across which, when charged with one coulomb, there is a potential difference of one volt. Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt, the relationship between capacitance, charge and potential difference is linear. For example, if the difference across a capacitor is halved. For most applications, the farad is a large unit of capacitance. Most electrical and electronic applications are covered by the following SI prefixes,1 mF =1000 μF =1000000 nF1 μF =0.000001 F =1000 nF =1000000 pF1 nF =0. In 1881 at the International Congress of Electricians in Paris, the name farad was officially used for the unit of electrical capacitance, a capacitor consists of two conducting surfaces, frequently referred to as plates, separated by an insulating layer usually referred to as a dielectric. The original capacitor was the Leyden jar developed in the 18th century and it is the accumulation of electric charge on the plates that results in capacitance. Values of capacitors are specified in farads, microfarads, nanofarads and picofarads. The millifarad is rarely used in practice, while the nanofarad is uncommon in North America, the size of commercially available capacitors ranges from around 0.1 pF to 5000F supercapacitors. Capacitance values of 1 pF or lower can be achieved by twisting two short lengths of insulated wire together, the capacitance of the Earths ionosphere with respect to the ground is calculated to be about 1 F. The picofarad is sometimes pronounced as puff or pic, as in a ten-puff capacitor. Similarly, mic is sometimes used informally to signify microfarads, if the Greek letter μ is not available, the notation uF is often used as a substitute for μF in electronics literature. A micro-microfarad, an obsolete unit sometimes found in texts, is the equivalent of a picofarad. In texts prior to 1960, and on capacitor packages even more recently. Similarly, mmf or MMFD represented picofarads, the reciprocal of capacitance is called electrical elastance, the unit of which is the daraf. The abfarad is an obsolete CGS unit of equal to 109 farads. The statfarad is a rarely used CGS unit equivalent to the capacitance of a capacitor with a charge of 1 statcoulomb across a potential difference of 1 statvolt and it is 1/ farad, approximately 1.1126 picofarads
9.
Electronic filter
–
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, passive or active analog or digital high-pass, low-pass, band-pass, band-stop, see the article on linear filters for details on their design and analysis. The oldest forms of filters are passive analog linear filters. These are known as RC and RL single-pole filters respectively, more complex multipole LC filters have also existed for many years, and their operation is well understood. Hybrid filters are possible, typically involving a combination of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD delay lines have also used as discrete-time filters. With the availability of digital processing, active digital filters have become common. Passive implementations of filters are based on combinations of resistors, inductors and capacitors. These types are known as passive filters, because they do not depend upon an external power supply and/or they do not contain active components such as transistors. Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse, the inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter, in this context, an LC tuned circuit being used in a band-pass or band-stop filter is considered a single element even though it consists of two components. At high frequencies, sometimes the inductors consist of single loops or strips of metal. These inductive or capacitive pieces of metal are called stubs, the simplest passive filters, RC and RL filters, include only one reactive element, except hybrid LC filter which is characterized by inductance and capacitance integrated in one element. An L filter consists of two elements, one in series and one in parallel. Three-element filters can have a T or π topology and in either geometries, the components can be chosen symmetric or not, depending on the required frequency characteristics. The high-pass T filter in the illustration, has a low impedance at high frequencies. That means that it can be inserted in a line, resulting in the high frequencies being passed. Likewise, for the illustrated low-pass π filter, the circuit can be connected to a line, transmitting low frequencies
10.
Butterworth filter
–
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband. It is also referred to as a maximally flat magnitude filter and it was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled On the Theory of Filter Amplifiers. Butterworth had a reputation for solving mathematical problems. At the time, filter design required an amount of designer experience due to limitations of the theory then in use. The filter was not in use for over 30 years after its publication. Butterworth stated that, An ideal electrical filter should not only reject the unwanted frequencies. Such an ideal filter cannot be achieved but Butterworth showed that successively closer approximations were obtained with increasing numbers of elements of the right values. At the time, filters generated substantial ripple in the passband, if ω =1, the amplitude response of this type of filter in the passband is 1/√2 ≈0.707, which is half power or −3 dB. Butterworth only dealt with filters with an number of poles in his paper. He may have been unaware that such filters could be designed with an odd number of poles and he built his higher order filters from 2-pole filters separated by vacuum tube amplifiers. His plot of the response of 2,4,6,8, and 10 pole filters is shown as A, B, C, D. In 1930, low-loss core materials such as molypermalloy had not been discovered and air-cored audio inductors were rather lossy, Butterworth discovered that it was possible to adjust the component values of the filter to compensate for the winding resistance of the inductors. He used coil forms of 1. 25″ diameter and 3″ length with plug-in terminals, associated capacitors and resistors were contained inside the wound coil form. The coil formed part of the load resistor. Two poles were used per vacuum tube and RC coupling was used to the grid of the following tube, Butterworth also showed that his basic low-pass filter could be modified to give low-pass, high-pass, band-pass and band-stop functionality. The frequency response of the Butterworth filter is maximally flat in the passband, when viewed on a logarithmic Bode plot, the response slopes off linearly towards negative infinity. A first-order filters response rolls off at −6 dB per octave, a second-order filter decreases at −12 dB per octave, a third-order at −18 dB and so on. Butterworth filters have a monotonically changing magnitude function with ω, unlike other types that have non-monotonic ripple in the passband and/or the stopband
11.
Current source
–
A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source, the term, constant-current sink, is sometimes used for sources fed from a negative voltage supply. Figure 1 shows the symbol for an ideal current source. An independent current source delivers a constant current, a dependent current source delivers a current which is proportional to some other voltage or current in the circuit. An ideal current source generates a current that is independent of the changes across it. An ideal current source is a model, which real devices can approach very closely. If the current through a current source can be specified independently of any other variable in a circuit, it is called an independent current source. Conversely, if the current through a current source is determined by some other voltage or current in a circuit, it is called a dependent or controlled current source. Symbols for these sources are shown in Figure 2, the internal resistance of an ideal current source is infinite. An independent current source with zero current is identical to an open circuit. The voltage across a current source is completely determined by the circuit it is connected to. When connected to a circuit, there is zero voltage. When connected to a resistance, the voltage across the source approaches infinity as the load resistance approaches infinity. Thus, a current source, if such a thing existed in reality, could supply unlimited power. No physical current source is ideal, for example, no physical current source can operate when applied to an open circuit. There are two characteristics that define a current source in real life, one is its internal resistance and the other is its compliance voltage. The compliance voltage is the voltage that the current source can supply to a load. Over a given range, it is possible for some types of real current sources to exhibit nearly infinite internal resistance
12.
Complex number
–
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i2 = −1. In this expression, a is the part and b is the imaginary part of the complex number. If z = a + b i, then ℜ z = a, ℑ z = b, Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point in the complex plane, a complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the numbers are a field extension of the ordinary real numbers. As well as their use within mathematics, complex numbers have applications in many fields, including physics, chemistry, biology, economics, electrical engineering. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers and he called them fictitious during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to equations that have no solutions in real numbers. For example, the equation 2 = −9 has no real solution, Complex numbers provide a solution to this problem. The idea is to extend the real numbers with the unit i where i2 = −1. According to the theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. A complex number is a number of the form a + bi, for example, −3.5 + 2i is a complex number. The real number a is called the part of the complex number a + bi. By this convention the imaginary part does not include the unit, hence b. The real part of a number z is denoted by Re or ℜ. For example, Re = −3.5 Im =2, hence, in terms of its real and imaginary parts, a complex number z is equal to Re + Im ⋅ i. This expression is known as the Cartesian form of z. A real number a can be regarded as a number a + 0i whose imaginary part is 0