In electronics, a differentiator is a circuit, designed such that the output of the circuit is directly proportional to the rate of change of the input. An active differentiator includes some form of amplifier. A passive differentiator circuit is made of only capacitors. A true differentiator cannot be physically realized, because it has infinite gain at infinite frequency. A similar effect can be achieved, however, by limiting the gain above some frequency. Therefore, a passive differentiator circuit can be made using a simple first-order high-pass filter, with the cut-off frequency set to be far above the highest frequency in the signal; this is a four-terminal network consisting of two passive elements as shown in figures 1 and 2. The analysis here is for the capacitive circuit in figure 1; the inductive case in figure 2 can be handled in a similar way. The transfer function shows the dependence of the network gain on the signal frequency for sinusoidal signals. According to Ohm's law, Y = X Z R Z R + Z C = X R R + 1 j ω C = X 1 1 + 1 j ω R C, where X and Y are input and output signals' amplitudes and Z R and Z C are the resistor's and capacitor's impedances.
Therefore, the complex transfer function is K = 1 1 + 1 j ω R C = 1 1 + ω 0 j ω, where ω 0 = 1 R C. The amplitude transfer function H ≜ | K | = 1 1 + 2, the phase transfer function ϕ ≜ arg K = arctan ω 0 ω, which are both shown in Figure 3. Transfer functions for the second circuit are the same; the circuit's impulse response, shown in figure 4, can be derived as an inverse Laplace transform of the complex transfer function: h = L − 1 = δ − ω 0 e − ω 0 t = δ − 1 τ e − t τ where τ = 1 ω 0 is a time constant, δ is a delta function. A differentiator circuit consists of an operational amplifier in which a resistor R provides negative feedback and a capacitor is used at the input side; the circuit is based on the capacitor's current to voltage relationship V = V + e − t τ, I = C d V d t, where I is the current through the capacitor, C is the capacitance of the capacitor, V is the voltage across the capacitor. The current flowing through the capacitor is proportional to the derivative of the voltage across the capacitor.
This current can be connected to a resistor, which has the current to voltage relationship I = V R, where R is the resistance of the r
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that contains information to be transmitted. Most radio systems in the 20th century used frequency modulation or amplitude modulation for radio broadcast. A modulator is a device. A demodulator is a device that performs the inverse of modulation. A modem can perform both operations; the aim of analog modulation is to transfer an analog baseband signal, for example an audio signal or TV signal, over an analog bandpass channel at a different frequency, for example over a limited radio frequency band or a cable TV network channel. The aim of digital modulation is to transfer a digital bit stream over an analog communication channel, for example over the public switched telephone network or over a limited radio frequency band. Analog and digital modulation facilitate frequency division multiplexing, where several low pass information signals are transferred over the same shared physical medium, using separate passband channels.
The aim of digital baseband modulation methods known as line coding, is to transfer a digital bit stream over a baseband channel a non-filtered copper wire such as a serial bus or a wired local area network. The aim of pulse modulation methods is to transfer a narrowband analog signal, for example, a phone call over a wideband baseband channel or, in some of the schemes, as a bit stream over another digital transmission system. In music synthesizers, modulation may be used to synthesize waveforms with an extensive overtone spectrum using a small number of oscillators. In this case, the carrier frequency is in the same order or much lower than the modulating waveform. In analog modulation, the modulation is applied continuously in response to the analog information signal. Common analog modulation techniques include: Amplitude modulation Double-sideband modulation Double-sideband modulation with carrier Double-sideband suppressed-carrier transmission Double-sideband reduced carrier transmission Single-sideband modulation Single-sideband modulation with carrier Single-sideband modulation suppressed carrier modulation Vestigial sideband modulation Quadrature amplitude modulation Angle modulation, constant envelope Frequency modulation Phase modulation Transpositional Modulation, in which the waveform inflection is modified resulting in a signal where each quarter cycle is transposed in the modulation process.
TM is a pseudo-analog modulation. Where an AM carrier carries a phase variable phase f. TM is f. Digital modulation methods can be considered as digital-to-analog conversion and the corresponding demodulation or detection as analog-to-digital conversion; the changes in the carrier signal are chosen from a finite number of M alternative symbols. A simple example: A telephone line is designed for transferring audible sounds, for example and not digital bits. Computers may, communicate over a telephone line by means of modems, which are representing the digital bits by tones, called symbols. If there are four alternative symbols, the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11. If the modem plays a melody consisting of 1000 tones per second, the symbol rate is 1000 symbols/second, or 1000 baud. Since each tone represents a message consisting of two digital bits in this example, the bit rate is twice the symbol rate, i.e. 2000 bits per second. This is similar to the technique used by dial-up modems as opposed to DSL modems.
According to one definition of digital signal, the modulated signal is a digital signal. According to another definition, the modulation is a form of digital-to-analog conversion. Most textbooks would consider digital modulation schemes as a form of digital transmission, synonymous to data transmission; the most fundamental digital modulation techniques are based on keying: PSK: a finite number of phases are used. FSK: a finite number of frequencies are used. ASK: a finite number of amplitudes are used. QAM: a finite number of at least two phases and at least two amplitudes are used. In QAM, an in-phase signal and a quadrature phase signal are amplitude modulated with a finite number of amplitudes and summed, it can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK. In all of the above methods, each of these phases, frequencies or amplitudes are assigned a u
An inductor called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor consists of an insulated wire wound into a coil around a core; when the current flowing through an inductor changes, the time-varying magnetic field induces an electromotive force in the conductor, described by Faraday's law of induction. According to Lenz's law, the induced voltage has a polarity which 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, 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 named for 19th century American scientist Joseph Henry. In the measurement of magnetic circuits, it is equivalent to weber/ampere. Inductors have values that range from 1 µH to 20 H. Many inductors have a magnetic core made of iron or ferrite inside the coil, which serves to increase the magnetic field and thus the inductance.
Along with capacitors and resistors, inductors are one of the three passive linear circuit elements that make up electronic circuits. Inductors are used in alternating current electronic equipment in radio equipment, they are used to block AC while allowing DC to pass. They are used in electronic filters to separate signals of different frequencies, 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; the magnetic flux linkage Φ B generated by a given current I depends on the geometric shape of the circuit. Their ratio defines the inductance L, thus L:= Φ B I. The inductance of a circuit depends on the geometry of the current path as well as the magnetic permeability of nearby materials. An inductor is a component consisting of a wire or other conductor shaped to increase the magnetic flux through the circuit in the shape of a coil or helix. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, increasing the field and thus the inductance.
The more turns, the higher the inductance. The inductance depends on the shape of the coil, separation of the turns, many other factors. 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 ferromagnetic 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, inducing a voltage across the inductor. By Faraday's law of induction, the voltage induced by any change in magnetic flux through the circuit is given by E = − d Φ B d t. Reformulating the definition of L above, we obtain Φ B = L I, it follows. So inductance is a measure of the amount of electromotive force generated for a given rate of change of current. 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 taken to be the constitutive relation of the inductor. The dual of the inductor is the capacitor, which stores energy in an electric field rather than a magnetic field, its current–voltage relation is obtained by exchanging current and voltage in the inductor equations and replacing L with the capacitance C. The polarity of the induced voltage is given by Lenz's law, which states that the induced voltage will be such as to oppose the change in current. For example, if the current through an inductor is increasing, the induced voltage will be positive at the terminal through which the current enters and negative at the terminal through which it leaves, tending to oppose the additional current; the energy from the external circuit necessary to overcome this potential "hill" is being stored in the magnetic field of the inductor. If the current is decreasing, the induced voltage will be negative at the terminal through which the current enters and positive at the terminal through which it leaves, tending to maintain the current.
In this case energy from the magnetic field is being returned to the circuit. One intuitive explanation as to why a potential difference is induced on a change of current in an inductor goes as follows: When there is a change in current, there is a change in the strength of the induced magnetic field
Intermodulation or intermodulation distortion is the amplitude modulation of signals containing two or more different frequencies, caused by nonlinearities or time variance in a system. The intermodulation between frequency components will form additional components at frequencies that are not just at harmonic frequencies of either, like harmonic distortion, but at the sum and difference frequencies of the original frequencies and at sums and differences of multiples of those frequencies. Intermodulation is caused by non-linear behaviour of the signal processing being used; the theoretical outcome of these non-linearities can be calculated by generating a Volterra series of the characteristic, or more by a Taylor series. All audio equipment has some non-linearity, so it will exhibit some amount of IMD, which however may be low enough to be imperceptible by humans. Due to the characteristics of the human auditory system, the same percentage of IMD is perceived as more bothersome when compared to the same amount of harmonic distortion.
Intermodulation is usually undesirable in radio, as it creates unwanted spurious emissions in the form of sidebands. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel interference, which can reduce audio clarity or increase spectrum usage. IMD is only distinct from harmonic distortion; the same nonlinear system will produce both total harmonic distortion and IMD. In music, for instance, IMD is intentionally applied to electric guitars using overdriven amplifiers or effects pedals to produce new tones at subharmonics of the tones being played on the instrument. See Power chord#Analysis. IMD is distinct from intentional modulation where signals to be modulated are presented to an intentional nonlinear element. See non-linear mixers such as mixer diodes and single-transistor oscillator-mixer circuits. However, while the intermodulation products of the received signal with the local oscillator signal are intended, superheterodyne mixers can, at the same time produce unwanted intermodulation effects from strong signals near in frequency to the desired signal that fall within the passband of the receiver.
A linear system cannot produce intermodulation. If the input of a linear time-invariant system is a signal of a single frequency the output is a signal of the same frequency. Non-linear systems generate harmonics in response to sinusoidal input, meaning that if the input of a non-linear system is a signal of a single frequency, f a the output is a signal which includes a number of integer multiples of the input frequency signal. Intermodulation occurs. Consider an input signal that contains three frequency components at f a, f b, f c. We obtain our output signal, y, by passing our input through a non-linear function G: y = G y will contain the three frequencies of the input signal, f a, f b, f c, as well as a number of linear combinations of the fundamental frequencies, each of the form k a f a + k b f b + k c f c where k a, k b, k c are arbitrary integers which can assume positive or negative values; these are the intermodulation products. In general, each of these frequency components will have a different amplitude and ph
A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core. Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil. Transformers are used for increasing or decreasing the alternating voltages in electric power applications, for coupling the stages of signal processing circuits. Since the invention of the first constant-potential transformer in 1885, transformers have become essential for the transmission and utilization of alternating current electric power. A wide range of transformer designs is encountered in electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid.
An ideal transformer is a theoretical linear transformer, lossless and coupled. Perfect coupling implies infinitely high core magnetic permeability and winding inductances and zero net magnetomotive force. A varying current in the transformer's primary winding attempts to create a varying magnetic flux in the transformer core, encircled by the secondary winding; this varying flux at the secondary winding induces a varying electromotive force in the secondary winding due to electromagnetic induction and the secondary current so produced creates a flux equal and opposite to that produced by the primary winding, in accordance with Lenz's law. The windings are wound around a core of infinitely high magnetic permeability so that all of the magnetic flux passes through both the primary and secondary windings. With a voltage source connected to the primary winding and load impedance connected to the secondary winding, the transformer currents flow in the indicated directions and the core magnetomotive force cancels to zero.
According to Faraday's law, since the same magnetic flux passes through both the primary and secondary windings in an ideal transformer, a voltage is induced in each winding proportional to its number of windings. Thus, referring to the equations shown in the sidebox at right, according to Faraday's law, we have primary and secondary winding voltages defined by eq. 1 & eq. 2, respectively. The primary EMF is sometimes termed counter EMF; this is in accordance with Lenz's law, which states that induction of EMF always opposes development of any such change in magnetic field. The transformer winding voltage ratio is thus shown to be directly proportional to the winding turns ratio according to eq. 3. However, some sources use the inverse definition. According to the law of conservation of energy, any load impedance connected to the ideal transformer's secondary winding results in conservation of apparent and reactive power consistent with eq. 4. The ideal transformer identity shown in eq. 5 is a reasonable approximation for the typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to the corresponding current ratio.
By Ohm's law and the ideal transformer identity: the secondary circuit load impedance can be expressed as eq. 6 the apparent load impedance referred to the primary circuit is derived in eq. 7 to be equal to the turns ratio squared times the secondary circuit load impedance. The ideal transformer model neglects the following basic linear aspects of real transformers: Core losses, collectively called magnetizing current losses, consisting of Hysteresis losses due to nonlinear magnetic effects in the transformer core, Eddy current losses due to joule heating in the core that are proportional to the square of the transformer's applied voltage. Unlike the ideal model, the windings in a real transformer have non-zero resistances and inductances associated with: Joule losses due to resistance in the primary and secondary windings Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance. Similar to an inductor, parasitic capacitance and self-resonance phenomenon due to the electric field distribution.
Three kinds of parasitic capacitance are considered and the closed-loop equations are provided Capacitance between adjacent turns in any one layer. However, the capacitance effect can be measured by comparing open-circuit inductance, i.e. the inductance of a primary winding when the secondary circuit is open, to a short-circuit inductance when the secondary winding is shorted. The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths; such flux is termed leakage flux, results in leakage inductance in series with the mutually coupled transformer windings. Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply, it is not directly a power loss, but results in inferior voltage regulation, causing the secondary voltage not to be directly proportional to the primary voltage under heavy load. Transformers are therefore designed to have low
Sound recording and reproduction
Sound recording and reproduction is an electrical, electronic, or digital inscription and re-creation of sound waves, such as spoken voice, instrumental music, or sound effects. The two main classes of sound recording technology are analog digital recording. Acoustic analog recording is achieved by a microphone diaphragm that senses changes in atmospheric pressure caused by acoustic sound waves and records them as a mechanical representation of the sound waves on a medium such as a phonograph record. In magnetic tape recording, the sound waves vibrate the microphone diaphragm and are converted into a varying electric current, converted to a varying magnetic field by an electromagnet, which makes a representation of the sound as magnetized areas on a plastic tape with a magnetic coating on it. Analog sound reproduction is the reverse process, with a bigger loudspeaker diaphragm causing changes to atmospheric pressure to form acoustic sound waves. Digital recording and reproduction converts the analog sound signal picked up by the microphone to a digital form by the process of sampling.
This lets the audio data be transmitted by a wider variety of media. Digital recording stores audio as a series of binary numbers representing samples of the amplitude of the audio signal at equal time intervals, at a sample rate high enough to convey all sounds capable of being heard. A digital audio signal must be reconverted to analog form during playback before it is amplified and connected to a loudspeaker to produce sound. Prior to the development of sound recording, there were mechanical systems, such as wind-up music boxes and player pianos, for encoding and reproducing instrumental music. Long before sound was first recorded, music was recorded—first by written music notation also by mechanical devices. Automatic music reproduction traces back as far as the 9th century, when the Banū Mūsā brothers invented the earliest known mechanical musical instrument, in this case, a hydropowered organ that played interchangeable cylinders. According to Charles B. Fowler, this "...cylinder with raised pins on the surface remained the basic device to produce and reproduce music mechanically until the second half of the nineteenth century."
The Banū Mūsā brothers invented an automatic flute player, which appears to have been the first programmable machine. Carvings in the Rosslyn Chapel from the 1560s may represent an early attempt to record the Chladni patterns produced by sound in stone representations, although this theory has not been conclusively proved. In the 14th century, a mechanical bell-ringer controlled by a rotating cylinder was introduced in Flanders. Similar designs appeared in barrel organs, musical clocks, barrel pianos, music boxes. A music box is an automatic musical instrument that produces sounds by the use of a set of pins placed on a revolving cylinder or disc so as to pluck the tuned teeth of a steel comb; the fairground organ, developed in 1892, used a system of accordion-folded punched cardboard books. The player piano, first demonstrated in 1876, used a punched paper scroll that could store a long piece of music; the most sophisticated of the piano rolls were hand-played, meaning that the roll represented the actual performance of an individual, not just a transcription of the sheet music.
This technology to record a live performance onto a piano roll was not developed until 1904. Piano rolls were in continuous mass production from 1896 to 2008. A 1908 U. S. Supreme Court copyright case noted that, in 1902 alone, there were between 70,000 and 75,000 player pianos manufactured, between 1,000,000 and 1,500,000 piano rolls produced; the first device that could record actual sounds as they passed through the air was the phonautograph, patented in 1857 by Parisian inventor Édouard-Léon Scott de Martinville. The earliest known recordings of the human voice are phonautograph recordings, called phonautograms, made in 1857, they consist of sheets of paper with sound-wave-modulated white lines created by a vibrating stylus that cut through a coating of soot as the paper was passed under it. An 1860 phonautogram of Au Clair de la Lune, a French folk song, was played back as sound for the first time in 2008 by scanning it and using software to convert the undulating line, which graphically encoded the sound, into a corresponding digital audio file.
On April 30, 1877, French poet, humorous writer and inventor Charles Cros submitted a sealed envelope containing a letter to the Academy of Sciences in Paris explaining his proposed method, called the paleophone. Though no trace of a working paleophone was found, Cros is remembered as the earliest inventor of a sound recording and reproduction machine; the first practical sound recording and reproduction device was the mechanical phonograph cylinder, invented by Thomas Edison in 1877 and patented in 1878. The invention soon spread across the globe and over the next two decades the commercial recording and sale of sound recordings became a growing new international industry, with the most popular titles selling millions of units by the early 1900s; the development of mass-production techniques enabled cylinder recordings to become a major new consumer item in industrial countries and the cylinder was the main consumer format from the late 1880s until around 1910. The next major technical development was the invention of the gramophone record credited to Emile Berliner and patented in 1887, though others had demonstrated simi
A scientific calculator is a type of electronic calculator but not always handheld, designed to calculate problems in science and mathematics. They have completely replaced slide rules in traditional applications, are used in both education and professional settings. In certain contexts such as higher education, scientific calculators have been superseded by graphing calculators, which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device. There is some overlap with the financial calculator market. Modern scientific calculators have many more features than a standard four or five-function calculator, the feature set differs between manufacturers and models. A few have multi-line displays, with some models from Hewlett-Packard, Texas Instruments, Casio and Canon using dot matrix displays similar to those found on graphing calculators. Scientific calculators are used in situations that require quick access to certain mathematical functions those that were once looked up in mathematical tables, such as trigonometric functions or logarithms.
They are used for calculations of large or small numbers, as in some aspects of astronomy and chemistry. They are often required for math classes from the junior high school level through college, are either permitted or required on many standardized tests covering math and science subjects; the first scientific calculator that included all of the basic ideas above was the programmable Hewlett-Packard HP-9100A, released in 1968, though the Wang LOCI-2 and the Mathatronics Mathatron had some features identified with scientific calculator designs. The HP-9100 series was built from discrete transistor logic with no integrated circuits, was one of the first uses of the CORDIC algorithm for trigonometric computation in a personal computing device, as well as the first calculator based on Reverse Polish Notation entry. HP became identified with RPN calculators from on, today some of their high-end calculators still offer RPN as their default input mode due to having garnered a large following; the HP-35, introduced on February 1, 1972, was Hewlett-Packard's first pocket calculator and the world's first handheld scientific calculator.
Like some of HP's desktop calculators it used RPN. Introduced at US$395, the HP-35 was available from 1972 to 1975. Texas Instruments, after the introduction of several units with scientific notation, came out with a handheld scientific calculator on January 15, 1974, in the form of the SR-50. TI continues to be a major player in the calculator market, with their long-running TI-30 series being one of the most used scientific calculators in classrooms. Casio and Sharp have been major players, with Casio's fx series being a common brand, used in schools. Casio is a major player in the graphing calculator market, was the first company to produce one. Formula calculator Calculator input methods