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Distortion A distortion is the alteration of the original shape (or other characteristic) of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted. In some fields, distortion is desirable, such as electric guitar (where distortion is often induced purposely with the amplifier to achieve the electric guitar's desired, electrifying, aggressive sound). The slight distortion of analog tapes and vacuum tubes is considered pleasing in certain situations. The addition of noise or other extraneous signals (hum, interference) is not considered to be distortion, though the effects of distortion are sometimes considered noise. Electronic signals Graph of a waveform and the distorted versions of the same waveform In telecommunication and signal processing, a noise-free "system" can be characterised by a transfer function, such that the output y(t) can be written as a function of the input x as y(t) = F(x(t)) When the transfer function comprises only a perfect gain constant A and perfect delay T the output is undistorted. Distortion occurs when the transfer function F is more complicated than this. If F is a linear function, for instance a filter whose gain and/or delay varies with frequency, then the signal will experience linear distortion. Linear distortion will not change the shape of a single sinuosoid, but will usually change the shape of a multi-tone signal. This diagram shows the behaviour of a signal (made up of a square wave followed by a sine wave) as it is passed through various distorting functions. 1. The first trace (in black) shows the input. It also shows the output from a non-distorting transfer function (straight line). 2. A high-pass filter (green trace) will distort the shape of a square wave by reducing its low frequency components. This is the cause of the "droop" seen on the top of the pulses. This "pulse distortion" can be very significant when a train of pulses must pass through an AC-coupled (high-pass filtered) amplifier. As the sine wave contains only one frequency, its shape is unaltered. 3. A low-pass filter (blue trace) will round the pulses by removing the high frequency components. All systems are low pass to some extent. Note that the phase of the sine wave is different for the lowpass and the highpass cases, due to the phase distortion of the filters. 4. A slightly non-linear transfer function (purple), this one is gently compressing as may be typical of a tube audio amplifier, will compress the peaks of the sine wave. This will cause small amounts of low order harmonics to be generated. 5. A hard-clipping transfer function (red) will generate high order harmonics. Parts of the transfer function are flat, which indicates that all information about the input signal has been lost in this region. The transfer function of an ideal amplifier, with perfect gain and delay, is only an approximation. The true behavior of the system is usually different. Nonlinearities in the transfer function of an active device (such as vacuum tubes, transistors, and operational amplifiers) are a common source of non-linear distortion; in passive components (such as a coaxial cable or optical fiber), linear distortion can be caused by inhomogeneities, reflections, and so on in the propagation path. Amplitude distortion Amplitude distortion is distortion occurring in a system, subsystem, or device when the output amplitude is not a linear function of the input amplitude under specified conditions. Frequency distortion This form of distortion occurs when different frequencies are amplified by different amounts, mainly caused by combination of active device and components. For example, the non-uniform frequency response curve of RC-coupled cascade amplifier is an example of frequency distortion. Phase distortion This form of distortion mostly occurs due to the reactive component, such as capacitive reactance or inductor capacitance. Here, all the components of the input signal are not amplified with the same phase shift, hence causing some parts of the output signal to be out of phase with the rest of the output. Group delay distortion Can be found only in dispersive media. In a waveguide, propagation velocity varies with frequency. In a filter, group delay tends to peak near the cut-off frequency, resulting in pulse distortion. When analog long distance trunks were commonplace, for example in 12 channel carrier, group delay distortion had to be corrected in repeaters. Correction of distortion As the system output is given by y(t) = F(x(t)), then if the inverse function F-1 can be found, and used intentionally to distort either the input or the output of the system, then the distortion will be corrected. An example of such correction is where LP/Vinyl recordings or FM audio transmissions are deliberately pre-emphasised by a linear filter, the reproducing system applies an inverse filter to make the overall system undistorted. Correction is not possible if the inverse does not exist, for instance if the transfer function has flat spots (the inverse would map multiple input points to a single output point). This results in a loss of information, which is uncorrectable. Such a situation can occur when an amplifier is overdriven, resulting in clipping or slew rate distortion, when for a moment the output is determined by the characteristics of the amplifier alone, and not by the input signal. Teletypewriter or modem signaling In binary signaling such as FSK, distortion is the shifting of the significant instants of the signal pulses from their proper positions relative to the beginning of the start pulse. The magnitude of the distortion is expressed in percent of an ideal unit pulse length. This is sometimes called 'bias' distortion. Telegraphic distortion is a similar older problem, distorting the ratio between "mark" and "space" intervals. [1] Audio distortion A graph of a waveform and the distorted version of the same waveform In this context, distortion refers to any kind of deformation of a waveform, compared to an input. Clipping, compression, non-linear behavior of electronic components, modulation, aliasing, and mixing phenomena or power supply inefficiencies can cause distortion. In most fields, distortion is characterized as unwanted change to a signal. Gabber Distortion is one of the most important elements of Gabber music. Usually Distortion filters are added on drum patterns and bassline to achieve a very hard and raw sound. Guitar sound Distortion is an important part of an electric guitar's sound in many musical genres, including rock, hard rock, punk rock, garage punk, psychedelic rock and heavy metal. Typically, the signal coming from the guitar is distorted by a "clipping" of its waveform. This is commonly done with an effects pedal that is connected between the guitar and its amplifier. Optics In optics, image distortion is a divergence from rectilinear projection caused by a change in magnification with increasing distance from the optical axis of an optical system. Map projections In cartography, a distortion is the misrepresentation of the area or shape of a feature. The Mercator projection, for example, distorts Greenland because of its high latitude, in the sense that its shape and size are not the same as those on a globe. Noise In common use, the word noise means unwanted sound or noise pollution. In electronics noise can refer to the electronic signal corresponding to acoustic noise (in an audio system) or the electronic signal corresponding to the (visual) noise commonly seen as 'snow' on a degraded television or video image. In signal processing or computing it can be considered data without meaning; that is, data that is not being used to transmit a signal, but is simply produced as an unwanted by-product of other activities. In Information Theory, however, noise is still considered to be information. In a broader sense, film grain or even advertisements in web pages can be considered noise. Noise can block, distort, or change the meaning of a message in both human and electronic communication. In many of these areas, the special case of thermal noise arises, which sets a fundamental lower limit to what can be measured or signaled and is related to basic physical processes at the molecular level described by well known simple formulae. Acoustic noise When speaking of noise in relation to sound, what is commonly meant is meaningless sound of greater than usual volume. Thus, a loud activity may be referred to as noisy. However, conversations of other people may be called noise for people not involved in any of them, and noise can be any unwanted sound such as the noise of aircraft, neighbours playing loud music, or road sounds spoiling the quiet of the countryside. For film sound theorists and practitioners at the advent of talkies c.1928/1929, noise was nonspeech sound or natural sound and for many of them noise (especially asynchronous use with image) was desired over the evils of dialogue synchronized to moving image. The director and critic René Clair writing in 1929 makes a clear distinction between film dialogue and film noise and very clearly suggests that noise can have meaning and be interpreted: "...it is possible that an interpretation of noises may have more of a future in it. Sound cartoons, using "real" noises, seem to point to interesting possibilities" ('The Art of Sound' (1929)). Alberto Cavalcanti uses noise as a synonym for natural sound ('Sound in Films' (1939)) and as late as 1960, Siegfried Kracauer was referring to noise as non-speech sound ('Dialogue and Sound' (1960)). Audio noise In audio, recording, and broadcast systems audio noise refers to the residual low level sound (usually hiss and hum) that is heard in quiet periods of programme. In audio engineering it can also refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as 'hiss'. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting Electronic noise Electronic noise exists in all circuits and devices as a result of thermal noise, also referred to as Johnson Noise. Semiconductor devices can also contribute flicker noise and generationrecombination noise. In any electronic circuit, there exist random variations in current or voltage caused by the random movement of the electrons carrying the current as they are jolted around by thermal energy. The lower the temperature the lower is this thermal noise. This same phenomenon limits the minimum signal level that any radio receiver can usefully respond to, because there will always be a small but significant amount of thermal noise arising in its input circuits. This is why radio telescopes, which search for very low levels of signal from stars, use front-end low-noise amplifier circuits, usually mounted on the aerial dish, and cooled with liquid nitrogen. Headphones . Radio headphones, circa 1919 Headphones (also known as earphones, earbuds, stereophones, headsets, or by the slang term cans or face plugs) are a pair of small loudspeakers, or less commonly a single speaker, with a way of holding them close to a user's ears and a means of connecting them to a stereophonic, monophonic or binaural audio-frequency signal source such as an audio amplifier, radio or CD player. In the context of telecommunication, the term headset is used to describe a combination of headphone and microphone used for two-way communication, for example with a telephone. History Old telephone earpiece [1] The telephone earpiece such as the one pictured at the right was common around the turn of the 20th century. Sensitive headphones were the only way to listen to audio signals before amplifiers were developed. Very sensitive headphones such as those manufactured by Brandes (Fig.1) around 1919 were commonly used for early radio work. These early headphones used moving iron drivers, either single ended or balanced armature. The requirement for high sensitivity meant no damping was used, thus the sound quality was crude. They also had very poor comfort compared to modern types, with typically no padding and too often excessive clamping force to the head. Impedance varied, but 1k - 2k ohms was common, which suited both triodes and crystal sets. When used with early powered radios, the headphone was normally connected to the positive high voltage battery terminal, and the other battery terminal was securely earthed. The use of bare electrical connections meant some users could be shocked if they touched the bare headphone connections while adjusting an uncomfortable headset. At the time, pre-war headphones were called telephones, or sometimes phones, rather than headphones. Applications Headphones can be used both with fixed equipment such as CD or DVD players, home theater, personal computers and with portable devices (e.g. digital audio player/mp3 player, mobile phone, etc.). Some cordless headphones do not need to be connected via a wire, receiving a radio or infrared signal encoded using a radio or infrared transmission link, like FM, Bluetooth or WiFi. These are actually made of powered receiver systems of which the headphone is only a component. Headphones are widely used for listening to audio sources for recreation. In the professional audio sector headphones are used in live situations by disc jockeys (DJ) and sound engineers for monitoring signal sources. In radio studios, DJs use a pair of headphones when talking to the microphone while the speakers are turned off, to eliminate acoustic feedback and monitor their own voice. In studio recordings, musicians and singers use headphones to play along to a backing track. Wired headphones are attached to an audio source. The most common connectors are 1/4" and 3.5 mm stereophonic jack plugs and sockets. The older 1/4" standard is used on professional equipment, and is often used on fixed equipment. Sony introduced the smaller and cheaper, and now widely-used, 3.5 mm stereo connector in 1979, adapting the older monophonic 3.5 mm connector for use with its Walkman portable stereo tape player. Adapters are available for converting between 1/4" and 3.5 mm devices. [edit] Headsets Headphones that include a microphone are more commonly known as Headsets, and are more targeted for communication than audio listening. Communication headsets include mainly three types, Telephone, Computer and Mobile Phone. Telephone headsets are usually connected to a fixed-line (PSTN) telephone terminal, replacing its handset, so users can talk on the phone while they work on other things. Telephone headsets are very commonly used in Call Centers and offices, but are sometimes used at home also. Computer Headsets come in two types, standard 3.5mm plugs for connecting to sound-card of your PC, or USB connection. Both types are very commonly used for VoIP communication, but USB Headsets tend to have much better sound quality. Mobile Phone Headsets also comes in two types, wired and wireless. Wired Mobile Phone Headsets are also known as Mobile Handsfree, which is basically a pair of earphone with a microphone module connected to the cable. Wireless Mobile Handsfree also comes in different types, and the most common type nowadays is Bluetooth headset. Types of Headphones Circumaural headphones have large pads that surround the outer ear. There are many different types of headphone designs, with the listening situation and the needs of the listener determining what type of headphone will be used. Generally, headphone formfactors can be divided into four separate categories: Circumaural, supra-aural, earbud, and in-ear. Circumaural headphones have circular or ellipsoid earpads that fit around the ears. This type of headphone is commonly used in recording studios and among audio enthusiasts. A pair of supra-aural headphones. Supra-aural headphones have pads that sit on top of the ears, rather than around them. They were commonly bundled with personal stereos during the 1980s. Earbuds or earphones, such as these that ship with the Apple's iPod, rest in the outer part of the ear canal. Earbuds or earphones are headphones of a smaller size that are placed directly outside of the ear canal, but without fully enveloping it. They are generally inexpensive and are favored for their portability and convenience. However, due to their inability to provide isolation, they are not capable of delivering the same dynamic range offered by many full-sized headphones and canalphones for a given volume level. As a result, they are often used at higher volumes in order to drown out noise from the user's surroundings, which increases the risk of hearing-loss.[1] During the 1990s and 2000s, earbuds became a common type bundled with personal music devices. Canalphones extend into the ear canal, facilitating high quality sound[citation isolation from outside noise. needed] as well as Canalphones, also known as in-ear monitors, or IEMs, are earbuds that are inserted directly into the ear canal. Canalphones offer portability similar to earbuds, and also act as earplugs to block out environmental noise. There are two main types of IEMs — universal and custom. Universal canalphones provide one or more stock sleeve size(s) to fit various ear canals, which are commonly made out of silicone rubber, elastomer, or foam, for noise isolation. Universal canalphones are typically marketed to casual listeners and are relatively inexpensive. Custom canalphones are fitted to individuals. Castings of the ear canals are made, usually by an audiologist. The manufacturer uses the castings to create custom-molded silicone rubber or elastomer plugs that provide added comfort and noise isolation. Because of the individualized labor involved, custom IEMs are more expensive than universal IEMs. Typically, the housing, or earcup of a headphone will be either open or closed. Open headphones, sometimes marketed as “open air” headphones, have an open grille on the back of the earcup, exposing the driver to the outside and allowing sound waves to propagate away from the ear freely. This backing type does not isolate the listener from outside sounds; in addition, sound through open headphones can be heard by others in the vicinity of the user. They usually have less distortion due to the lack of earcup resonances. Closed headphones have a sealed backing, which attenuates sound waves propagating away from the ear. As a result, listeners away from the headphones cannot hear the produced sound easily. In addition, sound from outside is attenuated by the sealed backing, providing a level of isolation to the listener. A sealed chamber is often claimed to have the negative effect of distorting sound in certain frequencies due to resonances within the earcup housing. Technology Headphone transducers employ one or more of several methods of sound reproduction. A typical moving-coil headphone transducer Moving-Coil The moving coil driver, more commonly referred to as a "dynamic" driver is the most common type used in headphones. The operating principle consists of a stationary magnetic element affixed to the frame of the headphone which sets up a static magnetic field. The magnetic element in headphones is typically composed of ferrite or neodymium. The diaphragm, typically fabricated from lightweight, high stiffness to mass ratio cellulose, polymer, carbon material, or the like, is attached to a coil of wire (voice coil) which is immersed in the static magnetic field of the stationary magnet. The diaphragm is actuated by the attached voice coil, when an audio current is passed through the coil. The alternating magnetic field produced by the current flowing through the coil reacts against the static magnetic field in turn, causing the coil and attached diaphragm to move the air, thus producing sound. Modern moving-coil headphone drivers are derived from microphone capsule technology. Electrostatic Electrostatic drivers consist of a thin, electrically charged diaphragm, typically a coated PET film membrane, suspended between two perforated metal plates (electrodes). The electrical sound signal is applied to the electrodes creating an electrical field; depending on the polarity of this field, the diaphragm is drawn towards one of the plates. Air is forced through the perforations; combined with a continuously changing electrical signal driving the membrane, a sound wave is generated. Electrostatic headphones are usually more expensive than moving coil ones, and are comparatively uncommon. In addition, a special amplifier is required to amplify the signal to deflect the membrane, which often requires electrical potentials in the range of 100 to 1000 volts. Due to the extremely thin and light diaphragm membrane, often only a few micrometers thick, and the complete absence of moving metalwork, the frequency response of electrostatic headphones usually extends well above the audible limit of approximately 20kHz. The high frequency response means that the low midband distortion level is maintained to the top of the audible frequency band, which is generally not the case with moving coil drivers. Also, the frequency response peakiness regularly seen in the high frequency region with moving coil drivers is absent. The result is significantly better sound quality, if designed properly. The listener impression with electrostatics is one of great clarity. Electrostatic headphones are powered by anything from 100v to over 1kV, and are in close proximity to a user's head. The usual method of making this safe is to limit the possible fault current to a low and safe value with resistors. Balanced Armature Balanced armature transducer with armature balanced and exerting no force on diaphragm. Balanced armature transducer with armature torqued and exerting a force on diaphragm. A balanced armature is a sound transducer design primarily intended to increase the electrical efficiency of the element by eliminating the stress on the diaphragm characteristic of many other magnetic transducer systems. As shown schematically in the first diagram, it consists of a moving magnetic armature that is pivoted so it can move in the field of the permanent magnet. When precisely centered in the magnetic field there is no net force on the armature, hence the term 'balanced.' As illustrated in the second diagram, when electric current flows through the coil, it magnetizes the armature one way or the other, causing it to rotate slightly one way or the other about the pivot thus moving the diaphragm to make sound. The design is not mechanically stable, a slight imbalance makes the armature stick to one pole of the magnet. A fairly stiff restoring force is required to hold the armature in the ‘balance’ position. Although this reduces its efficiency, this design can still produce more sound from less power than any other. Popularized in the 1920s as Baldwin Mica Diaphragm radio headphones, balanced armature transducers were refined during World War II for use in 'sound-powered' telephones for military use. Some of these achieved astonishing electro-acoustic conversion efficiencies in the 20% to 40% for narrow bandwidth voice signals. Today they are typically used only in canalphones and hearing aids due to their diminutive size and low impedance. They generally are limited at the extremes of the hearing spectrum (<20Hz, >16kHz) and require a seal more than other types of drivers to deliver their full potential. Higher end models may employ multiple armature drivers, dividing the frequency ranges between them using a passive crossover network. Some combine an armature driver with a small moving coil driver for increased bass output. Orthodynamic Orthodynamic, or magnetostatic drivers, are either comprised of a thinly pressed disc made of tightly coiled fine aluminium wire affixed to a mylar sheet or of a printed circuit. This disc is the diaphragm. The diaphragm is then sandwiched between two magnets which have the same polarity facing each other. As a result the magnets repel from each other and so the whole assembly is clamped together. An electrical signal is passed through the disc as it would be through the voice coil of a moving coil driver and the motion produced generates the sound. Once a popular choice for manufacturers such as Yamaha for their headphones, the technology has fallen generally into disuse as companies increasingly favour moving coil designs. Fostex continue to make orthodynamic headphones, although their fidelity is not generally well regarded in comparison with older orthodynamic designs. AMT/Piezo/Plasma AMTs and Piezoelectric drivers are very uncommonly used (when compared to those above) diaphragm technologies, however both have been utilised as headphone drivers in the past. Current production models utilising the technologies total only one for each, although the TakeT piezoelectric headphone is technically a piezoelectric-AMT hybrid design because of the shape of its diaphragm. There has also been one attempt to market a plasma-ionisation drive headphone. Benefits and limitations Headphones may be used to prevent other people from hearing the sound either for privacy or to prevent disturbance, as in listening in a public library. They can also provide a level of sound quality that could only be matched by speakers costing a great deal more. This is especially true in the bass (low frequency) region, where loudspeaker-listening room interactions normally cause resonant nodes, so that even with the best speakers, a listener in a given place hears some bass notes too loudly and others too softly. Good headphones, with a good seal to the ear, can have an extremely flat low-frequency response down to 20 Hz within 3dB. Marketed claims such as 'frequency response 4 Hz to 20 kHz' are usually overstatements; the product's response at frequencies lower than 20 Hz is typically very small. Those of the 'closed back' type are also used to exclude external sounds, particularly in sound recording studios and in noisy environments. Headphones have been reputed to better portray subtle layers of sound.[2] Headphones can also be useful for videogames that use 3D positional audio, allowing players to better judge the position of an off-screen sound source (such as the footsteps of an opponent). Although modern headphones are widely sold and used for listening to stereo recordings, especially since the invention of the Walkman, some say they are fundamentally unsuited to such use. They supposedly produce the disconcerting effect of sound coming from the middle of the listener's head, with unnaturally isolated sounds occasionally appearing predominantly in one ear, giving the impression that the other has suddenly gone deaf. This is because stereo recordings represent the position of each sound by large amplitude differences between two channels intended for reproduction through a pair of loudspeakers. When the sounds from the two speakers mix, they create the phase difference the brain uses to locate direction. Others claim that stereo sounds better through headphones, because the right and left channels haven't mixed. This makes panning effects more easily appreciated, and adds a sense of immersion to the listening experience. Binaural recordings use a different microphone technique to encode direction directly as phase, with very little amplitude difference (except above 2 kHz) often using a dummy head, and can produce a surprisingly life-like spatial impression through headphones. Commercial recordings almost always use stereo recording, because historically loudspeaker listening has been more popular than headphone listening. It is possible to improve the spatial effect from stereo on headphones by using frequency-dependent cross-feed between the channels, or—better still—a Blumlein shuffler (a custom EQ employed to augment the lowfrequency content of the difference information in a stereo signal), though this is rarely done. While cross-feed can reduce the feeling of deafness in one ear, only the use of a dummy head during recording, with artificial pinnae, can convincingly take away the "middle of the head" effect. Optimal sound is achieved when the dummy head matches the listener's head, since pinnae vary greatly in size and shape. Headphones can have an ergonomic benefit over the traditional handset at office desks. They save space and many new models are wireless. They also allow call center agents to maintain good posture instead of tilting their head sideways to cradle a handset. They are also used in professional sound editing, so that more than one person can work on an audio track without interfering with another. Over time, many wired headphone cables fail. A common scenario in which a replacement set might need to be purchased is the physical breakdown of copper wiring within the cords of many popular headphones. Over time, the connection formed to close the circuit may become severed due to stress fatigue. Dangers and volume solutions Using headphones at a sufficiently high volume level can cause temporary or permanent hearing impairment or deafness due to an effect called "masking." The headphone volume has to compete with the background noise, especially in excessively loud places such as subway stations, airplanes, and large crowds. This leads to the disappearance of the normal pain associated with higher levels of volumes. Extended periods of the excessively loud volume are extremely damaging. Some manufacturers of portable music devices have attempted to introduce safety circuitry that limited output volume or warned the user when dangerous volume was being used, but the concept has been rejected by most of the buying public, which favors the personal choice of high volume. Koss introduced the "Safelite" line of cassette players in 1983 with such a warning light. The line was discontinued two years later for lack of interest. The French government has imposed a limit on all music players sold in the country: they must not be capable of producing more than 100dBA (the threshold of hearing damage during extended listening is 80dB, and the threshold of pain, or of immediate hearing loss, is 130dB). Many users decry this as an infringement on personal choice, and use third-party options to reverse the software volume caps placed on such devices. Still, other users welcome the government's pro-health stance. Other risks arise from the reduced awareness of external sounds—some jurisdictions regulate the use of headphones while driving vehicles, usually limiting the use of earphones to a single ear. The complete isolation from outside noise can be a hazard in itself, as a user could miss the sound of a car horn and walk into traffic with fatal consequences. Losing situational awareness can also lead to getting robbed, particularly in busy environments where bumping into another person would be ignored, e.g., subway stations. Canalphones are generally believed to be safer than open-air headphones for use in noisy environments. The reason for this is that much of the external noise which is usually heard while using earphones or headphones is blocked out by canalphones, therefore allowing the user to listen at lower volume levels without having to turn up the listening device to compete with background noise. Canalphones are a passive counterpart to active noise canceling headphones, which use circuitry and destructive wave interference to attenuate sound. Manufacturers of canalphones quote that their products reach isolation levels of -30dB to -40dB, while noise cancellers isolate by a degree of -15dB to -20dB. Closed and noise-cancelling headphones can have a similar effect, although sound attenuation of the latter is usually limited in frequency range and amplitude: closed headphones do not isolate low frequency sounds very well, and noise cancellers do not attempt to attenuate high frequency sounds. Suitable amplification The amount of “load” or impedance on the line is an important differentiating factor among headphone driver technologies. Common moving-coil headphones typically have an impedance of 32 ohms. Smaller, in-ear types may have an impedance as low as 16 or 11 ohms. Studio monitoring headphones tend to have much higher impedances, ranging from 300 in some cases to as high as 5000 ohms in others. Portable audio devices are designed to work with lowimpedance headphones and are often unable to drive high-impedance headphones to high volume levels. Electrostatic and piezoelectric headphones, because of their capacitive rather than resistive operating nature, have massively high electromechanical load, which is why they require a different nature of amplification. Both are voltage driven rather than current driven as moving-coil, orthodynamic, balanced armature and AMT drivers are. The electromechanical load on its own though should be used as no more than a rough guide figure for the amplification requirements that a driver may require. Other factors such as sensitivity are also very important.