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56-454: At low power levels, the fundamental output power rises in a one-to-one ratio (in terms of dB ) of the input power, while the second-order output power rises in a two-to-one ratio. If the input power is high enough for the device to reach saturation, the output power flattens out in both the first- and second-order cases. The second order intercept point is the output power point at which the extrapolated first- and second-order lines intersect on

112-612: A s = 1 G p , 2 G p , 3 G p , 4 . . . G p , n O S O I 1 + 1 G p , 3 G p , 4 . . . G p , n O S O I 2 + . . . + 1 O S O I n {\displaystyle {\frac {1}{OSOI_{cas}}}={\frac {1}{G_{p,2}G_{p,3}G_{p,4}...G_{p,n}OSOI_{1}}}+{\frac {1}{G_{p,3}G_{p,4}...G_{p,n}OSOI_{2}}}+...+{\frac {1}{OSOI_{n}}}} In

168-689: A s = 1 G p , 2 G p , 3 G p , 4 . . . G p , n O S O I 1 + 1 G p , 3 G p , 4 . . . G p , n O S O I 2 + . . . + 1 O S O I n {\displaystyle {\frac {1}{\sqrt {OSOI_{cas}}}}={\frac {1}{\sqrt {G_{p,2}G_{p,3}G_{p,4}...G_{p,n}OSOI_{1}}}}+{\frac {1}{\sqrt {G_{p,3}G_{p,4}...G_{p,n}OSOI_{2}}}}+...+{\frac {1}{\sqrt {OSOI_{n}}}}} 1 I S O I c

224-609: A s = 1 I S O I 1 + 1 I S O I 2 / G p , 1 + . . . + 1 I S O I n / G p , 1 G p , 2 G p , 3 . . . G p , n − 1 {\displaystyle {\frac {1}{ISOI_{cas}}}={\frac {1}{ISOI_{1}}}+{\frac {1}{ISOI_{2}/G_{p,1}}}+...+{\frac {1}{ISOI_{n}/G_{p,1}G_{p,2}G_{p,3}...G_{p,n-1}}}} 1 O S O I c

280-641: A s = 1 I S O I 1 + 1 I S O I 2 / G p , 1 + . . . + 1 I S O I n / G p , 1 G p , 2 G p , 3 . . . G p , n − 1 {\displaystyle {\frac {1}{\sqrt {ISOI_{cas}}}}={\frac {1}{\sqrt {ISOI_{1}}}}+{\frac {1}{\sqrt {ISOI_{2}/G_{p,1}}}}+...+{\frac {1}{\sqrt {ISOI_{n}/G_{p,1}G_{p,2}G_{p,3}...G_{p,n-1}}}}} 1 O S O I c

336-446: A 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km. The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see Weber–Fechner law ), making the dB scale a useful measure. The decibel is commonly used in acoustics as a unit of sound power level or sound pressure level . The reference pressure for sound in air

392-407: A bel would normally be written 0.05 dB, and not 5 mB. The method of expressing a ratio as a level in decibels depends on whether the measured property is a power quantity or a root-power quantity ; see Power, root-power, and field quantities for details. When referring to measurements of power quantities, a ratio can be expressed as a level in decibels by evaluating ten times

448-422: A change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude. The definition of

504-502: A decibel is one-tenth of a bel). P and P 0 must measure the same type of quantity, and have the same units before calculating the ratio. If P = P 0 in the above equation, then L P = 0. If P is greater than P 0 then L P is positive; if P is less than P 0 then L P is negative. Rearranging the above equation gives the following formula for P in terms of P 0 and L P  : When referring to measurements of root-power quantities, it

560-698: A favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit (TU). 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power. The definition was conveniently chosen such that 1 TU approximated 1 MSC; specifically, 1 MSC

616-437: A frequency of 5000   radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to a listener. A standard telephone cable was "a cable having uniformly distributed resistance of 88 ohms per loop-mile and uniformly distributed shunt capacitance of 0.054  microfarads per mile" (approximately corresponding to 19  gauge wire). In 1924, Bell Telephone Laboratories received

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672-453: A linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations: The logarithmic mean is obtained from the logarithmic sum by subtracting 10 log 10 ⁡ 2 {\displaystyle 10\log _{10}2} , since logarithmic division

728-428: A manner similar to scientific notation . This allows one to clearly visualize huge changes of some quantity. See Bode plot and Semi-log plot . For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing". Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as

784-451: A plot, since the actual power levels will flatten off due to saturation at much lower power level typically. In other words, the response is assumed to be perfect all the way to infinity. There are actually values for both the input and output SOI (known as the ISOI & OSOI or IIP2 & OIP2) of a device or system, being related by the small signal gain of the device or system. The OSOI in dB

840-434: A power ratio of 10 , or 1.9953 , about 0.24% different from exactly 2, and a voltage ratio of 1.4125 , 0.12% different from exactly √ 2 . Similarly, an increase of 6.000 dB corresponds to the power ratio is 10 ≈ 3.9811 , about 0.5% different from 4. The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along

896-459: A ratio between two root-power quantities of √ 10 :1. Two signals whose levels differ by one decibel have a power ratio of 10 , which is approximately 1.258 93 , and an amplitude (root-power quantity) ratio of 10 ( 1.122 02 ). The bel is rarely used either without a prefix or with SI unit prefixes other than deci ; it is customary, for example, to use hundredths of a decibel rather than millibels . Thus, five one-thousandths of

952-418: A series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log( A × B × C ) = log( A ) + log( B ) + log( C ). Practically, this means that, armed only with the knowledge that 1 dB is a power gain of approximately 26%, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it

1008-406: A signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations. The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in

1064-421: A subtraction ( C / N 0 ) dB = C dB − N 0 dB . However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz. According to Mitschke, "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values

1120-400: A unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio. The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point. (31.62 V / 1 V) ≈ 1 kW / 1 W , illustrating the consequence from the definitions above that L G has the same value, 30 dB, regardless of whether it

1176-428: Is a relative unit of measurement equal to one tenth of a bel ( B ). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale . Two signals whose levels differ by one decibel have a power ratio of 10 (approximately 1.26 ) or root-power ratio of 10 (approximately 1.12 ). The unit fundamentally expresses a relative change but may also be used to express an absolute value as

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1232-469: Is almost universally rounded to 3 dB in technical writing. This implies an increase in voltage by a factor of √ 2 ≈ 1.4142 . Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6 dB rather than ± 6.0206  dB. Should it be necessary to make the distinction, the number of decibels is written with additional significant figures . 3.000 dB corresponds to

1288-402: Is deprecated by that standard and root-power is used throughout this article. Although power and root-power quantities are different quantities, their respective levels are historically measured in the same units, typically decibels. A factor of 2 is introduced to make changes in the respective levels match under restricted conditions such as when the medium is linear and the same waveform

1344-416: Is linear subtraction. Attenuation constants, in topics such as optical fiber communication and radio propagation path loss , are often expressed as a fraction or ratio to distance of transmission. In this case, dB/m represents decibel per meter, dB/mi represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis , e.g., a 100-meter run with

1400-490: Is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations: if two machines each individually produce a sound pressure level of, say, 90 dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93 dB, but certainly not to 180 dB!; suppose that

1456-411: Is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared. A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB . A change in power ratio by a factor of 2 or ⁠ 1 / 2 ⁠ is approximately a change of 3 dB . More precisely, the change is ± 3.0103  dB, but this

1512-795: Is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example: However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, and is cumbersome and difficult to interpret. Quantities in decibels are not necessarily additive , thus being "of unacceptable form for use in dimensional analysis ". Thus, units require special care in decibel operations. Take, for example, carrier-to-noise-density ratio C / N 0 (in hertz), involving carrier power C (in watts) and noise power spectral density N 0 (in W/Hz). Expressed in decibels, this ratio would be

1568-590: Is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO). The IEC permits the use of the decibel with root-power quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST , which justifies the use of the decibel for voltage ratios. In spite of their widespread use, suffixes (such as in dBA or dBV) are not recognized by

1624-452: Is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure . As sound pressure is a root-power quantity, the appropriate version of the unit definition is used: where p rms is the root mean square of the measured sound pressure and p ref is the standard reference sound pressure of 20 micropascals in air or 1 micropascal in water. Use of

1680-457: Is simply the ISOI in dB plus the small signal gain of the device or system. To determine the second-order characteristics of a device, a strong signal is put through the device, and the output are measured. Both single- and two-tone techniques can be used, and while there will be frequencies components off to infinity, for SOI analysis the fundamental and second-order distortion products are the desired results. In single-tone analysis, one tone at

1736-409: Is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time. This relies on the relationship holding. In a nonlinear system, this relationship does not hold by the definition of linearity. However, even in a linear system in which the power quantity is the product of two linearly related quantities (e.g. voltage and current ), if

Second-order intercept point - Misplaced Pages Continue

1792-440: Is usual to consider the ratio of the squares of F (measured) and F 0 (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used: The formula may be rearranged to give Similarly, in electrical circuits , dissipated power is typically proportional to the square of voltage or current when

1848-441: Is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 10 and any two amounts of power differ by N decibels when they are in the ratio of 10 . The number of transmission units expressing

1904-414: The base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P 0 (reference power) is represented by L P , that ratio expressed in decibels, which is calculated using the formula: The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently,

1960-414: The gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1 MSC corresponded to the loss of power over one mile (approximately 1.6 km) of standard telephone cable at

2016-399: The impedance is constant. Taking voltage as an example, this leads to the equation for power gain level L G : where V out is the root-mean-square (rms) output voltage, V in is the rms input voltage. A similar formula holds for current. The term root-power quantity is introduced by ISO Standard 80000-1:2009 as a substitute of field quantity . The term field quantity

2072-415: The impedance is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes. For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities P 0 and F 0 need not be related), or equivalently, must hold to allow the power level difference to be equal to

2128-459: The IEC or ISO. The IEC Standard 60027-3:2002 defines the following quantities. The decibel (dB) is one-tenth of a bel: 1 dB = 0.1 B . The bel (B) is 1 ⁄ 2  ln(10) nepers : 1 B = 1 ⁄ 2 ln(10) Np . The neper is the change in the level of a root-power quantity when the root-power quantity changes by a factor of e , that is 1 Np = ln(e) = 1 , thereby relating all of

2184-458: The OSOI case, a similar process can be performed, except the distortion components are moved to the end of the cascade. Here, the OSOI of the first device is affected by the gain of all subsequent devices, and so on. For the OSOI, the gain of the first device has no effect on the cascade OSOI. Both coherent and non-coherent derivations of these equations exist, due to the possible phase differences of

2240-401: The decibel in underwater acoustics leads to confusion, in part because of this difference in reference value. Sound intensity is proportional to the square of sound pressure. Therefore, the sound intensity level can also be defined as: The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of

2296-561: The decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell , but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering , most prominently for sound power in acoustics , in electronics and control theory . In electronics,

Second-order intercept point - Misplaced Pages Continue

2352-419: The desired frequency is generated and put through the device. There will be output at the fundamental, and the output due to second-order effects will be at DC and twice the input frequency. The derivation follows: Single-tone analysis fails to illustrate several common linearity problems, therefore in two-tone analysis, two tones of approximately equal strength are put through the device. There will be output at

2408-428: The distortion components. In the coherent case, all of the components are exactly in phase, and their voltages simply add, while in the non-coherent case the phases are random and the distortion powers add together. The coherent case represents the most conservative (i.e. worst-case) answer, and the non-coherent case is generally a more accurate description for most systems. 1 I S O I c

2464-441: The earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit

2520-439: The following equations f refers to the fundamental frequency, and 2f refers to the second-order distortion component frequencies. △ S O , d B {\displaystyle \bigtriangleup _{SO,dB}} is the difference in power between the fundamental output and the output of the second-order components, as shown on the figure to the right. Decibel The decibel (symbol: dB )

2576-400: The following ways. For the ISOI, the second-order distortion components can be "moved" to the beginning of the cascade, where the ISOI of the first component is unaffected by any gain, the ISOI of the second component is divided by the gain of the first component, and this process continues to the end of the cascade. In this case the gain of the last device has no effect on the cascade ISOI. In

2632-404: The fundamental frequencies, and the output due to second-order effects will be at DC, twice the input frequencies, and the sum and difference of the input frequencies. The derivation follows: If multiple devices are connected in cascade, and their individual ISOI and OSOI are known, it is possible to calculate the ISOI and OSOI of the entire system. It is helpful to think of how they are derived in

2688-555: The name logit for "standard magnitudes which combine by multiplication", to contrast with the name unit for "standard magnitudes which combine by addition". In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the inclusion of the decibel in the International System of Units (SI), but decided against the proposal. However, the decibel

2744-416: The noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA.; in order to find a representative value of

2800-461: The quantities power spectral density and the associated root-power quantities via the Fourier transform , which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently. Since logarithm differences measured in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as

2856-428: The ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1  volt , a common suffix is " V " (e.g., "20 dBV"). Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm with base 10 . That is,

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2912-427: The ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit ... In 1954, J. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, and suggested

2968-459: The root-power level difference from power P 1 and F 1 to P 2 and F 2 . An example might be an amplifier with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0 dB, but the power gain depends on the changing spectral composition of the waveform being amplified. Frequency-dependent impedances may be analyzed by considering

3024-420: The sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. [...] Compare the logarithmic and arithmetic averages of [...] 70 dB and 90 dB: logarithmic average = 87 dB; arithmetic average = 80 dB. Addition on a logarithmic scale is called logarithmic addition , and can be defined by taking exponentials to convert to

3080-399: The units as nondimensional natural log of root-power-quantity ratios, 1 dB =  0.115 13 ... Np =  0.115 13 ... . Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity. Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of

3136-599: Was 1.056 TU. In 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel , in honor of the telecommunications pioneer Alexander Graham Bell . The bel is seldom used, as the decibel was the proposed working unit. The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931: Since

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