80-427: Intermodulation ( IM ) or intermodulation distortion ( IMD ) 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 ( integer multiples ) of either, like harmonic distortion , but also at
160-659: A {\displaystyle ~f_{a}} , f b {\displaystyle ~f_{b}} , and f c {\displaystyle ~f_{c}} (which are known as the fundamental frequencies), as well as a number of linear combinations of the fundamental frequencies, each in the form where k a {\displaystyle ~k_{a}} , k b {\displaystyle ~k_{b}} , and k c {\displaystyle ~k_{c}} are arbitrary integers which can assume positive or negative values. These are
240-401: A {\displaystyle ~f_{a}} , f b {\displaystyle ~f_{b}} , and f c {\displaystyle ~f_{c}} ; which may be expressed as where the M {\displaystyle \ M} and ϕ {\displaystyle \ \phi } are the amplitudes and phases of
320-503: A , f b , … , f N {\displaystyle f_{a},f_{b},\ldots ,f_{N}} , the output signal will contain a number of frequency components, each of which may be described by where the coefficients k a , k b , … , k N {\displaystyle k_{a},k_{b},\ldots ,k_{N}} are arbitrary integer values. The order O {\displaystyle \ O} of
400-463: A Taylor series . Practically 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 also usually undesirable in radio, as it creates unwanted spurious emissions , often in
480-440: A digital-to-analog converter , typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion). This low-level method for AM is used in many Amateur Radio transceivers. AM may also be generated at a low level, using analog methods described in
560-505: A buzz in receivers. In effect they were already amplitude modulated. The first AM transmission was made by Canadian-born American researcher Reginald Fessenden on 23 December 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter , over a distance of one mile (1.6 km) at Cobb Island, Maryland, US. His first transmitted words were, "Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?". The words were barely intelligible above
640-436: A compromise in terms of bandwidth) in order to reduce the required channel spacing. Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there
720-409: A decade to establish PASS / FAIL specifications for radio frequency components. Slew-induced distortion (SID) can produce intermodulation distortion (IMD) when the first signal is slewing (changing voltage) at the limit of the amplifier's power bandwidth product. This induces an effective reduction in gain, partially amplitude-modulating the second signal. If SID only occurs for a portion of
800-563: A dedicated spectrum analyzer , or when determining intermodulation effects in communications equipment, may be made using the receiver under test itself. In radio applications, intermodulation may be measured as adjacent channel power ratio . Hard to test are intermodulation signals in the GHz-range generated from passive devices (PIM: passive intermodulation). Manufacturers of these scalar PIM-instruments are Summitek and Rosenberger. The newest developments are PIM-instruments to measure also
880-493: A faithful reproduction of the original program, including its varying modulation levels, is expected. In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation: Amplitude modulation was used in experiments of multiplex telegraph and telephone transmission in the late 1800s. However, the practical development of this technology is identified with
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#1732783040062960-491: A given intermodulation product is the sum of the absolute values of the coefficients, For example, in our original example above, third-order intermodulation products (IMPs) occur where | k a | + | k b | + | k c | = 3 {\displaystyle \ |k_{a}|+|k_{b}|+|k_{c}|=3} : In many radio and audio applications, odd-order IMPs are of most interest, as they fall within
1040-455: A great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War II. At the same time as AM radio began, telephone companies such as AT&T were developing
1120-408: A human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted above the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times,
1200-468: A precise carrier frequency reference signal (usually as shifted to the intermediate frequency ) from a greatly reduced "pilot" carrier (in reduced-carrier transmission or DSB-RC) to use in the demodulation process. Even with the carrier eliminated in double-sideband suppressed-carrier transmission , carrier regeneration is possible using a Costas phase-locked loop . This does not work for single-sideband suppressed-carrier transmission (SSB-SC), leading to
1280-471: A previous section , intermodulation can only occur in non-linear systems. Non-linear systems are generally composed of active components, meaning that the components must be biased with an external power source which is not the input signal (i.e. the active components must be "turned on"). Passive intermodulation (PIM), however, occurs in passive devices (which may include cables, antennas etc.) that are subjected to two or more high power tones. The PIM product
1360-673: A problem. Early experiments in AM radio transmission, conducted by Fessenden, Valdemar Poulsen , Ernst Ruhmer , Quirino Majorana , Charles Herrold , and Lee de Forest , were hampered by the lack of a technology for amplification . The first practical continuous wave AM transmitters were based on either the huge, expensive Alexanderson alternator , developed 1906–1910, or versions of the Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation
1440-584: A rather small (or zero) remaining carrier amplitude. Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain—followed by amplification for transmission—or in the high-power domain of the transmitted signal). In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with
1520-424: A receive antenna). Although the power in the passive intermodulation signal is typically many orders of magnitude lower than the power of the transmit signal, the power in the passive intermodulation signal is often times on the same order of magnitude (and possibly higher) than the power of the receive signal. Therefore, if a passive intermodulation finds its way to receive path, it cannot be filtered or separated from
1600-454: A result, radio frequency equipment manufacturers perform factory PIM tests on components, to eliminate passive intermodulation caused by these design and manufacturing defects. Passive intermodulation can also be inherent in the design of a high power radio frequency component where radio frequency current is forced to narrow channels or restricted. In the field, passive intermodulation can be caused by components that were damaged in transit to
1680-408: A single broadband carrier. These PIMs would show up as sidebands in a telecommunication signal, which interfere with adjacent channels and impede reception. Passive intermodulations are a major concern in modern communication systems in cases when a single antenna is used for both high power transmission signals as well as low power receive signals (or when a transmit antenna is in close proximity to
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#17327830400621760-499: A single sine wave, as treated above. However, by the principle of Fourier decomposition , m(t) can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of 1 + m(t) with c(t) as above, the result consists of a sum of sine waves. Again, the carrier c(t) is present unchanged, but each frequency component of m at f i has two sidebands at frequencies f c + f i and f c – f i . The collection of
1840-403: A special modulator produces such a waveform at a low level followed by a linear amplifier . What's more, a standard AM receiver using an envelope detector is incapable of properly demodulating such a signal. Rather, synchronous detection is required. Thus double-sideband transmission is generally not referred to as "AM" even though it generates an identical RF waveform as standard AM as long as
1920-538: Is intentionally applied to electric guitars using overdriven amplifiers or effects pedals to produce new tones at sub harmonics of the tones being played on the instrument. See Power chord#Analysis . IMD is also distinct from intentional modulation (such as a frequency mixer in superheterodyne receivers ) where signals to be modulated are presented to an intentional nonlinear element ( multiplied ). See non-linear mixers such as mixer diodes and even single- transistor oscillator-mixer circuits. However, while
2000-400: Is a carrier with a frequency of 0 Hz. It is modulated by a microphone ( transmitter ) in the telephone set according to the acoustic signal from the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber. An additional function provided by the carrier in standard AM, but which
2080-448: Is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband ( single-sideband suppressed-carrier transmission ) or with both sidebands remaining ( double sideband suppressed carrier ). While these suppressed carrier transmissions are efficient in terms of transmitter power, they require more sophisticated receivers employing synchronous detection and regeneration of
2160-407: Is a signal of a single frequency, then the output is a signal of the same frequency; only the amplitude and phase can differ from the input signal. 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 , {\displaystyle ~f_{a},} then the output
2240-504: Is a signal which includes a number of integer multiples of the input frequency signal; (i.e. some of f a , 2 f a , 3 f a , 4 f a , … {\displaystyle ~f_{a},2f_{a},3f_{a},4f_{a},\ldots } ). Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider an input signal that contains three frequency components at f
2320-451: Is always positive for undermodulation. If m > 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier c(t) is multiplied by the positive quantity (1 + m(t)/A) : In this simple case m is identical to the modulation index , discussed below. With m = 0.5 the amplitude modulated signal y ( t ) thus corresponds to
2400-456: Is based, heterodyning , and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or "liquid baretter", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector (1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not
2480-412: Is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so
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2560-404: Is shown in the first waveform, below. For m = 1.0 {\displaystyle m=1.0} , it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible signal-to-noise ratio ) but mustn't be exceeded. Increasing
2640-417: Is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio etc.). AM is also inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal contains none of
2720-418: Is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio , say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation
2800-624: Is the result of the two (or more) high power tones mixing at device nonlinearities such as junctions of dissimilar metals or metal-oxide junctions, such as loose corroded connectors. The higher the signal amplitudes, the more pronounced the effect of the nonlinearities, and the more prominent the intermodulation that occurs — even though upon initial inspection, the system would appear to be linear and unable to generate intermodulation. The requirement for "two or more high power tones" need not be discrete tones. Passive intermodulation can also occur between different frequencies (i.e. different "tones") within
2880-465: The envelope of the transmitted waveform. In the frequency domain , amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands . Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" (DSBAM). A disadvantage of all amplitude modulation techniques, not only standard AM,
2960-506: The instantaneous phase deviation ϕ ( t ) {\displaystyle \phi (t)} . This description directly provides the two major groups of modulation, amplitude modulation and angle modulation . In angle modulation, the term A ( t ) is constant and the second term of the equation has a functional relationship to the modulating message signal. Angle modulation provides two methods of modulation, frequency modulation and phase modulation . In amplitude modulation,
3040-425: The intermodulation products (or IMPs ). In general, each of these frequency components will have a different amplitude and phase, which depends on the specific non-linear function being used, and also on the amplitudes and phases of the original input components. More generally, given an input signal containing an arbitrary number N {\displaystyle N} of frequency components f
3120-405: The 20th century beginning with Roberto Landell de Moura and Reginald Fessenden 's radiotelephone experiments in 1900. This original form of AM is sometimes called double-sideband amplitude modulation ( DSBAM ), because the standard method produces sidebands on either side of the carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly
3200-517: The AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However it is absolutely undesired for music or normal broadcast programming, where
3280-487: The angle term is held constant and the first term, A ( t ), of the equation has a functional relationship to the modulating message signal. The modulating message signal may be analog in nature, or it may be a digital signal, in which case the technique is generally called amplitude-shift keying . For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The message signal determines
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3360-411: The background buzz of the spark. Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced sinusoidal continuous waves , was needed. This
3440-401: The bandwidth of an AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inefficient. Within a frequency band, only half as many transmissions (or "channels") can thus be accommodated. For this reason analog television employs a variant of single-sideband (known as vestigial sideband , somewhat of
3520-451: The carrier frequency. For that reason, standard AM continues to be widely used, especially in broadcast transmission, to allow for the use of inexpensive receivers using envelope detection . Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and
3600-454: The carrier frequency. Passing the modulated signal through another nonlinear device can extract the original baseband signal. His analysis also showed that only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW-II, it
3680-400: The carrier itself remains constant, and of greater power than the total sideband power. The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or " baseband ") signal, since the upper and lower sidebands around the carrier frequency each have a bandwidth as wide as the highest modulating frequency. Although
3760-473: The carrier represent a net advantage and are frequently employed. A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing
3840-428: The carrier signal, which improves the ratio of message power to total transmission power , reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium. AM remains in use in many forms of communication in addition to AM broadcasting : shortwave radio , amateur radio , two-way radios , VHF aircraft radio , citizens band radio , and in computer modems in
3920-493: The cell site, installation workmanship issues and by external passive intermodulation sources. Some of these include: IEC 62037 is the international standard for passive intermodulation testing and gives specific details as to passive intermodulation measurement setups. The standard specifies the use of two +43 dBm (20 W) tones for the test signals for passive intermodulation testing. This power level has been used by radio frequency equipment manufacturers for more than
4000-507: The characteristic "Donald Duck" sound from such receivers when slightly detuned. Single-sideband AM is nevertheless used widely in amateur radio and other voice communications because it has power and bandwidth efficiency (cutting the RF bandwidth in half compared to standard AM). On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs
4080-492: The distance to the PIM-source. Anritsu offers a radar-based solution with low accuracy and Heuermann offers a frequency converting vector network analyzer solution with high accuracy. Amplitude modulation Amplitude modulation ( AM ) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave . In amplitude modulation, the amplitude (signal strength) of
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#17327830400624160-444: The extra power cost to greatly increase potential audience. A simple form of digital amplitude modulation which can be used for transmitting binary data is on–off keying , the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. On–off keying is likewise used by radio amateurs to transmit Morse code where it is known as continuous wave (CW) operation, even though
4240-400: The form of QAM . In electronics , telecommunications and mechanics , modulation means varying some aspect of a continuous wave carrier signal with an information-bearing modulation waveform, such as an audio signal which represents sound, or a video signal which represents images. In this sense, the carrier wave, which has a much higher frequency than the message signal, carries
4320-453: 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 in that the stimulus signal is different. The same nonlinear system will produce both total harmonic distortion (with a solitary sine wave input) and IMD (with more complex tones). In music, for instance, IMD
4400-493: The former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation m(t) may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation m(t) having simply been shifted in frequency by f c as depicted at the bottom right of figure 2. The short-term spectrum of modulation, changing as it would for
4480-441: The information. At the receiving station, the message signal is extracted from the modulated carrier by demodulation . In general form, a modulation process of a sinusoidal carrier wave may be described by the following equation: A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency ω {\displaystyle \omega } , and
4560-411: The intermodulation products of the received signal with the local oscillator signal are intended, superheterodyne mixers can, at the same time, also produce unwanted intermodulation effects from strong signals near in frequency to the desired signal that fall within the passband of the receiver. A linear time-invariant system cannot produce intermodulation. If the input of a linear time-invariant system
4640-489: The modulating signal beyond that point, known as overmodulation , causes a standard AM modulator (see below) to fail, as the negative excursions of the wave envelope cannot become less than zero, resulting in distortion ("clipping") of the received modulation. Transmitters typically incorporate a limiter circuit to avoid overmodulation, and/or a compressor circuit (especially for voice communications) in order to still approach 100% modulation for maximum intelligibility above
4720-443: The modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter. So if m = 0.5 {\displaystyle m=0.5} , carrier amplitude varies by 50% above (and below) its unmodulated level, as
4800-409: The modulation index is below 100%. Such systems more often attempt a radical reduction of the carrier level compared to the sidebands (where the useful information is present) to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In all such cases the term "modulation index" loses its value as it refers to the ratio of the modulation amplitude to
4880-534: The next section. High-power AM transmitters (such as those used for AM broadcasting ) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage. Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter's final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors): The simplest form of AM demodulator consists of
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#17327830400624960-542: The noise. Such circuits are sometimes referred to as a vogad . However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of double-sideband reduced-carrier transmission . In that case, negative excursions beyond zero entail a reversal of the carrier phase, as shown in the third waveform below. This cannot be produced using the efficient high-level (output stage) modulation techniques (see below) which are widely used especially in high power broadcast transmitters. Rather,
5040-467: The original information being transmitted (voice, video, data, etc.). However its presence provides a simple means of demodulation using envelope detection , providing a frequency and phase reference to extract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex because they must provide
5120-404: The other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called frequency division multiplexing . In 1915, John Renshaw Carson formulated the first mathematical description of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device creates a sideband on both sides of
5200-489: The overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80's onwards. The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as: where M {\displaystyle M\,} and A {\displaystyle A\,} are
5280-518: The period between 1900 and 1920 of radiotelephone transmission, that is, the effort to send audio signals by radio waves. The first radio transmitters, called spark gap transmitters , transmitted information by wireless telegraphy , using pulses of the carrier wave to spell out text messages in Morse code . They could not transmit audio because the carrier consisted of strings of damped waves , pulses of radio waves that declined to zero, and sounded like
5360-719: The receive signal. The receive signal would therefore be clobbered by the passive intermodulation signal. Ferromagnetic materials are the most common materials to avoid and include ferrites, nickel, (including nickel plating) and steels (including some stainless steels). These materials exhibit hysteresis when exposed to reversing magnetic fields, resulting in PIM generation. Passive intermodulation can also be generated in components with manufacturing or workmanship defects, such as cold or cracked solder joints or poorly made mechanical contacts. If these defects are exposed to high radio frequency currents, passive intermodulation can be generated. As
5440-563: The signal, it is called "transient" intermodulation distortion. Intermodulation distortion in audio is usually specified as the root mean square (RMS) value of the various sum-and-difference signals as a percentage of the original signal's root mean square voltage, although it may be specified in terms of individual component strengths, in decibels , as is common with radio frequency work. Audio system measurements (Audio IMD) include SMPTE standard RP120-1994 where two signals (at 60 Hz and 7 kHz, with 4:1 amplitude ratios) are used for
5520-407: 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 (physical equipment or even algorithms) being used. The theoretical outcome of these non-linearities can be calculated by generating a Volterra series of the characteristic, or more approximately by
5600-943: The sum of these sine waves you will get sine waves at various frequencies including 2 × f 2 − f 1 {\displaystyle 2\times f_{2}-f_{1}} and 2 × f 1 − f 2 {\displaystyle 2\times f_{1}-f_{2}} . If f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} are large but very close together then 2 × f 2 − f 1 {\displaystyle 2\times f_{2}-f_{1}} and 2 × f 1 − f 2 {\displaystyle 2\times f_{1}-f_{2}} will be very close to f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} . As explained in
5680-473: The test; many other standards (such as DIN, CCIF) use other frequencies and amplitude ratios. Opinion varies over the ideal ratio of test frequencies (e.g. 3:4, or almost — but not exactly — 3:1 for example). After feeding the equipment under test with low distortion input sinewaves, the output distortion can be measured by using an electronic filter to remove the original frequencies, or spectral analysis may be made using Fourier transformations in software or
5760-400: The three components, respectively. We obtain our output signal, y ( t ) {\displaystyle \ y(t)} , by passing our input through a non-linear function G {\displaystyle G} : y ( t ) {\displaystyle \ y(t)} will contain the three frequencies of the input signal, f
5840-422: The top graph (labelled "50% Modulation") in figure 4. Using prosthaphaeresis identities , y ( t ) can be shown to be the sum of three sine waves: Therefore, the modulated signal has three components: the carrier wave c(t) which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency f c . A useful modulation signal m(t) is usually more complex than
5920-425: The transmission is not strictly "continuous". A more complex form of AM, quadrature amplitude modulation is now more commonly used with digital data, while making more efficient use of the available bandwidth. A simple form of amplitude modulation is the transmission of speech signals from a traditional analog telephone set using a common battery local loop. The direct current provided by the central office battery
6000-421: The vicinity of the original frequency components, and may therefore interfere with the desired behaviour. For example, intermodulation distortion from the third order ( IMD3 ) of a circuit can be seen by looking at a signal that is made up of two sine waves , one at f 1 {\displaystyle f_{1}} and one at f 2 {\displaystyle f_{2}} . When you cube
6080-411: The wave is varied in proportion to that of the message signal, such as an audio signal . This technique contrasts with angle modulation , in which either the frequency of the carrier wave is varied, as in frequency modulation , or its phase , as in phase modulation . AM was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of
6160-427: Was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn't have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked
6240-475: Was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters – the Alexanderson alternator , with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM
6320-402: Was developed for military aircraft communication. The carrier wave ( sine wave ) of frequency f c and amplitude A is expressed by The message signal, such as an audio signal that is used for modulating the carrier, is m ( t ), and has a frequency f m , much lower than f c : where m is the amplitude sensitivity, M is the amplitude of modulation. If m < 1, (1 + m(t)/A)
6400-652: Was usually accomplished by a carbon microphone inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled. The 1912 discovery of the amplifying ability of the Audion tube , invented in 1906 by Lee de Forest , solved these problems. The vacuum tube feedback oscillator , invented in 1912 by Edwin Armstrong and Alexander Meissner ,
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