Amplitude modulation- the type of modulation, in which the variable parameter of the carrier signal is its amplitude.
Amplitude modulation (AM) is a modulation in which sustained oscillations change in amplitude in accordance with the oscillations of a lower frequency modulating it.
With amplitude modulation (AM), the amplitude of the high-frequency oscillation (carrier) changes according to the law of the modulating (primary) signal.
With AM, the spectrum of the modulating signal is transferred to the carrier frequency region, forming the upper and lower side components of the spectrum. Since this transformation produces new frequencies, the modulation procedure is a non-linear transformation. But since with AM the spectrum of the modulating signal does not change, but only is transferred to the high frequency region, AM is considered a linear type of modulation.
The goal of any modulation is undistorted signal transmission over a given communication line with less interference.
The principles of spectrum transformation with AM are widely used in technology,
for example, in the development of circuits for broadcasting and television receivers, multichannel telephony systems with frequency division multiplexing of communication lines and, in particular, form the basis of a spectrum analyzer device.
Carrier frequency, the frequency of harmonic oscillations subjected to modulation by signals for the purpose of transmitting information. The low-frequency waveform is sometimes referred to as the carrier wave. The vibrations with low frequencies themselves do not contain information, they only "carry" it. The spectrum of modulated oscillations contains, in addition to the LF side frequencies, which contain the transmitted information.
If a signal having a sinusoidal formula is taken as the primary signal, then the amplitude-modulated signal will have the form shown in the figure.
Qualitatively, amplitude modulation (AM) can be defined as the change in carrier amplitude in proportion to the amplitude of the modulating signal.
Harmonic oscillation of high frequency w is modulated in amplitude by harmonic oscillation of low frequency W (t = 1 / W is its period), t is time, A is the amplitude of high-frequency oscillation, T is its period.
Amplitude modulation with a sinusoidal signal, w is the carrier frequency, W is the frequency of modulating oscillations, Amax and Amin are the maximum and minimum values of the amplitude.
For a modulating signal of large amplitude, the corresponding amplitude of the modulated carrier must be large and for small values of the amplitude. This modulation scheme can be implemented by multiplying two signals.
Amplitude modulation depth- the maximum relative deviation of the amplitude from the mean
The spectral density of the modulated signal represents two spectra of the modulating function plotted with respect to the frequencies w = w 0 and w = -w 0 (shifted by the carrier frequency).
Example... Single-tone modulation spectrum
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The radio signal consists of a carrier waveform and two sinusoidal waveforms called sidebands.
With conventional amplitude modulation, information is contained in each of the two sidebands
Carrier signal- a signal, one or several parameters of which are subject to change during modulation. The degree of parameter change is determined by the instantaneous value of the information (modulating) signal.
Any stationary signal can be used as a carrier. Most often, a high-frequency (relative to the information signal) harmonic oscillation is used as a carrier signal, due to the simplicity of demodulation and a narrow spectrum. However, in some cases, it is advisable to use other types of carrier signal, for example, rectangular.
Carrier signal is often referred to simply as carrier(from carrier frequency), or carrier (oscillation). All of these terms mean almost the same thing. In English terminology, a carrier signal is denoted by the word carrier.
The U / U 0 ratio is called the modulation factor mАМ. It is often expressed as a percentage. If U 0> = Umax, then the mАМ coefficient will change from 0 to 1.
Amplitude modulation coefficient(AM coefficient, old modulation depth) - the main characteristic of amplitude modulation - the ratio of the difference between the maximum and minimum values of the amplitudes of the modulated signal to the sum of these values, expressed as a percentage
AM vibrations are the result of the addition of three high-frequency vibrations; oscillations with a frequency f 0 and an amplitude U 0 and two oscillations with frequencies f 0 + F and f 0 - F and an amplitude of 0.5 mA * U 0.
In amplitude modulation (AM) systems, the modulating wave changes the amplitude of the high frequency carrier wave. Analysis of the output frequencies shows the presence of not only the input frequencies f 0 and F, but also their sum and difference: f n + F and f n - F. If the baseband wave is complex, such as a speech signal, which consists of many frequencies, then the sums and differences of the various frequencies will occupy two bands, one below and one above the carrier frequency. The frequencies f n + F and f n - F are called the upper and lower side frequencies, respectively.
Upper side stripe is a copy of the original spoken signal, only shifted by the frequency Fc. The lower band is an inverted copy of the original signal, i.e. the treble in the original is the bass in the lower side.
Lower side stripe it is a mirroring of the upper side of the carrier frequency Fc.
An AM system that transmits both side and carrier is known as double sidebaud (DSB). The carrier carries no useful information and can be removed, but with or without carrier, the DSB signal bandwidth is twice the original signal bandwidth. To narrow the strip, it is possible to displace not only the carrier, but also one of the side ones, since they carry the same information. This type of operation is known as Single SideBand Suppressed Carrier (SSB-SC).
Amplitude modulation of a complex signal
Any transmitting radio station operating in the amplitude modulation mode emits not one frequency, but a whole set (spectrum) of frequencies. In the simplest case (with a sinusoidal signal), this spectrum contains only three components - a carrier and two side ones. If the modulating signal is not sinusoidal, but more complex, then instead of two side frequencies in the modulated oscillation there will be two side bands, the frequency composition of which is determined by the frequency composition of the modulating signal.
Therefore, each transmitting station occupies a certain frequency interval on the air. To avoid interference, the carrier frequencies of the various stations must be separated from each other by a distance greater than the sum of the sidebands. The sideband width depends on the nature of the transmitted signal: for radio broadcasting - 10 kHz, for television - 6 MHz. Based on these values, the interval between the carrier frequencies of different stations is selected. To obtain an amplitude-modulated oscillation, the carrier frequency oscillation and the modulating signal are fed to a special device - a modulator.
Demodulation of the AM signal is achieved by mixing the modulated signal with a carrier of the same frequency as on the modulator.
The original signal is then received as a separate frequency (or bandwidth) and can be filtered from other signals. The carrier for demodulation is generated locally and may not coincide in any way with the carrier frequency on the modulator. The small difference between the two frequencies is the reason for the frequency mismatch that is inherent in telephone circuits.
Due to the amplitude modulation of the complex signal, the data transmission rate increases.
On the panel of any modern radio receiver there is an AM-FM switch. As a rule, an ordinary consumer does not think about what these letters mean, it is enough for him to remember that on FM there is his favorite VHF radio station, broadcasting a signal in stereo sound and with excellent quality, and on AM you can catch "Mayak". If you delve into the technical details at least at the level of the user manual, it turns out that AM is amplitude modulation, and FM is frequency modulation. How are they different?
In order for music to sound from the radio loudspeaker, it must undergo certain changes. First of all, it should be made suitable for broadcasting. Amplitude modulation was the first way communications engineers learned to broadcast speech and music programs over the air. American Fessenden in 1906 with the help of a mechanical generator received oscillations of 50 kilohertz, which became the first carrier frequency in history. Then he solved the technical problem in the simplest way, by installing a microphone at the output of the winding. When exposed to coal powder inside the membrane box, its resistance changed, and the value of the signal coming from the generator to the transmitting antenna decreased or increased depending on them. This is how amplitude modulation was invented, that is, changing the swing of the carrier signal in such a way that the shape of the envelope line corresponded to the shape of the transmitted signal. In the twenties, mechanical generators were superseded by vacuum tubes. This has significantly reduced the size and weight of the transmitters.
It differs from the amplitude one in that the sweep of the carrier wave remains unchanged, its frequency changes. With the development of the electronic base and circuitry, other methods appeared, with the help of which the information signal "sat down" on the frequency of the radio range. Changing the phase and width of the pulse gave the name phase and pulse-width modulation. It seemed that amplitude modulation as a method of broadcasting was outdated. But it turned out differently, it retained its position, albeit in a slightly modified form.
The growing requirements for informational saturation of frequencies prompted engineers to look for ways to increase the number of channels transmitted on one wavelength. The capabilities of multichannel broadcasting are also determined by the Nyquist barrier, however, in addition to quantizing the signal, it became possible to increase the information load by changing the phase. Quadrature amplitude modulation is a transmission method in which different signals are transmitted at the same frequency, which are 90 degrees out of phase with each other. Four-phaseness forms a quadrature or a combination of two components described by the trigonometric functions sin and cos, hence the name.
Quadrature amplitude modulation is widely used in digital communications. At its core, it is a combination of phase and amplitude modulation.
With amplitude modulation, in accordance with the law of the transmitted message, the amplitude of the modulated signal changes. Amplitude modulation is the most common type of analog modulation in radio communication, broadcasting and television systems.
The simplest form of amplitude modulation is single-tone(from the word tone - the sound of one frequency), at which the modulating signal is a harmonic oscillation:
where 
- the amplitude of the modulating signal (maximum height of the sinusoid);
- circular (angular) frequency, 
;
- the period of the modulating oscillation;
- the initial phase.
A high-frequency harmonic signal is almost always used as a carrier wave in communication and broadcasting systems.
Let's take a sinusoidal signal as a test analog message:
(40)
Carriers, i.e. modulated oscillations
(41)
where the frequency of the carrier waves 
- the frequency of the modulating oscillation.
As a result of the influence of the oscillation (40) on the amplitude of the carrier oscillations (41), we obtain a signal with amplitude modulation:
where 
is the amplitude modulation factor.
The graphs of the three named fluctuations are shown in Fig. 13 and fig. 14.
For the sake of clarity, Fig. 15, a,
b the graphs of the modulating oscillation are shown at 
, carrying - at 
.
Amplitude-modulated signal spectrum
From (42) we get the expression:
which, in accordance with the formula for the product of trigonometric functions, we reduce to the form
from which it follows that the spectrum of oscillations with amplitude modulation by a tone signal consists of three components with frequencies: 
(coincides with the carrier frequency), ( 
) (lower side), ( 
) (top side). A 
m lateral component amplitude 
.
Rice. 15. Amplitude modulation
a - modulating (control) signal; b- carrier vibration (radio frequency signal); v- amplitude-modulated signal.
AM spectrum width 
... Therefore, having a base B = 1, the signal with amplitude modulation belongs to the class of narrowband.
When modulating with a more complex message occupying a spectrum from 
before 
(Fig. 16, a), the spectrum of AM oscillations, shown in Fig. 1, will change accordingly. 16, b.
The spectrum of an amplitude-modulated signal is a set of simple (harmonic) oscillations (components) of different frequencies and amplitudes, into which a complex oscillatory process can be decomposed along the frequency axis, i.e. AM signal. An analytical expression for such a signal, taking into account the trigonometric formula of the product of cosines, can be represented as a sum of oscillations:
(45)
From formula (44) it can be seen that with single-tone modulation, the spectrum of the AM signal consists of three high-frequency components: the initial carrier oscillation with the amplitude 
and frequency 
, as well as two new harmonic oscillations with different frequencies 
and 
, but with the same amplitudes 
/2
that appear in the course of amplitude modulation and reflect the transmitted message.
Oscillations with frequencies 
and 
are called respectively the upper and lower side components (frequencies). They are located symmetrically with respect to the carrier frequency. 
.
The spectrum of a single-tone AM signal is shown in Fig. 17. It is clearly seen from the figure that the width of the AM signal spectrum ( 
) with single-tone modulation is equal to the doubled value of the modulation frequency:
(46)
where F is the cyclic modulation frequency (modulating signal).
In the absence of modulation (M = 0), the amplitudes of the side components are equal to zero and the spectrum of the AM signal is converted into the spectrum of the carrier vibration (component 
at frequency 
). In the case of modulating a carrier with a signal of a complex shape, consisting of several harmonics of different frequencies, each harmonic of the modulating (control) signal creates two side frequencies in the spectrum of the radio signal, located symmetrically with respect to the carrier frequency. Consequently, the spectrum of such an AM signal consists of a carrier and two side bands - an upper and a lower one. The width of each side stripe is 
, and the spectrum width of the complex AM signal turns out to be equal to the doubled value of the highest frequency in the spectrum of the modulating signal (Fig. 18).
Amplitude modulation - a type of modulation in which the variable parameter of the carrier signal is its amplitude
The first experience of transmitting speech and music by radio using the amplitude modulation method was made in 1906 by the American engineer R. Fessenden. The carrier frequency of 50 kHz of the radio transmitter was generated by a machine generator (alternator); for its modulation, a carbon microphone was switched on between the generator and the antenna, changing the signal attenuation in the circuit. Since 1920, vacuum tube generators have been used instead of alternators. In the second half of the 1930s, as the development of ultrashort waves, amplitude modulation gradually began to be supplanted from radio broadcasting and radio communication on VHF frequency modulation. Since the middle of the 20th century, single sideband modulation (SSB) has been introduced in service and amateur radio communications at all frequencies, which has a number of important advantages over AM. The question of transferring to the SSB and radio broadcasting was raised, but this would require replacing all broadcasting receivers with more complex and expensive ones, therefore it was not carried out. At the end of the 20th century, the transition to digital broadcasting using amplitude-shift keying signals began.
Audio signal can modulate the amplitude (AM) or frequency (FM) of the carrier. Let S (t) be an information signal, | S (t) |<1, U_c(t) — несущее колебание. Тогда амплитудно-модулированный сигнал U_\text{am}(t) может быть записан следующим образом: U_\text{am}(t)=U_c(t).\qquad\qquad(1) Здесь m — некоторая константа, называемая коэффициентом модуляции. Формула (1) описывает несущий сигнал U_c(t), модулированный по амплитуде сигналом S(t) с коэффициентом модуляции m. Предполагается также, что выполнены условия: |S(t)|<1,\quad 0
For transmission over a distance without wires of speech, music, images, an alternating voltage of high frequency (over 100 kHz) is used, emitted in the space of the antenna of the radio transmitter. To carry out radiotelephone transmission of a signal, the amplitude of the high frequency of the transmitter or its frequency must change according to the law of low (audio) frequency.Amplitude modulation is characterized by the modulation depth coefficient (m), which expresses the ratio of the increase in the amplitude of the high frequency (dUm) to its mean value (Um): m = dUm / Um * 100% In the course of radio transmission, it can vary from 0 to 80 percent - it is impractical to increase it more, since nonlinear distortions of a low frequency signal may appear. If the high frequency modulation is performed with a signal of one low frequency (Fн), then the modulated signal will represent a combination of three frequencies: carrier, upper side and lower side. If the modulation is performed with a whole spectrum of frequencies, then you get a high-frequency spectrum with upper and lower side bands. Therefore, one broadcast radio transmitter occupies a bandwidth of at least 10 kHz in the high-frequency range.
Amplitude modulation is the process of forming an amplitude-modulated signal, i.e. signal, the amplitude of which changes according to the law of the modulating signal (transmitted message). This process is carried out by an amplitude modulator.
The amplitude modulator should form a high-frequency vibration, the analytical expression for which in the general case has the form
where is the envelope of the modulated oscillation, described by a function that characterizes the law of amplitude change;
Modulating signal;
And - the frequency and the initial phase of the high-frequency oscillation.
To obtain such a signal, it is necessary to multiply the high-frequency (carrier) oscillation and the low-frequency modulating signal in such a way that an envelope of the form is formed. The presence of a constant component in the envelope structure ensures unipolarity of its change, the coefficient excludes overmodulation, i.e. provides depth of modulation. It is clear that such a multiplication operation will be accompanied by a transformation of the spectrum, which makes it possible to consider amplitude modulation as an essentially nonlinear or parametric process.
The structure of the amplitude modulator in the case of using a nonlinear element is shown in Fig. 8.4.
Rice. 8.4. Amplitude modulator block diagram
The non-linear element converts the carrier wave and the modulating signal, as a result of which a current (or voltage) is formed, the spectrum of which contains components in the frequency band from to, and is the highest frequency in the spectrum of the modulating signal. A bandpass filter separates these components of the spectrum, forming an amplitude-modulated signal at the output.
Multiplication of two signals can be performed using a non-linear element, the characteristic of which is approximated by a polynomial containing a quadratic term. Due to this, the square of the sum of the two signals is formed, containing their product.
The essence of what has been said and the general idea of the formation of an amplitude-modulated oscillation are illustrated by rather simple mathematical transformations under the assumption that tonal (one frequency) modulation is carried out.
1. As a nonlinear element, we use a transistor, the I – V characteristic of which is approximated by a polynomial of the second degree 
.
2. The input of the nonlinear element is supplied with a voltage equal to the sum of two oscillations: carrier and modulating, i.e.
3. The spectral composition of the current is determined as follows:
In the expression obtained, the spectral components are arranged in ascending order of their frequencies. Among them there are components with frequencies, and, which form an amplitude-modulated oscillation, i.e.
Transmitting devices usually combine modulation and amplification processes, which ensures minimal distortion of modulated signals. For this purpose, amplitude modulators are built according to the scheme of resonant power amplifiers, in which a change in the amplitude of high-frequency oscillations is achieved by changing the position of the operating point according to the law of the modulating signal.
Amplitude modulator circuit and operating modes
The diagram of an amplitude modulator based on a resonant amplifier is shown in Fig. 8.5.
Rice. 8.5. Amplitude modulator circuit based on a resonant amplifier
To the input of a resonant amplifier operating in a nonlinear mode, the following are fed:
carrier oscillation from an auto-generator using high-frequency transformer connection of the input circuit circuit with the base of the transistor;
modulating signal using a low-frequency transformer.
Capacitors and - blocking, provide decoupling of the input circuits at the frequencies of the carrier oscillation and the modulating signal, i.e. decoupling at high and low frequencies. The oscillatory circuit in the collector circuit is tuned to the frequency of the carrier oscillation, the Q-factor of the circuit provides the bandwidth, where is the highest frequency in the spectrum of the modulating signal.
The operating mode of the modulator is determined by the choice of the operating point. Two modes are available: small signal mode and large signal mode.
a. Small input mode
This mode is set by choosing the operating point in the middle of the quadratic section of the I - V characteristic of the transistor. The choice of the amplitude of the carrier oscillation ensures the operation of the modulator within this section (Fig. 8.6).
Rice. 8.6. Amplitude modulator small input mode
The amplitude of the voltage on the oscillatory circuit, the resonant frequency of which is equal to the carrier frequency, is determined by the amplitude of the first harmonic of the current, i.e. , where is the resonant resistance of the circuit. Considering that the average slope of the I - V characteristic within the working section is equal to the ratio of the amplitude of the first harmonic to the amplitude of the carrier vibration, i.e. 
, you can write
.
Under the influence of the modulating voltage applied to the base of the transistor, the position of the operating point will change, which means that the average slope of the I – V characteristic will also change. Since the amplitude of the voltage on the oscillatory circuit is proportional to the average slope, then to ensure the amplitude modulation of the carrier wave, it is necessary to provide a linear dependence of the slope on the modulating signal. Let us show that this is possible when using the working section of the I – V characteristic approximated by a polynomial of the second degree.
So, within the quadratic section of the I - V characteristic, described by a polynomial, there is an input voltage equal to the sum of two oscillations: the carrier and modulating, i.e.
The spectral composition of the collector current is determined as follows:
We select the first harmonic of the current:
Thus, the amplitude of the first harmonic is:
As can be seen from the obtained expression, the amplitude of the first harmonic of the current linearly depends on the modulating voltage. Therefore, the average slope will also be linear with the modulating voltage.
Then the voltage on the oscillatory circuit will be equal to:
Therefore, at the output of the modulator under consideration, an amplitude-modulated signal of the form is formed:
Here is the modulation depth coefficient;
- the amplitude of the high-frequency oscillation at the output of the modulator in the absence of modulation, i.e. at .
When designing transmission systems, an important requirement is the formation of high-power amplitude-modulated oscillations with sufficient efficiency. It is obvious that the considered mode of operation of the modulator cannot meet these requirements, especially the first of them. Therefore, the so-called large signal mode is most often used.
b. Large input mode
This mode is set by choosing the operating point on the I - V characteristic of the transistor, at which the amplifier operates with current cutoff. In turn, the choice of the amplitude of the carrier oscillation ensures the change in the amplitude of the collector current pulses according to the law of the modulating signal (Fig. 8.7). This leads to a similar change in the amplitude of the first harmonic of the collector current and, consequently, to a change in the voltage amplitude on the oscillatory circuit of the modulator, since
and .
Rice. 8.7. Amplitude modulator large input mode
The change in the amplitude of the input high-frequency voltage over time is accompanied by a change in the cutoff angle, and hence the coefficient. Consequently, the shape of the voltage envelope on the circuit may differ from the shape of the modulating signal, which is a disadvantage of the considered modulation method. To ensure minimal distortion, it is necessary to set certain limits for changing the cutoff angle and work with a not too high modulation factor.
In the amplitude modulator circuit shown in Fig. 8.8, the modulating signal is applied to the base of the constant current generator transistor. The value of this current is proportional to the input voltage. At small values of input voltages, the amplitude of the output voltage will depend on the modulating signal as follows
where are the proportionality coefficients.
Amplitude modulator characteristics
To select the operating mode of the modulator and assess the quality of its operation, various characteristics are used, the main of which are: static modulation characteristic, dynamic modulation characteristic and frequency response.
Rice. 8.8. Amplitude modulator circuit with current generator
a. Static modulation characteristic
Static modulation characteristic (CMX) is the dependence of the amplitude of the output voltage of the modulator on the bias voltage at a constant amplitude of the carrier voltage at the input, i.e. 
.
In the experimental determination of the static modulation characteristic, only the carrier frequency voltage is applied to the modulator input (the modulating signal is not supplied), the value changes (as if the change in the modulating signal in static is simulated), and the change in the amplitude of the carrier oscillation at the output is recorded. The type of characteristic (Fig. 8.9, a) is determined by the dynamics of the change in the average slope of the I – V characteristic when the bias voltage is changed. The linear increasing section of the CMX corresponds to the quadratic section of the I - V characteristic, since in this section, with an increase in the bias voltage, the average steepness increases. The horizontal section of the CMX corresponds to the linear section of the I - V characteristic, i.e. a section with a constant average steepness. When the transistor enters the saturation mode, a horizontal section of the I - V characteristic with zero slope appears, which is reflected by the decrease in the CMX
The static modulation characteristic allows you to determine the magnitude of the offset voltage and the acceptable range of the modulating signal in order to ensure its linear dependence on the output voltage. The modulator should operate within the linear section of the CMX. The value of the bias voltage should correspond to the middle of the linear section, and the maximum value of the modulating signal should not go beyond the limits of the linear section of the CMX. You can also define the maximum modulation factor at which there is no distortion yet. Its value is 
.
Rice. 8.9. Amplitude modulator characteristics
b. Dynamic modulation response
Dynamic modulation characteristic (DMX) is the dependence of the modulation factor on the amplitude of the modulating signal, i.e. ... This characteristic can be obtained experimentally, or by the static modulation characteristic. The DMX type is shown in Fig. 8.9, b. The linear section of the characteristic corresponds to the operation of the modulator within the linear section of the CMX.
v. Frequency response
Frequency response is the dependence of the modulation factor on the frequency of the modulating signal, i.e. ... The influence of the input transformer leads to a drop in characteristics at low frequencies (Fig. 8.9, c). With an increase in the frequency of the modulating signal, the side components of the amplitude-modulated oscillation move away from the carrier frequency. This leads to their less amplification due to the selective properties of the oscillatory circuit, which causes a drop in characteristics at higher frequencies. If the bandwidth occupied by the modulating signal is within the horizontal section of the frequency response, then modulation distortion will be minimal.
Balanced amplitude modulator
For efficient use of transmitter power, balanced amplitude modulation is used. In this case, an amplitude-modulated signal is formed, in the spectrum of which there is no component at the carrier frequency.
A balanced modulator circuit (Figure 8.10) is a combination of two typical amplitude modulator circuits with specific connections to their inputs and outputs. The inputs on the frequency of the carrier are connected in parallel, and the outputs are connected with inversion relative to each other, forming a difference in output voltages. The modulating signal is applied to the modulators in antiphase. As a result, at the outputs of the modulators we have
And, and at the output of the balanced modulator
Rice. 8.10. Balanced amplitude modulator circuit
Thus, the spectrum of the output signal contains components with frequencies and. There is no component with the carrier frequency.
