Amplitude modulation: definition, graphs, diagrams, formulas. Carrier modulation and transmission noise immunity Energy characteristics of the AM signal

Amplitude-modulated oscillations are described by the expression u(t) = U(t)cos(2nf 0 t + fo). Let us assume that the initial phase of the carrier oscillation is zero (φ 0 = 0), and the modulating message has the form of a harmonic oscillation s(/) = UQcosQt with amplitude?/n, frequency Q = 2nF M and zero initial phase.

With undistorted modulation

Where and they say- amplitude value in silent mode, i.e. at $(/) = = 0; A - scale factor; |C/(/)| ? 1.

With tonal (harmonic) modulation, the radio signal is recorded in the form

Where T- modulation coefficient (depth) (T = oUq/U^); for undistorted harmonic AM it is necessary to have T

The amplitude spectrum of the AM signal has even symmetry relative to the carrier frequency, while the phase spectrum has odd symmetry relative to the initial phase of the carrier oscillation. The modulation components of the modulated signal spectrum are symmetrical in the same sidebands in the vicinity of the frequency

During the process of changing the amplitude, the period of the modulating frequency F M significantly longer than the period of the carrier frequency, therefore the following modes of operation of the modulated cascade are considered: silence, maximum, minimum and modulation.

IN silent mode there is no amplitude modulation and U(t) = U0.

IN maximum mode vibration amplitude Umax = (1 + T)?/ they say, and the maximum power is (1 + t) 2 times the power in silent mode: Pmax = (1 + t) 2 R" 0L.

IN minimum mode vibration amplitude Umin= (1 - a minimum power Pmin = (1 - t) 2 R MOL.

IN modulation mode the amplitude of oscillations changes according to a harmonic law; instantaneous power varies proportionally to the square of the modulating voltage: P(t) = (1 + + mcosCU) 2 P u average power over the modulation period R MOD = = (1 + t 2 /2)P mol. At 100% modulation R max= 4 R mol; R t1P= 0; People = (3/2 )P mol.

If the spectrum of the information signal s(t) uniformly distributed in the frequency band then when T= 100% spectral

The power density of an AM signal occupies sidebands located symmetrically around the carrier frequency, as shown in Fig. 1.6. The frequency band occupied by the PSD signal from AM is 2 Fb. At T= 100% half of the high-frequency power of the modulated signal is concentrated in the discrete spectral component of the carrier frequency R say, and the remaining part is in two side stripes, according to R nol /4 in each.

Rice. 1.6. Power spectrum of AM oscillations with a baseband signal in the frequency band F H ...F B

With pulse amplitude modulation, the main parameters of the radio signal are u(t) are the carrier frequency //, the duration of the radio pulse envelope t and, the repetition period T p and the initial phase of high-frequency filling of the fn pulse sequence. The amplitude Fourier spectrum of a periodic sequence of radio pulses consists (Fig. 1.7) of discrete spectral components, following at intervals in frequency Fn = /Т„. Its envelope A(f) is symmetrical with respect to the carrier frequency and varies according to the law

Where x = l(/-/ 0)t„/G„.

Between the first zeros of the main lobe of the amplitude spectrum, the frequency interval is 2/t, and they are located symmetrically relative to the frequency f-J q.

If radio pulses are formed by periodic manipulation of the amplitude of a continuous harmonic oscillation with an unstable carrier frequency, then the initial phases of the radio pulses fluctuate. Therefore, the frequencies of the discrete components of the spectrum of the sequence are symmetrical relative to the carrier frequency Uo. If the source of the manipulation signal imposes the same initial phase

Rice. 1.7. Amplitude spectrum of a sequence of radio pulses with a rectangular envelope at repetition rate Fn = 10 MHz and high-frequency fill frequency^ = 100 MHz

is used in the harmonic generator when forming a grid of simultaneously existing stable frequencies.

With angular modulation, the amplitude of the radio signal is constant: U = = U0. The difference between phase and frequency modulations is manifested only in the law of correspondence between the message $(/) and changes in the phase f(/) of the radio signal: with FM cp(/) = as(t), and during the World Cup

If the input modulating signal has a harmonic form s(0 = U n cos Q/, then with undistorted phase modulation the radio signal has the form

Where t 9- phase modulation index.

The phase modulation index is determined by the formula

where is the slope of the modulation characteristic of the phase modulator.

The phase modulation index represents the amplitude (half peak-to-peak) of the phase deviation of a harmonic modulating signal. The frequency of a signal with tonal phase modulation changes according to the law /(/) = 7о - m v QsinQ/.

If undistorted frequency modulation is performed with the same harmonic signal, then the frequency-modulated radio signal has the form

Where T c - frequency modulation index.

The frequency modulation index is determined by the formula

where is the slope of the modulation characteristic of the frequency modulator.

The frequency modulation index is the ratio of the deviation of the carrier frequency of the frequency-modulated signal Dso to the modulation frequency Q: t sh= Dso/P.

An FM signal according to law (1.4) can be represented as a Fourier series for discrete components of the amplitude spectrum:

Where Jn (mJ - Bessel functions of the first kind of order P from argument t and J_(mJ =

Thus, the amplitude spectrum of a Fourier signal with tone angle modulation has a discrete component at the carrier frequency with an amplitude U Q J 0 (mJ, and the side bands are composed of symmetrically located discrete components at frequencies from 0 ± lP, and their amplitudes UoJ„(mJ are proportional to the values ​​of the Bessel functions of the corresponding number P.

If the World Cup index is small (T"" 1), then J 0 (mJ *1, J(mJ * mJ2,Jn(mJ* 0 for P> 2. In this case, the amplitude spectrum of the frequency-modulated signal has two side components located symmetrically relative to the carrier frequency, as in AM. The difference compared to the spectrum of an amplitude-modulated signal is only that the phase of the component at frequency с0 + П is opposite to the phase of the component at frequency со - П.

If the FM index is not small, then the frequency band occupied by the |S U (/)I spectrum increases. In Fig. Figure 1.8 shows the spectrum of a frequency-modulated signal with a modulation index = 5. From this figure it can be seen that the components at the carrier frequency and at frequencies symmetrical to it f 0 ± nF M may have different values ​​in accordance with the values ​​of the functions, but with large detunings from the carrier frequency, amounting to approximately p > t w, they decrease monotonically. If You " 1, then the doubled spectrum width (occupied frequency band) can be estimated by the empirical relation

Angular modulation leads to the appearance of unwanted out-of-band modulations outside the occupied frequency band.

Rice. 1.8. Amplitude spectrum of a signal with harmonic FM at a carrier frequency/ 0 = 100 MHz, modulation frequencyF 4 = 1 MHz and frequency modulation indext s = 5

Rice. 1.9. Message waveforms(t ) and high-frequency FM-2 signal m(/)

emission (VMI): amplitude spectrum for tonal (harmonic) FM with t sh»1 decreases by approximately 30 dB if the detuning from the carrier frequency is 2 times the occupied FM frequency band.

A signal with two-level phase shift keying FM-2 is characterized by abrupt changes in phase by ±n/2 relative to the phase of the carrier oscillation at the moments when the logical level of the transmitted symbol s(/) changes (Fig. 1.9). In FM-2 signal modulators, measures are taken to ensure that the manipulation moments correspond to transitions of the instantaneous value of the output signal u(t) through zero, since there are no jumps in the instantaneous value of the signal u(t) reduces the level of IUI.

The envelope of the amplitude spectrum of FM-2 radio signals is shown in Fig. 1.10. It has a petal structure. The width of the main lobe, approximately equal to the required bandwidth of the digital communication line, is:

where t is the duration of the elementary pulse.

Outside the occupied frequency band, the VMI level decreases: the level of the first side lobe is 13.2 dB below the main level, the level of the second side lobe is by 22 dB, and the maxima of the far lobes decrease by 6 dB for every 2/t detuning from the carrier frequency.

To reduce the level of VMI and reduce interference in adjacent frequency bands, frequency filters are used that are configured to pass the minimum required frequency band. However, changing the phase of the input oscillation to the opposite one with PM-2 (phase manipulation by i) causes amplitude dips to zero at the output of such a filter at times that are delayed relative to the moment of manipulation by the circuit time constant T k(Fig. 1.11). The reason for this is the imposition of damping

Rice. 1.10. Envelope of the amplitude spectrum of FM-2 radio signals (curve1) and MFM (curve2) at the same transmission speed

a falling oscillation with the phase of the preceding and a rising oscillation with the phase of the current subpulse. The duration of such amplitude variations is the reciprocal of the filter passband.

When using signals with multi-level phase keying (PM-LO), the depth of amplitude modulation at the filter output depends on the combination of phases of the previous and subsequent subpulses. Amplitude dips to zero at the output of a bandpass filter can also appear if, with random alternation of transmitted symbols, the next level phase will differ from the previous one by the amount L. Methods have been developed to eliminate such situations (see Chapter 6).

Modern mobile communication systems use signals with minimum frequency shift keying (MFM) without phase break. The minimum frequency deviation for an MFM type signal is 2 times

Rice. 1.11. Amplitude modulation of the PM-2 signal at the output of a first-order bandpass filter with a P PM-2 band

Rice. 1.12. Oscillogram of a frequency-shift keyed signalu(t) with continuous phase

less than the transmission bit rate. An example of an oscillogram of such a signal is shown in Fig. 1.12, the operation of the modulator is discussed in Chapter. 6. VMI level for the MFM signal (see Fig. 1.10, curve 2) decreases outside the main modulation spectrum much faster than for FM-2.

Frequency manipulation, even with continuous phase, leads to unwanted amplitude changes at the filter output. An example of an oscillogram of a frequency-shift keyed signal with a continuous phase at the output of a bandpass filter is shown in Fig. 1.13.

In addition to the classical types of modulation - only amplitude and only angular - combined types of modulation are used: balanced modulation (BM) and BBP modulation.

Rice. 1.13.

With BM, compared to conventional amplitude modulation, the carrier frequency is completely suppressed, and frequencies symmetrical with respect to frequency f 0 the side stripes remain. If modulating

hesitation to submit next to Fourier i, where

F u- the lower frequency of the spectrum of modulating frequencies, then the signal with balanced modulation can be written in the form

Balanced modulation is carried out by multiplying the instantaneous values ​​of the modulating and carrier oscillations. The advantage of balanced modulation is the reduction of the total electromagnetic power by suppressing the power of the carrier wave. The occupied frequency band coincides with the band occupied by the amplitude-modulated oscillation and is determined by the upper limit frequency of the modulating frequency spectrum:

OBP modulation differs in that not only the spectral component of the carrier frequency is suppressed, but also one of the sidebands. The output signal when modulating the OBP can be written in the form

if the top sidebar is selected. If the bottom sidebar is selected, the “+” sign in parentheses is replaced with a “-” sign. Sometimes this type of modulation is called single-sideband amplitude modulation, or modulation with suppression of the mirror channel and carrier. The circuitry implementation of OBP modulation is based on multiplying the modulating signal $(/) with the carrier oscillation u 0 (t) in four mixers, the reference oscillations of which differ in phase shift by 0, 90, 180 and 270 e. In the direct order of phase alternation, after pairwise summation of the output oscillations of the channels, compensation of the upper band and carrier oscillation is obtained, and in the reverse order, the lower sideband and carrier oscillation are compensated .

The frequency band occupied by a signal with OBP modulation is 2 times less than with AM and is equal to the modulating frequency band: Pobp = F B - F H .

OBP modulation is widely used in transceiver signal generation and processing equipment to convert the bandpass spectrum up or down with improved filtering due to suppression of the mirror band without a frequency filter. Mixers and modulators with mirror channel suppression are discussed in more detail in subsection. 3.4 and 6.4.

The use of OBP modulation for transmitting information over a radio channel leads to reproduction errors when the carrier frequency value is not accurately restored at the receiving end, as a result of which all values ​​of the frequency of the modulating signal receive the same absolute offset. Therefore, in such cases, the remainder of the carrier vibration is partially retained at a level of 5... 10% of the total.

To transmit information in radio engineering, radio waves are used - high-frequency electromagnetic oscillations, which can be effectively emitted using antenna devices and which can propagate in space.

The transmitted information must be embedded in a high-frequency (carrier) oscillation in one way or another. This is done using modulation. Modulation is the change in the parameters of a carrier wave according to the law of the transmitted message. Modulation, as a rule, does not affect the ability of high-frequency oscillations to propagate in space.

In the most general case, a modulated signal can be represented as an oscillation:

a (t)=A m (t) cos [ωt+ψ (t)]=A m (t) cos θ (t), (15.37)

in which the amplitude A t or the phase φ changes according to the law of the transmitted message.

If A t and ψ are constant values, then this expression describes a simple harmonic carrier vibration that does not contain any information.

Depending on which of the two parameters changes - the amplitude A t or angle θ - there are two main types of modulation: amplitude and angular.

Angle modulation is in turn divided into frequency and phase modulation. These two types of modulation are closely related to each other; the difference between them is manifested only in the characteristics

the change in time of the angle θ under the same modulation law.

For most signals used in radio engineering, it is characteristic that during modulation the parameters of the radio signal change so slowly that within one period of high-frequency oscillation it can be considered sinusoidal. Therefore the functions A m (t), ψ(t), θ(t) can be considered slowly varying functions of time.

Modulated oscillations are generally not periodic and are classified as quasi-harmonic, almost periodic functions. Such functions can be expanded into a trigonometric series and presented as a sum of harmonic components, the frequencies of which in the general case are not multiples; they represent combinations of frequencies and are called combinational. In contrast to such a series, the Fourier series contains harmonic components with multiple frequencies.

The works of L. I. Mandelstam, P. D. Papaleksi, M. V. Shuleikin, V. I. Siforov, I. S. Gonorovsky and other Soviet scientists played a major role in the development of the theory of modulated oscillations. In its most complete form, a rigorous mathematical formulation of the basic properties of modulated oscillations and unified methods for their study was first given in S. M. Rytov’s monograph “Modulated oscillations and waves” (1940).

Amplitude modulation (AM) is one of the simplest and widely used due to its ease of implementation and use. With AM, the amplitude of the carrier vibration is a function of time of the form

A m (t) = A m 0 (l+F(t)],(15.38)

where A m 0 is a constant equal to the average amplitude;

F(t)- a function of time that changes according to the same law as the modulating signal, and is called the modulation function.

Methods for implementing AM are usually based on changing the potentials of electronic devices included in the radio transmitting device. In the simplest case, an amplitude-modulated (AM) current oscillation can be obtained in a circuit with a changing resistance to which a high-frequency voltage is applied, and the law of change is determined by the modulation function. A similar variable impedance could be, for example, a carbon microphone.

Analytically, AM oscillations are determined by an expression of the form

α(t) = A m0 cos( t+ ). (15.39)

With harmonic (single-tone) modulation, when

F(t)=mcos (Ω t+ φ 0), (15.40)

for AM oscillations we get

Where T- modulation coefficient;

Ω - modulation frequency.

Modulation factor T proportional to the intensity of the transmitted signal, it is also called the modulation depth. When the amplitude of AM oscillations does not take negative values. Such modulation is called undistorted (Fig. 15.14, a). At m>1 values Am(t) at some time intervals they become negative (Fig. 15.14.6), which leads to overmodulation associated with distortion of the oscillation envelope. To avoid this, the modulation coefficient is chosen to be no more than one.

With undistorted modulation, the amplitude of the AM oscillation varies from A t min = A mo (1 - T) up to A mmax =A mo (1 + m). In this case, the modulation coefficient can be found as the ratio of the maximum increment ΔA t amplitude of oscillations to its average value A m0:

It should be noted that even when modulated by the simplest harmonic signal, the AM oscillation is a complex signal consisting of a number of harmonic components . This feature was established back in 1913 . Moscow professor N.N. . Andreev, and then studied in detail in the works of M . V. Shuleikina (1916) . Nevertheless, at one time (1930), the American scientist Fleming raised a discussion about the “reality” of additional harmonic components in AM oscillations with far-reaching practical conclusions. He argued that the temporal representation of the AM oscillation (15.39) reflects the real situation, and its spectral representation is a mathematical fiction. According to Fleming, in reality there are no additional frequencies, only the carrier frequency is real, and therefore the width of the AM spectrum is infinitely small and accurate signal reproduction is possible with an arbitrarily small bandwidth of the receiver tuned exactly to the carrier frequency. From this the conclusion was drawn about the possibility of limitless densification of the ether.

At present, there is no doubt about the validity of the spectral representation, and Fleming's final conclusion seems naive. For commonly used constant parameter filters, the harmonic spectrum of the AM signal is no less real than its temporal representation. The spectrum can be observed and examined using spectrum analyzers.

As follows from formula (15.41), with harmonic (single-tone) amplitude modulation

The first term here represents the carrier vibration with frequency ω n. The second and third terms correspond to new harmonic components appearing in the process of amplitude modulation. They are a product of modulation and are called side harmonics. The frequencies of these oscillations (ω n + Ω) and (ω n -Ω) are called side frequencies: upper and lower side frequencies, respectively. The amplitudes of these components are the same and depend on the modulation depth ( rice. 15.15,a), and their phases are symmetrical relative to the phase of the carrier vibration. The lower the coefficient T, the smaller the amplitude of the side components, and in the limit at T=0 they are missing.

If the modulating signal is complex

then each of its harmonic components gives a pair of side frequencies:

The result is a spectrum consisting of two frequency bands located symmetrically relative to the carrier frequency ω n. These frequency bands, located on both sides of the carrier, are called sidebands: upper and lower sideband (Fig. 15.15.6).

Comparing the spectra of the modulating signal (modulating function) and the corresponding AM vibration, we can conclude that the spectrum of the upper sideband of the AM vibration is similar to the spectrum of the modulating signal. The only difference is that it is shifted along the frequency axis by an amount ω n. With AM, only the spectrum of the modulating signal is transformed along the frequency axis.

If the frequency band of the modulating signal is limited above by the maximum frequency ymax, then the corresponding AM signal will have a spectrum (see Fig. 15.15.6), the width of which is twice as large:

For TV signals, e.g. MHz MHz.

When several radio transmitting devices operate simultaneously in this frequency range, in order to avoid interference during reception due to overlap, it is necessary that the carrier frequencies of the nearest (on the frequency scale) stations be separated from each other by at least .

The rather wide frequency range occupied by AM signals is a disadvantage of this type of modulation. Other serious disadvantages of AM include poor noise immunity And low efficiency of radio transmitters. These disadvantages are eliminated or significantly reduced with other types of modulation, in particular with angular modulation.

A special case of AM oscillations is a sequence of coherent rectangular radio pulses (Fig. 15.11). Such fluctuations are called manipulated. A distinction is made between amplitude-, phase- and frequency-shift keyed signals, respectively.

"Amplitude modulation" is the change in the amplitude of the carrier signal in accordance with the modulated oscillation. For example, we have a high-frequency carrier oscillation (Formula) and a primary signal (Formula), where U0 is a constant component. The resulting amplitude-modulated signal is obtained by multiplying the carrier wave and the primary signal:

Let x(t) be a harmonic oscillation with frequency Ω, i.e. x(t) = XcosΩt. Then (Formula). Here x(t) is a slowly varying function in time compared to the high-frequency oscillation ω0, i.e. Ω<< ω0.

Let us introduce the following notation:

- maximum increment of the envelope amplitude.

Time diagrams illustrating the process of amplitude modulation by tonal vibration are shown in Fig. 4.1.

Rice. 4.1. Timing diagrams illustrating amplitude modulation:
a - primary signal; b - high-frequency carrier vibration; c - modulated signal

The modulation coefficient is the ratio of the amplitude (Formula) of the envelope to the amplitude (Formula) of the carrier vibration, i.e. (Formula). Usually 0< m < 1.

Modulation depth is the modulation coefficient expressed as a percentage. Therefore, we can write

Let us expand this expression, which will allow us to determine the spectrum of the AM signal:

From this expression it is clear that the AM vibration, the spectrum of which when modulated by one harmonic signal is shown in Fig. 4.2 contains three components.

• oscillation of the carrier frequency ω0 with amplitude U0;
• oscillations of the upper side frequency ω0 + Ω with amplitude (Formula);
• oscillations of the lower side frequency ω0 − Ω s (Formula).

From the above, the following conclusions can be drawn.

1. The spectrum width is equal to twice the modulation frequency Δω = 2Ω.
2. The amplitude of the carrier oscillation does not change during modulation, and the amplitudes of the oscillations of the side frequencies are proportional to the modulation depth, i.e. amplitude of the modulating signal.
3. At m = 1, the amplitudes of the side-frequency oscillations are equal to half the amplitude of the carrier oscillation, i.e. (Formula). At m = 0 there are no side frequencies, which corresponds to an unmodulated oscillation.

In practice, single-tone AM signals are used extremely rarely. A more realistic case is when the low-frequency modulated signal has a complex spectral composition:

Here the frequencies (Formula) form an ordered increasing sequence (Formula), and the amplitudes Xk and phases φk are arbitrary.

In this case, the following analytical relationship can be written for the AM signal:

where (Formula) are partial modulation coefficients, which are the modulation coefficients of the corresponding components of the primary signal.

Rice. 4.2. Spectrum of oscillations during amplitude modulation by one low-frequency harmonic signal

Spectral decomposition is performed in the same way as for a single-tone AM signal:

From this decomposition it is clear that the spectrum, in addition to the carrier vibration, contains groups of upper and lower lateral vibrations. In this case, the spectrum of the upper lateral oscillations is a copy of the spectrum of the modulating signal, shifted to the high frequency region by the value ω0, and the spectrum of the lower lateral oscillations is mirrored relative to ω0.

The spectra of the original bandpass signal and the amplitude-modulated signal are shown in Fig. 4.3.

Let us determine the power of the AM oscillation, for which we again consider the case of modulation of one harmonic. We will assume that ω0 >> Ω. In this case, the amplitude U(t) = U0(1 + mcosΩt) during the period of high-frequency oscillation practically does not change, so the average power released at a resistance of 1 Ohm during this time.

Rice. 4.3. Spectra of the original bandpass (a) and amplitude-modulated (b) signals

From this formula it is clear that if m ≈ 1, at Ωt = 0 power (Formula), and at Ωt = π power (Formula).

Thus, with 100% modulation, when m = 1, the power of the AM oscillation varies within .

Let us now find the average power value for the low frequency period. In this case, the average power of the entire AM oscillation is the sum of the powers of the carrier frequency and two side frequencies - lower and upper, therefore, with a load resistance of 1 Ohm, the average power of the carrier frequency

and each of the side components has a power
Now it is easy to obtain the total AM signal power over the low frequency oscillation period Ω:

From this formula it is clear that with 100% modulation, 66.6% of the total power emitted by the transmitter is spent on transmitting the carrier frequency and only 33.3% of the power is accounted for by both oscillations of the side frequencies, which contain useful information.

Therefore, for more efficient use of transmitter power, it is advisable to transmit a modulated signal without oscillating the carrier frequency. In addition, to reduce the spectral width occupied by the signal, it is desirable to transmit only one of the sidebands, since both sidebands contain the same information.

The carrier oscillation (CV) recovery system of demodulators of bandpass digital modulation signals is designed to generate a reference harmonic oscillation, the phase of which coincides with the phase of the carrier on the basis of which the demodulated signal is formed.

Already in the 30s of the last century, it became clear that FM-2 signals have the highest noise immunity. To use these signals in transmission systems, it was necessary to solve the problem of restoring the carrier (reference) oscillation in the demodulator, which is necessary for the operation of a synchronous detector. In those years it was proposed carrier oscillation recovery circuit with frequency multiplication by 2 (Fig. 13.1).

In the case of FM-2. Odds a i specified by the signal constellation (Fig. 11.1). Channel symbols:

“Weakly” filtered pulses have been used for many decades A(t), which were close in shape to the P-pulse over an interval of duration T

(13.2)

After multiplying the frequency by 2, as a signal s 1 (t), and the signal s 0 (t) give . A notch filter has a middle passband frequency of 2 f 0 . It is designed to reduce interference. A frequency divider by 2 can produce one of two possible reference oscillations:

Case 1:

Case 2:

Both oscillations are possible, since the result depends on the initial conditions in the divider circuit. The reference vibration is said to have phase uncertainty about 180°.

In case 1, an algorithm for optimal signal demodulation is implemented
FM-2. In case 2, the output of the multiplier, and then the matched filter and sampler, will have voltages opposite to those in case 1. The decision circuit will make inverse decisions: instead of 1, it produces 0 and vice versa. This phenomenon is called inverse (reverse) demodulator robot. It turned out that during the operation of the demodulator, random jump-like transitions from the oscillation u op1 ( t) to oscillation u op2 ( t) and vice versa.

In the FM-4 signal demodulator it is necessary to use a frequency multiplier by 4, a filter with an average passband frequency of 4 f 0 and a frequency divider by 4. After the frequency divider, one of the reference oscillations occurs, which differ in phase in increments of 90°. There is an uncertainty in the phase of the reference vibration of the order of 90°.

It is possible to eliminate the manifestation of uncertainty in the phase of the reference oscillation in the demodulator by using difference (relative) coding. Such transmission methods are called phase-difference (relative phase) modulation.

The VN system with exponentiation is discussed above. However, it works well when the pulse amplitude A(t) is close to a rectangular shape. Nowadays Nyquist pulses are used - pulses with a significantly smoothed shape A(t). With this pulse shape, the VN system with exponentiation does not work well.

The reference oscillation is necessary for the operation of a synchronous detector (Fig. 13.2). Let the FM-2 signal arrive at the detector input. The channel symbol is described

If the oscillation phase from the generator

differs from the carrier phase of the input signal by the amount Dj, then the signal at the output of the synchronous detector receives the multiplier cosDj:

Since the maximum cosine value is equal to unity and is achieved only in the case of Dj = 0, the presence of a phase difference leads to a decrease in the signal level at the detector output. If Dj = p/2, then there is no signal at the output of the detector at all: .

Nowadays the HV system is phase automatic frequency control system(PLL) (Fig. 13.3) with a special phase error detector, which is capable of operating in the absence of a carrier in the signal spectrum. Here the VCO is a voltage controlled oscillator. When a phase error voltage e appears, this voltage adjusts the frequency and phase of the oscillation produced by the VCO so as to reduce the magnitude of the phase error.

Let's consider the construction of a phase error detector in the case of an PM-2 signal. The detector circuit contains one more additional synchronous detector, the reference vibration of which is . Recall that the operation of a synchronous detector can be considered as calculating the projection s(t) on u op ( t). The two synchronous detectors feature reference oscillations that are 90° out of phase. Therefore, the voltages obtained from the outputs of synchronous detectors are quadrature components of the detected signal.

In Fig. Figure 13.4 shows the signal constellation of the demodulated FM-2 signal and the calculated quadrature components at the sampling time, provided that the channel symbol with amplitude is demodulated A: I– common-mode component, Q– quadrature component. In Fig. 13.4, A reference phase error Dj = 0; in this case, synchronous detectors calculate I = A, Q= 0. In Fig. 13.4, b reference phase error Dj > 0; in this case, synchronous detectors calculate I = A×cosDj, Q < 0. На рис. 13.4, V reference phase error Dj< 0; при этом синхронные детекторы вычисляют I = A×cosDj, Q > 0.

We see that the sign of the value Q corresponds to a phase error: namely, if Q < 0, то Dj >0 and it is necessary to reduce the frequency and phase of the VCO, if Q> 0, then Dj< 0 и необходимо увеличивать частоту и фазу ГУН. Таким образом, значение Q can be taken as phase error e. But the situation is with a sign Q the opposite when demodulating a channel symbol with amplitude – A.

Amplitude modulation- a type of modulation in which the variable parameter of the carrier signal is its amplitude.

Amplitude modulation (AM) is a modulation in which undamped oscillations change in amplitude in accordance with the lower frequency oscillations 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 nonlinear transformation. But since with AM the spectrum of the modulating signal does not change, but is only 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 conversion in AM are widely used in technology,

for example, in the development of circuits for broadcasting and television receivers, multi-channel 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 that are modulated by signals for the purpose of transmitting information. Low-frequency vibrations are sometimes called carrier vibrations. The oscillations with low frequencies themselves do not contain information, they only “carry” it. The spectrum of modulated oscillations contains, in addition to low frequencies, side frequencies that contain transmitted information.

If we take a signal having a sinusoid formula as the primary signal, then the amplitude-modulated signal will have the form shown in the figure.

On the qualitative side, amplitude modulation (AM) can be defined as a change in the amplitude of the carrier in proportion to the amplitude of the modulating signal.

A harmonic oscillation of high frequency w is modulated in amplitude by a harmonic oscillation of low frequency W (t = 1/W is its period), t is time, A is the amplitude of the high-frequency oscillation, T is its period.

Amplitude modulation by a sinusoidal signal, w - carrier frequency, W - frequency of modulating oscillations, Amax and Amin - maximum and minimum amplitude values.

For a large amplitude modulating signal, the corresponding amplitude of the modulated carrier must be large and for small amplitude values, this modulation scheme can be implemented by multiplying two signals.

Amplitude modulation depth- maximum relative deviation of the amplitude from the average

The spectral density of the modulated signal represents two spectra of the modulating function, constructed relative to the frequencies w = w 0 and w = -w 0 (shifted to the carrier frequencies).

Example. Single tone modulation spectrum

A radio signal consists of a carrier wave and two sine waves called sidebands.

In conventional amplitude modulation, information is contained in each of the two sidebands

Carrier signal- a signal, one or more parameters of which are subject to change during the modulation process. 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 signal. Most often, a high-frequency (relative to the information signal) harmonic oscillation is used as a carrier signal, which is 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, square wave.

The carrier signal is often called simply carrier(from carrier frequency), or carrier (oscillation). All these terms mean practically the same thing. In English terminology, a carrier signal is denoted by the word carrier.

The ratio U /U 0 is called the modulation coefficient mAM. It is often expressed as a percentage. If U 0 >=Umax, then the coefficient mAM will vary from 0 to 1.

Amplitude modulation coefficient(AM coefficient, legacy modulation depth) - the main characteristic of amplitude modulation is 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 oscillations are the result of the addition of three high-frequency oscillations; oscillations with frequency f 0 and amplitude U 0 and two oscillations with frequencies f 0 + F and f 0 - F and amplitude 0.5 mAM*U 0 .

In amplitude modulation (AM) systems, the modulating wave changes the amplitude of a 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 modulating wave is complex, such as a speech signal, which consists of many frequencies, then the sums and differences of various frequencies will occupy two bands, one below and the other above the carrier frequency. The frequencies f n + F and f n - F are called the upper and lower side frequencies, respectively.

Top side stripe is a copy of the original conversational signal, only shifted to the Fc frequency. The lower band is an inverted copy of the original signal, i.e. the high frequencies in the original are the low frequencies in the lower side.

Lower side strip this is a mirror image of the upper side with respect to the carrier frequency Fc.

An AM system that transmits both sidebaud and carrier is known as a double sidebaud (DSB) system. The carrier carries no useful information and can be removed, but with or without the carrier, the DSB signal has twice the bandwidth of the original signal. To narrow the band, 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 modulation (SSB-SC - Single SideBand Suppressed Carrier).

Amplitude modulation of a complex signal

Any transmitting radio station operating in amplitude modulation mode emits not just 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 slot on the air. To avoid interference, the carrier frequencies of different stations must be separated from each other by a distance greater than the sum of the sidebands. The width of the sideband 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 oscillation of the carrier frequency and the modulating signal are fed to a special device - a modulator.

Demodulation of an AM signal is achieved by mixing the modulated signal with a carrier of the same frequency as the modulator.

The original signal is then obtained as a separate frequency (or frequency band) and can be filtered from other signals. The demodulation carrier is generated locally and may not coincide in any way with the carrier frequency at the modulator. The slight difference between the two frequencies causes frequency mismatch, which is inherent in telephone circuits.

Due to amplitude modulation of a complex signal, the data transfer rate increases.