To transfer information from a source to a consumer, it is necessary to perform a number of transformations, which are called radio engineering processes.
1. Converting a message into electricity
function. This action takes place in devices called converters. For example, the transformation of sound pressure p (t) into electric current i (t) occurs when
Rice. 1.1. Converter
the power of the microphone, and the transformation of the image into potential - using a television transmission
giving tube. The signal b (t) obtained in this way is called the primary
nym. The transducer designation is shown in Fig. 1.1.
2. Generation harmonic vibrations... This transformation is
comes in devices called generators. In them, the power of the constant current source P0 is converted into the power P1 of harmonic oscillations.
It is interesting to note that the entire history of the development of radio engineering and communications is the history of mastering ever higher-frequency wave ranges, including the optical range. Many generators have been developed, ranging from lamp generators to optical quantum generators (LQGs). The main requirement for such generators is high frequency stability.
3. Modulation. Without this process, it is impossible
would transmit messages, usually consisting of a collection of low-frequency vibrations, over long distances. From the position of the course "Theory electrical circuits The modulator is six-
pole, to the inputs of which the primary
signal b (t) and high-frequency harmonic
Rice. 1.2. Modulator
oscillation u (t) (Fig. 1.2.). The result is a high-frequency signal s (t),
one of the parameters of which changes according to the law b (t).
4. Detection. This process is
S (t) b (t)
Rice. 1.3. Detector
Rice. 1.4. Amplifier
the opposite of the modulation process, with the help of which the transmitted message is extracted. The device performing this conversion is called a detector, the type of which must correspond to the modulation method (Fig. 1.3).
5. Gain. The purpose of this process is
increasing the power of the received signal while maintaining its shape. The device that implements this radio engineering process is called an amplifier (Fig. 1.4).
In addition to the listed processes, CEA uses
others are also used: frequency conversion, multiplication
frequency division and division, rectification, etc. But only the five above-mentioned radiotechnical processes are the main ones, since they determine the possibility of transmitting messages from the source to the consumer.
A communication channel is a complex of radio engineering devices, when
by means of which information is transmitted and received, plus the environment between them (Fig. 1.5). The communication channel includes devices that carry out all the basic radio engineering processes, as well as transmitting and receiving antennas. In this case, information is transmitted through free space, the wave impedance of which is 377 Ohm (radio channel). If the signal is transmitted through a cable, then the characteristic impedance of the communication line is determined by the type of cable, and instead of antennas, special matching devices (wired channel) are used.
A set of devices, with the help of which a signal is generated, and a radiating antenna (or a matching device) form a radio transmitting device (transmitter).
Receiving antenna (matching device) and signal processing devices
cash constitute a radio receiving device (receiver). Physical environment, software
which the signal propagates is called the communication line. Thus, depending on the type of medium, communication channels can be wired and wireless (radio channels).
7
Rice. 1.5. Structural scheme communication channel:
1 - message source, 2 - converter, 3 - modulator, 4 - self-oscillator,
5 - radio signal amplifier, 6 - transmitting antenna (matching device),
7 - communication line, 8 - receiving antenna (matching device),
9 - frequency selective device, 10 - radio signal amplifier, 11 - detector,
12 - video signal amplifier, 13 - message recipient
In the case of transmission of several signals over one communication line, the so-called multichannel communication is carried out (Fig. 1.6). In this case, there are problems with channel separation. Currently, frequency, time and address methods of channel separation are widely used. The essence of the frequency method is that each signal is assigned its own specific frequency band and the signal is extracted with special filters. The advantage of the frequency method is high speed, since information is transmitted in a parallel way. The disadvantage of the frequency method is the wide frequency band required for the organization of communication. With the time method, each signal is transmitted over the same frequency band, but at different time intervals. This method presupposes the presence of special temporary distribution and synchronizing devices, which complicates the communication channel. With economical use of the frequency band, we get a loss in performance. In address communication systems, channels differ in the form of transmitted signals.
Depending on the type of communication organization, various communication modes are possible. If the transmission of messages is carried out in one direction from the
source to the receiver, then this mode is called simplex, for example, data transmission from an automatic weather station. Communication mode in which it is possible to simultaneously transmit messages in direct and
the opposite direction is called duplex. The classic example is telephony. The communication mode, in which the exchange of information is carried out alternately, is called half-duplex, for example, the work of the announcer in the TV
zionic studio and a journalist at the scene.
Σ St.
Rice. 1.6. Block diagram of a multichannel communication system:
IsN - message sources, KN - communication channels, Σ - adder,
ФN - filters of the receiving device, DN - detectors, АN - message recipients
In real communication channels, for various reasons, a random effect on the signal is possible, which is called interference n (t). As a result of such influence, the reliability of the message reproduction deteriorates. If the input signal of the receiving device z (t) is the sum of the useful signal s (t) and the interference n (t), then the interference is called additive, i.e. z (t) = s (t) + n (t). In case of presentation input signal in the form z (t) = k (t) · s (t), the noise is called multiplicative. In real communication channels, both additive and multiplicative interference of various origins operate. If there is no interference in the communication channel, then such a communication channel is an ideal channel.
The main radio engineering processes are the processes of converting signals containing and carrying messages. The basic processes are approximately the same (similar) for all radio electronic systems, regardless of what class and to what generation of technology these systems belong, regardless of the structure and purpose of these systems.
13. Radiation of high-frequency radio signals and propagation of radio waves
13.1. Radio signals and electromagnetic waves
In accordance with the law of electromagnetic induction, an EMF arises in a circuit enclosing a changing magnetic field, which excites a current in this circuit. The guide does not play an essential role here. It only allows the induced current to be detected. The true essence of the phenomenon of induction, as established by J.K. Maxwell, is that in space where the magnetic field changes, an electric field that changes in time arises. This time-varying electric field Maxwell called the current of electric displacement.
Unlike the field of stationary charges, the lines of force of a time-varying electric field (electric displacement current) can be closed in the same way as the lines of force magnetic field... Therefore, there is a close connection and interaction between electric and magnetic fields. It is established by the following laws.
1. A time-varying electric field at any point in space creates a changing magnetic field. The lines of force of the magnetic field cover the lines of force of the electric field that created it, Fig. 13.1, a). At each point in space, the vector of electric field strength E and the vector of the magnetic field strength N are orthogonal to each other.
2. A time-varying magnetic field at any point in space creates a changing electric field. The lines of force of the electric field cover the lines of force of the alternating magnetic field in Figure 3.1. b). At each point of the considered space, the vector of magnetic field strength N and the vector of the electric field strength E mutually perpendicular.
3. An alternating electric field and an alternating magnetic field inseparably connected with it form an electromagnetic field.
Rice. 13.1. First a) and the second b) the laws electromagnetic field(Maxwell's laws)
The transfer of electromagnetic energy by a wave in space is characterized by the vector NS equal to the vector product of the strengths of the electric and magnetic fields:
.
Vector direction NS coincides with the direction of wave propagation, and the modulus is numerically equal to the amount of energy that the wave transfers per unit time through a unit area located perpendicular to the direction of wave propagation. The concept of the flow of energy of any kind was first introduced by N.A. Umov in 1874. The formula for the vector NS was obtained on the basis of the equations of the electromagnetic field by Poynting in 1884. Therefore, the vector NS, whose modulus is equal to the wave power flux density, is called the Umov-Poynting vector.
The most important feature of the electromagnetic field is that it moves in space in all directions from the point at which it originated. The field can exist even after the source of the electromagnetic disturbance has ceased to act. Changing electric and magnetic fields, passing from point to point in space, propagate in vacuum at the speed of light (310 8 m / s).
The process of propagation of a periodically changing electromagnetic field is a wave process. Electromagnetic waves of the radiated field, meeting conductors on their way, excite in them an EMF of the same frequency as the frequency of the electromagnetic field that creates the induced EMF. Part of the energy carried by electromagnetic waves is transferred to currents that occur in the conductors.
The distance that the wave front moves in a time equal to one period of the electromagnetic oscillation is called the wavelength
.
Radio waves, thermal and ultraviolet radiation, light, X-rays and -radiation are all waves of an electromagnetic nature, but of different lengths. And all these waves are used by different electronic systems. Scale of electromagnetic waves, ordered by frequency f, wavelength, and the name of the range is shown in Fig. 4.2.
Knowledge of the conditions of propagation of the electromagnetic field is very important for determining the range and coverage of radio-electronic systems, dangerous distances at which unauthorized access by technical means of reconnaissance to the information contained in the intercepted signals is possible. If possible, the area within which there is a danger of interception is monitored to exclude the presence of technical reconnaissance equipment. In other cases, it is necessary to take other measures to protect the information carried by signals informative for reconnaissance electromagnetic fields.
The conditions for the propagation of electromagnetic fields significantly depend on the frequency (wavelength). The propagation of radio waves differs significantly from the propagation of infrared radiation, visible light and more severe radiation.
The speed of propagation of radio waves in free space in a vacuum is equal to the speed of light. The total energy carried by the radio wave remains constant, and the energy flux density decreases with increasing distance r from the source in inverse proportion to r 2. The propagation of radio waves in other media occurs with a phase velocity that differs from with and is accompanied by the absorption of electromagnetic energy. Both effects are explained by the excitation of oscillations of electrons and ions of the pore medium by the action of the electric field of the wave. If the field strength | E | of a harmonic wave is small compared to the strength of the field acting on the charges in the medium itself (for example, on an electron in an atom), then the oscillations also occur according to a harmonic law with the frequency of the incoming wave. Oscillating electrons emit secondary radio waves of the same frequency, but with different amplitudes and phases. As a result of the addition of the secondary waves with the incoming one, a resultant wave with a new amplitude and phase is formed. The phase shift between the primary and re-emitted waves leads to a change in the phase velocity. Energy losses during the interaction of a wave with atoms are the reason for the absorption of radio waves.
The amplitude of the electric (and, of course, the magnetic) field of the wave decreases with distance according to the law
,
and the phase of the wave changes as
where – absorption rate, and n- refractive index, depending on the dielectric permeability medium, its conductivity o and wave frequency:
,
The medium behaves like a dielectric ,
if 
and as a conductor if 
... In the first case 
, absorption is small, in the second 
.
In a medium where and depend on frequency, wave dispersion is observed . The type of frequency dependence and is determined by the structure of the medium. The dispersion of radio waves is especially significant in those cases when the wave frequency is close to the characteristic natural frequencies of the medium, for example, when radio waves propagate in the ionospheric and cosmic plasma.
When radio waves propagate in media that do not contain free electrons (in the troposphere, in the Earth's interior), there is a displacement of bound electrons in the atoms and molecules of the medium in the direction opposite to the wave field E, wherein n> 1, and the phase velocity v f<with(a radio signal carrying energy propagates with a group velocity v gr<with). In a plasma, the wave field causes a displacement of free electrons in the direction E, wherein n<1 иv f<with.
In homogeneous media, radio waves propagate in a straight line, like light rays. The propagation of radio waves in this case obeys the laws of geometric optics. Given the sphericity of the Earth, the line-of-sight range can be estimated based on simple geometric constructions by the ratio
,
where h prd and h prm - heights of the location of the transmitting and receiving antennas in meters; R - line-of-sight range in kilometers.
However, real environments are not homogeneous. In them n and, consequently, vφ are different in different parts of the medium, which leads to a curvature of the trajectory of the radio wave. Refraction (refraction) of radio waves occurs. Taking into account the normal refraction of radio waves, the maximum range is determined more accurately than by the ratio
If NS depends on one coordinate, for example height h(flat-layered medium), then when a wave passes through each flat layer, a ray incident into an inhomogeneous medium at a point with n 0 = 1 at an angle 0 in space is curved so that at an arbitrary point of the medium h the ratio is observed:
.
If NS decreases with increasing h, then, as a result of refraction, the beam, as it propagates, deviates from the vertical and at a certain height h m becomes parallel to the horizontal plane and then extends downward. Maximum height h m, on which the ray can penetrate into an inhomogeneous flat-layered medium, depends on the angle of incidence 0. This angle can be determined from the condition:
To the area h>h m rays do not penetrate and, according to the geometrical optics approximation, the wave field in this region should be equal to 0. In fact, near the plane h=h m the wave field increases, and at h> h m decreases exponentially. Violation of the laws of geometrical optics during the propagation of radio waves is associated with wave diffraction due to which radio waves can penetrate into the region of the geometric shadow. A complex distribution of wave fields is formed on the boundary of the geometrical shadow region o6. Diffraction of radio waves occurs when there are obstacles in their path (opaque or translucent bodies). Diffraction is especially significant when the size of the obstacles is comparable to the wavelength.
If the propagation of radio waves occurs near a sharp boundary (on a scale of ) between two media with different electrical properties (for example, the atmosphere, the Earth's surface or the troposphere - the lower boundary of the ionosphere for sufficiently long waves), then when radio waves fall on the sharp boundary, reflected and refracted (transmitted ) radio waves.
In inhomogeneous media, waveguide propagation of radio waves is possible, in which the energy flux is localized between certain surfaces, due to which the wave fields between them decrease with distance more slowly than in a homogeneous medium. This is how atmospheric waveguides are formed .
In a medium containing random local inhomogeneities, secondary waves are radiated randomly in different directions. Scattered waves partially carry away the energy of the original wave, which leads to its attenuation. For scattering by inhomogeneities of size l<<рассеянные волны распространяются почти изотропно. В случае рассеяния на крупномасштабных прозрачных неоднородностях рассеянные волны распространяются правлениях, близких к направлению исходной волны. Приl strong resonance scattering occurs.
Influence of the Earth's surface on the propagation of radio waves depends on the location of the transmitter and receiver relative to it. Radio propagation is a process that covers a large area of space, but the most significant role in the propagation of radio waves is played by the area bounded by a surface in the form of a scattering ellipsoid, at the foci of which the distance r the transmitter and receiver are located.
If the heights h 1 and h 2, which summarize the transmitter and receiver antennas above the Earth's surface, are large compared to the wavelength, then it does not affect the propagation of radio waves .
When both or one of the endpoints of the radio path is lowered, a near-specular reflection from the Earth's surface will be observed. In this case, the radio wave at the receiving point is determined by the interference of the direct and reflected waves .
The interference maxima and minima determine the lobe structure of the field in the receiving area. This pattern is especially typical for meter and shorter radio waves. The quality of radio communication in this case is determined by the conductivity of the soil. The soils that form the surface layer of the earth's crust, as well as the waters of the seas and oceans, have electrical conductivity. But since NS and depend on frequency, then for centimeter waves all types of the earth's surface have the properties of a dielectric. For meter and longer waves, the Earth is a conductor into which waves penetrate to a depth 
( 0 is the wavelength in vacuum). Therefore, for underground and underwater radio communication, mainly long and super-long waves are used.
The bulge of the earth's surface limits the distance at which the transmitter is visible from the receiving point (line of sight). However, radio waves can penetrate the shadow area for a greater distance. 
(R h - the radius of the Earth), bending around the Earth, as a result of diffraction. In practice, only kilometers and longer waves can penetrate into this region due to diffraction. Over the horizon, the field grows with increasing height h 1, on which the emitter is raised, and rapidly (almost exponentially) decreases with distance from it.
The influence of the relief of the earth's surface on the propagation of radio waves depends on the height of the irregularities h, their horizontal length l, wavelength and angle of incidence of the wave on the surface. If the irregularities are small enough and shallow enough so that kh cos<1(
–
wave number) and the Rayleigh criterion is satisfied:
k 2 l 2 cos<1,
то они слабо влияют на распространение
радиоволн. Влияние неровностей зависит,
также от поляризации волн. Например,
для горизонтально поляризованных волн
оно меньше, чем для волн, поляризованных
вертикально. Когда не ровности не малы
и не пологи, энергия радиоволны может
рассеиваться (радиоволна отражается
от них). Высокие горы и холмы сh>
form shaded areas. Diffraction of radio waves on mountain ranges sometimes leads to wave amplification due to the interference of direct and reflected waves: the mountain top serves as a natural repeater.
The phase velocity of radio waves propagating along the earth's surface (earth waves) near the emitter depends on its electrical properties. However, at a distance of several from the emitter v f c. If radio waves propagate over an electrically inhomogeneous surface, for example, first over land and then over the sea, then when crossing the coastline, the amplitude and direction of propagation of radio waves changes dramatically (coastal refraction is observed).
Propagation of radio waves in the troposphere. Troposphere - the area in which the air temperature usually decreases with height h. The height of the tropopause above the globe is not the same: it is greater above the equator than above the poles, and in mid-latitudes, where there is a system of strong westerly winds, it changes abruptly. The troposphere consists of a mixture of gases and water vapor; its conductivity for radio waves with more than a few centimeters is negligible. The troposphere has properties close to vacuum, since the refractive index near the Earth's surface is 
and the phase velocity is only slightly less with... With increasing altitude, the air density decreases, and therefore NS decrease, approaching even closer to unity. This leads to a deviation of the trajectories of the radio beams to the Earth. This normal tropospheric refraction contributes to the propagation of radio waves beyond the line of sight, since, due to refraction, the waves can bend around the bulge of the Earth. In practice, this effect can play a role only for VHF. For longer wavelengths, bending of the Earth's bulge due to diffraction predominates.
Meteorological conditions can weaken or increase refraction compared to normal, since the density of air depends on pressure, temperature and humidity. Usually in the troposphere, gas pressure and temperature decrease with altitude, and water vapor pressure increases. However, under some meteorological conditions (for example, when air heated over land over the sea), the air temperature increases with height (temperature inversion). The deviations are especially large in summer at an altitude of 2 ... 3 km. Under these conditions, temperature inversions and cloud layers are often formed, and the refraction of radio waves in the troposphere can become so strong that a radio wave released at a small angle to the horizon at a certain height will change direction and return back to the Earth. In a space bounded from below by the earth's surface, and from above by a refracting layer of the troposphere, a wave can propagate over very long distances (waveguide propagation). In tropospheric waveguides, as a rule, waves with <1 м.
The absorption of radio waves in the troposphere is negligible for all radio waves up to the centimeter range. The absorption of centimeter and shorter waves increases sharply when the vibration frequency coincides with one of the natural vibration frequencies of air molecules (resonant absorption). Molecules receive energy from the incoming wave, which turns into heat and is only partially transferred to secondary waves. A number of lines of resonant absorption in the troposphere are known: = 1.35 cm, 1.5 cm, 0.75 cm (absorption in water vapor) and = 0.5 cm, 0.25 cm (absorption in oxygen). The regions of weaker absorption (transparency windows) lie between the resonance lines.
Attenuation of radio waves can also be caused by scattering on inhomogeneities arising from the turbulent movement of air masses. . The scattering increases sharply when there are drip irregularities in the air in the form of rain, snow, fog. Almost isotropic Rayleigh scattering on small-scale irregularities makes radio communication possible at distances far exceeding line-of-sight. Thus, the troposphere significantly affects the propagation of VHF. For decameter and longer waves, the troposphere is practically transparent and their propagation is influenced by the earth's surface and higher layers of the atmosphere (ionosphere).
Propagation of radio waves in the ionosphere. The ionosphere is formed by the upper layers of the earth's atmosphere, in which gases are partially (up to 1%) ionized under the influence of ultraviolet, X-ray and corpuscular solar radiation. The ionosphere is electrically neutral, it contains an equal number of positive and negatively charged particles, i.e. is plasma .
A sufficiently large ionization, which affects the propagation of radio waves, begins at an altitude of 60 km (layer D), increases to a height of 300 ... 400 km, forming layers E, F 1 , F 2 , and then slowly decreases. At the main maximum, the electron concentration N reaches 10 2 m -3. Addiction N from altitude changes with the time of day, year, with solar activity, as well as with latitude and longitude.
Depending on the frequency, the main role in the propagation of radio waves is played by certain types of natural oscillations. Therefore, the electrical properties are different for different parts of the radio range. At high frequencies, the ions do not have time to follow the field changes, and only electrons take part in the propagation of radio waves. Forced oscillations of free electrons of the ionosphere emanate in antiphase with the acting force and cause polarization of the plasma in the direction opposite to the electric field of the wave E... Therefore, the dielectric constant of the ionosphere<1.
Она уменьшается с уменьшением частоты:
... Taking into account the collisions of electrons with atoms and ions gives more accurate formulas for the dielectric constant and conductivity of the ionosphere:
,
where is the effective collision frequency.
For decameter and shorter waves in most of the ionosphere and refractive indices n and absorptions approach the values:
.
Since for the ionosphere n> 1, then the phase velocity of radio wave propagation 
, and the group velocity 
.
Absorption in the ionosphere is proportional to , since the more collisions, the more of the energy received by the electron is converted into heat. Therefore, absorption is greater in the lower regions of the ionosphere (layer D), where the gas density is higher. Absorption decreases with increasing frequency. Short waves are weakly absorbed and can travel long distances.
Refraction of radio waves in the ionosphere. Only radio waves with a frequency 0 can propagate in the ionosphere. At 0, the refractive index n becomes purely imaginary, and the electromagnetic field decreases exponentially deeper into the plasma. A radio wave with frequency incident vertically on the ionosphere is reflected from the level at which 0 and n= 0. In the lower part of the ionosphere, the electron concentration u0 increases with height, therefore, with an increase in, the wave emitted from the Earth penetrates deeper into the ionosphere. The maximum frequency of a radio wave that is reflected from the ionospheric layer during vertical incidence is called the critical frequency of the layer:
.
Critical layer frequency F 2 (main maximum) varies during the day and year over a wide range (from 3 ... 5 to 10 MHz). For waves with cr, the refractive index does not vanish and the vertically incident wave passes through the ionosphere without being reflected.
With an oblique incidence of a wave on the ionosphere, refraction occurs, as in the troposphere. In the lower part of the ionosphere, the phase velocity increases with height (together with an increase in the electron concentration N). Therefore, the trajectory of the beam is deflected towards the Earth. A radio wave incident on the ionosphere at an angle 0 turns toward the Earth at an altitude h, for which the condition = cr. The maximum frequency of a wave reflected from the ionosphere when it falls at an angle 0 is called the maximum usable frequency max = 
... Waves with< max отражаясь от ионосферы, возвращаются
на Землю. Этот эффект что используется
для дальней радиосвязи и загоризонтной
радиолокации. Вследствие сферичности
Земли величина угла 0 ограничена и дальность связи при
однократном отражении от ионосферы не
превосходит 3500…4000 км. Связь на большие
расстояния осуществляется за счет
нескольких последовательных отражений
от ионосферы и Земли (скачков). Возможны
и более сложные, волноводные траектории,
возникающие за счет горизонтального
градиентаN or scattering on ionospheric irregularities during propagation of radio waves with a frequency> max. As a result of scattering, the angle of incidence of the beam on the layer F 2 turns out to be larger than with conventional distribution. The beam experiences a series of successive reflections from the layer F 2 until it falls into an area with such a gradient. N, which will cause some of the energy to be reflected back to Earth.
Influence of the Earth's magnetic field with intensity H 0
comes down To
to that ,
what about an electron moving at a speed v,
the Lorentz force acts
, under the influence of which it rotates around a circle in a plane perpendicular to N 0, with a gyroscopic frequency N. The trajectory of each charged particle is a helical line with the axis along N 0. The action of the Lorentz force leads to a change in the nature of the forced oscillations of electrons under the action of the electric field of the wave, and, consequently, to a change in the electrical properties of the medium. As a result, the electrical properties of the ionosphere become dependent on the direction of propagation of radio waves and are described not by a scalar quantity, but by the permittivity tensor ij. A wave incident on such a medium experiences birefringence ,
that is, it splits into two waves, differing in speed and direction of propagation, absorption and polarization. If the direction of propagation of radio waves is perpendicular N 0, then the incident wave can be thought of as the sum of two linearly polarized waves with EN 0 and E || H 0 .
For the first "extraordinary" wave, the nature of the forced motion of electrons under the action of the wave field changes (an acceleration component appears perpendicular to E) and therefore changes NS. For the second "ordinary" wave, the forced motion remains the same as without the field N 0 .
Most of the energy of low-frequency (LF) and very low-frequency (VLF) radio waves practically does not penetrate into the ionosphere. Waves are reflected from its lower boundary (during the day - due to strong refraction in the D-layer, at night - from the E-layer, as from the boundary of two media with different electrical properties). The propagation of these waves is well described by the model, according to which the homogeneous and isotropic Earth and the ionosphere form a surface waveguide with sharp spherical walls. It is in this waveguide that radio waves propagate. This model explains the observed decrease in the field with distance and the increase in the amplitude of the field with height. The latter is associated with the sliding of waves along the concave surface of the waveguide, leading to a kind of focusing of the field. The amplitude of radio waves increases significantly at the point of the Earth that is antipode to the source. This is due to the addition of radio waves that bend around the Earth in all directions and converge on the opposite side.
The influence of the Earth's magnetic field determines a number of features of the propagation of LF waves in the ionosphere: ultra-long waves can leave the surface waveguide outside the ionosphere, propagating along the lines of force of the geomagnetic field between conjugate points A and V Earth.
Nonlinear effects in the propagation of radio waves in the ionosphere manifest themselves even for radio waves of relatively low intensity and are associated with the violation of the linear dependence of the polarization of the medium on the electric field of the wave . The "heating" nonlinearity plays the main role when the characteristic dimensions of the plasma region perturbed by the electric field are many times greater than the mean free path of electrons. Since the mean free path of electrons in a plasma is significant, the electron has time to receive appreciable energy from the field during one path. The transfer of energy in collisions from an electron to ions, atoms and molecules is difficult due to the large difference in their masses. As a result, the plasma electrons are strongly "heated" already in a relatively weak electric field, which changes the effective collision frequency. Therefore, and plasmas become dependent on the strength of the electric field E waves and radio wave propagation becomes non-linear.
Nonlinear effects can manifest themselves as self-action of the wave and as the interaction of waves with each other. Self-action of a powerful wave leads to a change in its absorption and modulation depth. The absorption of a powerful radio wave is nonlinearly dependent on its amplitude. The collision frequency with increasing temperature (electron energy) can both increase (in the lower layers, where collisions with neutral particles play the main role), and decrease (with collisions with ions). In the first case, absorption increases sharply with increasing wave power (saturation of the field in the plasma). In the second case, absorption decreases (this effect is called plasma bleaching for a high-power radio wave). Due to the nonlinear change in absorption, the amplitude of the wave is nonlinearly dependent on the amplitude of the incident field, therefore its modulation is distorted (self-modulation and demodulation of the wave). Refractive index change n in the field of a powerful wave leads to distortion of the ray trajectory. When narrowly directed beams of radio waves propagate, this effect can lead to self-focusing of the beam, similar to self-focusing light and to the formation of a waveguide channel in the plasma.
The interaction of waves under nonlinearity conditions leads to a violation of the superposition principle . In particular, if a powerful wave with frequency 1 is modulated in amplitude, then due to the change in absorption, this modulation can be transmitted to another wave with frequency 2, passing in the same region of the ionosphere. This phenomenon is called cross modulation.
Propagation of radio waves in outer space has features due to the fact that from outer space to the Earth comes a wide range of electromagnetic will, which on the way from space must pass through the ionosphere and troposphere. Waves of two main frequency ranges propagate through the Earth's atmosphere without noticeable attenuation: the "radio window" corresponds to the range from the ionospheric critical frequency to the frequencies of strong absorption by aerosols and atmospheric gases (10 MHz ... 20 GHz), the "optical window" covers the range of visible and IR radiation (1 THz ... 10 3 THz). The atmosphere is also partially transparent in the low frequency range up to 300 kHz, where whistling atmospheres and magnetohydrodynamic waves propagate.
Propagation of radio waves of different bands. Radio waves very low(3 ... 30 kHz) and low (30 ... 300 kHz) frequencies bend around the earth's surface due to waveguide propagation and diffraction, penetrate relatively weakly into the ionosphere and are little absorbed by it. They are characterized by high phase stability and the ability to uniformly cover large areas, including polar regions. This makes it possible to use them for stable long-range and ultra-long-range radio communications and radio navigation, despite the high level of atmospheric interference. The frequency range from 150 kHz to 300 kHz is used for broadcasting. Difficulties in using the very low frequency range are associated with the cumbersomeness of antenna systems with a high level of atmospheric interference, with a relative limited information transfer rate. The slow vibrations of very low frequency waves cannot be modulated by fast processes carrying information at high speed. As N. Wiener wrote about this, "You cannot play a jig in the lower register of an organ."
Medium waves(300 kHz… 3000 kHz) during the day propagate along the surface of the Earth (ground or direct wave). The wave reflected from the ionosphere is practically absent, since the waves are strongly absorbed in the layer D ionosphere. At night due to lack of solar radiation layer D disappears, an ionospheric wave appears, reflected from the layer E... At the same time, the range of propagation and, accordingly, reception increases. The addition of the direct and reflected waves entails a strong field variability at the receiving point. Therefore, the ionospheric wave is a source of interference for many services using earth wave propagation.
Short waves(3 MHz ... 30 MHz) poorly absorbed D- and E- layers and reflected from the layer F when their frequencies< max . В результате отражения от ионосферы возможна связь как на малых, так и на больших расстояниях при значительно меньшем уровне мощности передатчика и гораздо более простых антеннах, чем в более низкочастотных диапазонах. Особенность радиосвязи в этом диапазоне – наличие замираний (фединга) сигнала из-за изменений условий отражения от ионосферы и интерференционных эффектов. Коротковолновые линии связи подвержены влиянию атмосферных помех. Ионосферные бури вызывают прерывание связи.
For very high frequencies and VHF (30 ... 1000 MHz) is characterized by the predominance of radio wave propagation inside the troposphere and penetration through the ionosphere. The role of the earth wave is falling. Interference fields in the low frequency portion of this range can still be determined by reflections from the ionosphere, and up to 60 MHz, ionospheric scattering continues to play a significant role. All types of radio propagation, with the exception of tropospheric scatter, allow the transmission of signals with a bandwidth of several MHz.
UHF and microwave waves (1000 MHz ... 10,000 MHz) propagate mainly within the line of sight and are characterized by a low noise level. In this range, in the propagation of radio waves, the known regions of maximum absorption and radiation frequency of chemical elements play a role (for example, the lines of resonant absorption by hydrogen molecules near the frequency of 1.42 GHz).
Microwave waves (> 10 GHz) propagate only within the line of sight. Losses in this range are slightly higher than at lower frequencies, and their value is strongly influenced by the amount of precipitation. An increase in losses at these frequencies is partially offset by an increase in the efficiency of antenna systems. A diagram illustrating the features of the propagation of radio waves in different ranges is illustrated in Fig. 13.3.
Rice. 13.3. Propagation of electromagnetic waves in surface space
Despite the fact that historically the radiation of the optical range of waves began to be used by mankind much earlier than any other electromagnetic fields, the propagation of optical waves through the atmosphere is the least studied in comparison with the propagation of any waves in the radio range. This is explained by a more complex picture of propagation phenomena, as well as by the fact that a broader study of these phenomena began only recently, after the invention and the beginning of widespread use of optical quantum generators - lasers.
Three main phenomena determine the laws governing the propagation of optical waves through the atmosphere: absorption, scattering, and turbulence. The first two determine the average attenuation of the electromagnetic field under fixed atmospheric conditions and relatively slow field changes (slow fading) when the meteorological conditions change. The third phenomenon is turbulence causes rapid field changes (fast fading) that are observed in any weather. In addition, due to turbulence, the multipath effect is observed, when the structure of the received beam can change significantly in comparison with the structure of the beam at the output of the transmitter.
Basic radio engineering processes
Converting the original message into an electrical signal.
Generation of high-frequency oscillations.
Oscillation control (modulation).
Amplification of weak signals in the receiver.
Separation of a message from a high-frequency oscillation (detection and decoding).
Radio circuits and methods
their analysis
Circuit classification
And the elements used to implement the listed transformations of signals and oscillations can be divided into the following main classes:
Linear circuits with constant parameters;
Linear circuits with variable parameters;
Non-linear circuits.
^
Linear circuits with constant parameters
You can proceed from the following definitions:
A circuit is linear if the elements included in it do not depend on the external force (voltage, current) acting on the circuit.
The linear chain obeys the principle of superposition (overlay).
Where L is an operator characterizing the effect of the circuit on the input signal.
When several external forces act on a linear circuit, the behavior of the circuit (current, voltage) can be determined by superposition (superposition) of solutions found for each of the forces separately.
Otherwise: in a linear chain, the sum of effects from individual influences coincides with the effect from the sum of influences.
For any arbitrarily complex action in a linear circuit with constant parameters, no oscillations of new frequencies arise.
^ Variable linear circuits
These are circuits, one or several parameters of which change over time (but do not depend on the input signal). Such chains are often called linear. parametric.
Properties 1 and 2 from the previous paragraph are also valid for these circuits. However, even the simplest harmonic effect creates a complex oscillation with a frequency spectrum in a linear circuit with variable parameters.
^ Non-linear circuits
A radio circuit is nonlinear if it includes one or more elements, the parameters of which depend on the input signal level. The simplest non-linear element is a diode.
Basic properties of nonlinear circuits:
To non-linear circuits (and elements) superposition principle is not applicable.
An important property of a nonlinear circuit is the transformation of the signal spectrum.
^ Signal classification
From an informational point of view, signals can be divided into deterministic and random.
Deterministic any signal is called, the instantaneous value of which at any moment of time can be predicted with a probability of one.
TO random include signals whose instantaneous values are not known in advance and can be predicted only with a certain probability less than one.
Along with useful random signals, in theory and practice, one has to deal with random interference - noise. Wanted random signals, as well as interference, are often combined by the term random fluctuations or random processes.
Signals in a radio communication channel are often subdivided into control signals and on radio signals; the first is understood as modulating, and the second - modulated oscillations.
Signals used in modern radio electronics can be divided into the following classes:
Arbitrary in size and continuous in time (analog);
Arbitrary in size and discrete in time (discrete);
Quantized in magnitude and continuous in time (quantized);
Quantized in magnitude and discrete in time (digital).
^
Characteristics of deterministic
signals
Energy characteristics
The main energy characteristics of the real signal s (t) are its power and energy.
Instantaneous power is defined as the square of the instantaneous value s (t):
The signal energy in the interval t 2, t 1 is determined as an integral of the instantaneous power:
.
Attitude
It makes sense for the average signal power over the interval t 2, t 1.
^
Arbitrary waveform representation
as a sum of elementary vibrations
For the theory of signals and their processing, it is important to expand the given function f (x) into various orthogonal systems of functions j n (x). Any signal can be represented as a generalized Fourier series:
,
Where C i - weight coefficients,
J i - orthogonal expansion functions (basis functions).
For basic functions, the following condition must be met:
If the signal is defined in the interval from t 1 to t 2, then
The norm of the basis function.
If the function is not orthonormal, then it can be reduced in this way. With increasing n, C n decreases.
Suppose a set of basis functions (j n) is given. When specifying a set of basis functions and with a fixed number of terms in the generalized Fourier series, the Fourier series gives an approximation of the original function that has the minimum root-mean-square error in the definition of the original function. The generalized Fourier series gives
Such a series gives a minimum average error (error).
There are 2 problems of signal decomposition into the simplest functions:
^ Exact decomposition into simplest orthogonal functions (signal analytic model, signal behavior analysis).
^ Approximation of process signals and characteristics when it is required to minimize the number of members of the generalized series. These include: Chebyshev, Hermite, Legendre polynomials.
^ Harmonic analysis of periodic signals
When expanding the periodic signal s (t) in a Fourier series in trigonometric functions, we take as the orthogonal system
The orthogonality interval is determined by the norm of the function
Average value of the function over the period.
- basic formula for
definitions of the Fourier series
The module is an even function, the phase is an odd function.
Consider a pair for the kth term
- Fourier series expansion
^
Examples of spectra of periodic signals
Rectangular wobble... A similar hesitation, often called meander(Meander is the Greek word for "ornament") is especially widely used in measuring technology.
Let the signal s (t) be given in the form of some function different from zero in the interval (t 1, t 2). This signal must be integrable.
Take an infinite time interval T, including the interval (t 1, t 2). Then . The spectrum of the non-periodic signal is continuous. The given signal can be represented as a Fourier series 
, where
Based on this, we get:
Since Т®µ, the sum can be replaced by integration, and W 1 by dW and nW 1 by W. Thus, we pass to the double Fourier integral
,
where is the spectral density of the signal. When the interval (t 1, t 2) is not specified, the integral has infinite limits. This is the inverse and forward Fourier transform, respectively.
If we compare the expressions for the envelope of the continuous spectrum (modulus of spectral density) of the non-periodic signal and the envelope of the line spectrum of the periodic signal, it will be seen that they coincide in shape, but differ in scale 
.
Consequently, the spectral density S (W) has all the basic properties of a complex Fourier series. That is, you can write down where
, a 
.
Spectral density module 
is an odd function and can be viewed as an amplitude-frequency response. Argument 
- an odd function considered as a phase-frequency response.
Based on this, the signal can be expressed as follows
From the evenness of the modulus and the oddness of the phase, it follows that the integrand in the first case is even, and in the second - odd with respect to W. Therefore, the second integral is equal to zero (an odd function within even limits) and finally.
Note that at W = 0, the expression for the spectral density is equal to the area under the curve s (t)
.
^
Fourier transform properties
Time shift
Let a signal s 1 (t) of an arbitrary shape have a spectral density S 1 (W). If this signal is delayed by time t 0, we obtain a new function of time s 2 (t) = s 1 (t-t 0). The spectral density of the signal s 2 (t) will be as follows 
... Let's introduce a new variable. From here 
.
Any signal has its own spectral density. The shift of the signal along the time axis leads to a change in its phase, and the modulus of this signal does not depend on the position of the signal on the time axis.
^ Changing the time scale
Let the signal s 1 (t) be compressed in time. The new signal s 2 (t) is related to the original relationship.
The pulse duration s 2 (t) is n times shorter than the initial one. Compressed pulse spectral density 
... Let's introduce a new variable. We will receive.
When a signal is compressed n times, its spectrum expands by the same number. In this case, the modulus of the spectral density will decrease by a factor of n. When the signal is stretched over time, the spectrum narrows and the spectral density modulus increases.
^ Oscillation spectrum shift
Let's multiply the signal s (t) by the harmonic signal cos (w 0 t + q 0). The spectrum of such a signal
We split it into 2 integrals.
The resulting ratio can be written in the following form
Thus, the multiplication of the function s (t) by a harmonic vibration leads to the splitting of the spectrum into 2 parts, shifted by ± w 0.
^ Signal differentiation and integration
Let a signal s 1 (t) with a spectral density S 1 (W) be given. Differentiating this signal 
gives the ratio 
... Integration 
results in the expression 
.
^ Signal addition
When adding the signals s 1 (t) and s 2 (t) with the spectra S 1 (W) and S 2 (W), the total signal s 1 (t) + s 2 (t) corresponds to the spectrum S 1 (W) + S 2 (W) (since the Fourier transform is a linear operation).
^ Product of two signals
Let be . This signal corresponds to the spectrum
Let us represent the functions in the form of Fourier integrals.
Substituting the second integral into the expression for S (W), we obtain
Hence 
.
That is, the spectrum of the product of two functions of time is equal to the convolution of their spectra (with a coefficient of 1 / 2p).
If 
, then the signal spectrum will be 
.
^ Mutual reversibility of frequency and time
in the Fourier transform
Let s (t) be an even function with respect to time.
Assuming that s (t) is an even function. We write s (t) as
... We replace W with t and t with W, we get 
. If the spectrum has the shape of any signal, then the signal corresponding to this spectrum repeats the shape of the spectrum of a similar signal.
^
Energy distribution in the spectrum of a non-periodic signal
Consider an expression where f (t) = g (t) = s (t). In this case, this integral is equal to. This ratio is called Parseval's equality.
Energy bandwidth calculation: 
, where 
, a 
.
^
Examples of spectra of non-periodic signals
Rectangular impulse
Defined by the expression
Find the spectral density
.
With lengthening (stretching) of the pulse, the distance between the zeros decreases, the value of S (0) increases. The module of the function can be considered as the frequency response, and the argument as the phase response of the spectrum of a rectangular pulse. Each sign reversal takes into account the phase increment by p.
When counting the time not from the middle of the pulse, but from the front, the phase response of the pulse spectrum must be supplemented with a term that takes into account the pulse shift by time (the resulting phase response is shown by a dotted line).
Bell-shaped (Gaussian) pulse
Defined by expression. Constant a has the meaning of half the pulse duration, determined at the level of e -1/2 of the pulse amplitude. Thus, the full duration of the pulse.
Signal spectral density 
.
For convenience, we supplement the exponent to the square of the sum 
, where the quantity d is determined from the condition 
, where . Thus, the expression for the spectral density can be reduced to the form 
.
Moving on to a new variable 
get 
... Taking into account that the integral entering into this expression is equal, we finally obtain 
, where 
.
Pulse spectrum width
The Gaussian momentum and its spectrum are expressed by the same functions and have the property of symmetry. For it, the ratio of the pulse duration to the bandwidth is optimal, that is, for a given pulse duration, a Gaussian pulse has a minimum bandwidth.
delta pulse (single pulse)
The signal is given by the ratio 
... It can be obtained from the above impulses by tending t to zero.
It is known that, therefore, the spectrum of such a signal will be constant (this is the pulse area equal to unity).
All harmonics are needed to create such an impulse.
Exponential momentum
Signal of the form, c> 0.
The signal spectrum is found as follows
Let's write the signal in a different form 
.
If, then. This means that we will get a single jump. At 
we obtain the following expression for the signal spectrum 
.
Hence the module
Radio signals
Modulation
Let a signal be given, in it A (t) is amplitude modulation, w (t) is frequency modulation, j (t) is phase modulation. The last two form an angular modulation. The frequency w must be large compared to the highest frequency of the signal spectrum W (the width of the spectrum occupied by the message).
The modulated vibration has a spectrum, the structure of which depends both on the spectrum of the transmitted message and on the type of modulation.
Several types of modulation are possible: continuous, pulse, pulse-code.
^
Amplitude modulation
The general expression for the amplitude-modulated oscillation is as follows
The character of the envelope A (t) is determined by the type of the transmitted message.
If the signal is a message, then the envelope of the modulated waveform can be represented as. Where W is the modulation frequency, g is the initial phase of the envelope, k is the proportionality factor, DA m is the absolute change in amplitude. Attitude 
- modulation factor. Based on this, you can write. Then the amplitude-modulated oscillation will be written in the following form.
With undistorted modulation (M £ 1), the amplitude of the oscillation varies from 
before 
.
The maximum value corresponds to the peak power. The average power over the modulation period.
The power for transmitting an amplitude modulated signal is greater than that for transmitting a simple signal.
Amplitude-modulated signal spectrum
Let the modulated vibration be determined by the expression
We transform this expression
The first term is the original unmodulated oscillation. The second and third are the oscillations appearing in the process of modulation. The frequencies of these oscillations (w 0 ± W) are called side modulation frequencies. Spectrum width 2W.
In the case when the signal is the sum 
, where, and. Moreover, where 
.
From here we get
Each of the components of the spectrum of the modulating signal independently form two side frequencies (left and right). The spectrum width in this case is 2W 2 = 2W max 2 of the maximum frequency of the modulating signal.
In the vector diagram, the time axis rotates clockwise with an angular frequency w 0 (the count is from the horizontal axis). The amplitudes and phases of the side lobes are always equal to each other, so their resulting DF vector will always be directed along the OD line. The resulting vector OF changes only in amplitude without changing its angular position.
Let there be a signal Let us write it in a different form.
The spectrum corresponds to the signal 
, where, and S A is the spectral density of the envelope. Hence follows the final expression for the spectrum
This is explained by the strobing action of the d-function, that is, all components are equal to zero except for the frequencies w ± w n (these are the values at which the d-function is equal to zero). Even if the spectrum is not discrete, there are still side components.
^
Frequency modulation
Let there be a frequency modulated waveform. However, frequency is a derivative of phase. If you change the phase, then the current frequency will also change.
Frequency modulation
,
Where is the amplitude of the frequency deviation. For brevity, in what follows we will call frequency deviation or simply deviation.
Where w 0 t is the current phase change; is the angle modulation index.
Suppose where 
.
,
Where m is the modulation factor.
Thus, harmonic phase modulation with index is equivalent to frequency modulation with deviation.
With a harmonic modulating signal, the difference between FM and PM can only be detected by changing the modulation frequency.
At FM deviation W.
At FM, the quantity proportional to the amplitude of the modulating voltage and does not depend on the modulation frequencyW.
For a monochromatic baseband signal, phase modulation and frequency modulation are indistinguishable.
^
Signal spectrum at angular modulation
Let the swing be given
There are two amplitude modulated signals. Such components that differ in are called quadrature components.
Let be . This is the same as. Here q 0 = 0, g = 0.
Cos and sin are periodic functions and can be expanded in a Fourier series
J (m) - Bessel function of the 1st kind.
The spectrum for angular modulation is infinitely large, in contrast to the spectrum for amplitude modulation.
With angle modulation, the spectrum of a frequency-modulated vibration, even with modulation with 1 frequency, consists of an infinite number of harmonics grouped around the carrier frequency.
Disadvantages: the spectrum is very wide.
Advantages: most noise-immune.
Consider the case when m<< 1.
If m is very small, then only 2 side frequencies are present in the spectrum.
Spectrum width (m<< 1) будет равна 2W.
If m = 0.5¸1, then a second pair of side frequencies w ± 2W appears. The spectrum width is 4W.
If m = 1¸2, then the third and fourth harmonics w ± 3W, w ± 4W appear.
Spectrum width at m very large
SHS = 2mW = 2w d
If the modulation index is much less than one, then such modulation is called quick, then w d<< W.
If m >> 1, then this slow modulation, then w d >> W.
^
RF spectrum with frequency modulated
filling
, where
Where , 
The main parameter of the linear frequency modulated signal (chirp) or the base of the chirp signal.
B can be both positive and negative.
Suppose b> 0
The signal spectrum has 2 components:
1 - a burst near the frequency w about;
2 - a burst near the frequency -w о.
When determining the spectral density in the region of positive frequencies, the second term can be discarded.
Complement the exponent to a full square
, where C (x) and S (x) are the Fresnel integrals
Chirp spectral density module
The phase of the spectral density of the chirp signal
The larger m, the closer the spectrum shape is to rectangular with the width of the spectrum. The phase dependence is quadratic.
When m tends to large values, the shape of the frequency response tends to rectangular, and the phase consists of two parts:
1). gives a parabola
2). strives for
For large m and: 
Then the value of the module is:.
Mixed amplitude-frequency modulation
Cosine Quadrature Waveform Spectral Density 
at = 0 will be
When determining the spectrum of a sine quadrature oscillation 
the phase angle should be set equal to -90 °. Hence,
Thus, finally, the spectral density of the oscillation is determined by the expression
Passing to the variable, we get
.
The structure of the signal spectrum with mixed amplitude-frequency modulation depends on the ratio and form of the functions A (t) and q (t).
With frequency modulation, the phases of the odd harmonics are changed by 180 °. Simultaneous modulation in both frequency and amplitude for some ratios A (t) and q (t) leads to a violation of the symmetry of the spectrum not only in phase, but also in amplitude.
If q (t) is an odd function of t, then for any A (t) the spectrum of the output signal is asymmetric.
Let A (t) be an even function, then A c (t) is even, A s (t) is odd, is purely real, symmetric with respect to W, even, and is purely imaginary, asymmetric with respect to W and odd.
Taking into account the factor j, the spectrum of the output oscillation is real. As a result, the spectrum is asymmetric, but with respect to w = 0 it is symmetric. The same result can be obtained for an odd function A (t). In this case, the spectrum is purely imaginary and odd.
For the symmetry of the output spectrum, even q (t) is required, provided that A (t) was either even or odd with respect to t. If A (t) is the sum of even and odd functions, then the output spectrum is asymmetric under any conditions.
The phase of the chirp is even and the amplitude is even. 
And 
The output spectrum is symmetrical.
A (t) = even function + odd function, and q (t) is an even function.
.The spectrum turned out to be asymmetric.
Narrowband signal
It means any signal in which the frequency band occupied by the signal is significantly less than the carrier frequency:.
Where A s (t) is the in-phase amplitude, B s (t) is the quadrature amplitude.
Complex amplitude of a narrowband signal 
.
,
Where is the rotation operator.
The simplest hesitation 
can be presented in the form 
, where . In this expression, the envelope A (t), in contrast to A about, is a function of time, which can be determined from the condition of preserving the given function a (t)
It can be seen from this expression that the new function A (t) is essentially not an “envelope” in the conventional sense, since it can intersect the curve a (t) (instead of touching at the points where A (t) has a maximum value). That is, we did not correctly determine the envelope and frequency. There is a method of instantaneous frequency - the Hilbert method for determining the frequency.
If the signal then
The full phase of the signal, and the instantaneous frequency 
Physical envelope 
.
Suppose that we chose the reference frequency not w о, but w о + Dw, then
, where .
First
The modulus of the complex envelope is equal to the physical envelope and is constant, independent of the choice of frequency.
Second complex envelope property:
The signal modulus s (t) is always less than or equal to u s (t). Equality occurs when cos w o t = 1. At these moments, the signal derivative and the envelope derivative are equal.
The physical envelope matches the maximum signal amplitude.
Knowing the complex envelope, you can find its spectrum, and through it the signal itself.
,
.
Knowing G (w), we find U s (t).
Multiply by (-b-jt) and get the real and imaginary parts, respectively 
, 
... From here the amplitude will be 
.
^
Analytical signal
Let there be a signal s (t) defined as 
... Let's divide it into two parts 
.
In that expression 
–– analytical signal. If you enter a variable then. That is, we got 
... There is a real signal 
, the Hilbert conjugate signal 
... There is an analytical signal 
.
, 
–– direct and inverse Hilbert transform.
Determination of the carrier and envelope by the Hilbert method
Signal amplitude 
, its phase 
... Instantaneous frequency value 
.
Example: . .
–– precise definition of the envelope. The use of the Hilbert method allows one to give unambiguous and absolutely reliable values of the envelope and instantaneous frequency of the signal.
–– any signal can be expanded in a Fourier series.
–– Hilbert conjugate signal.
If the signal is represented not by the Fourier series, but by the Fourier integral, then the following relations are valid 
, 
.
^
Analytical signal properties
The product of the analytical signal z s (t) by its conjugate signal z s * (t) is equal to the square of the envelope of the original (physical) signal s (t).
Otherwise, where.
Hilbert transform for narrowband process
Let, then the Hilbert conjugate signal 
.
Based on this, we get
Properties of Hilbert transforms
–– the Hilbert transform, where Н () is the transformation operator. 
Example... The s (t) signal is an ideal low frequency signal.
Frequency and time characteristics
radio circuits
Let there be a linear active bipolar network.
1. Transfer function 
... It characterizes the change in the output signal relative to the input signal. The module is called the frequency response or simply the frequency response. The argument is phase-frequency response, or simply phase.
2. Impulse response 
–– the reaction of the circuit to a single impulse. It characterizes the change in the signal over time. The connection with the transfer function is carried out through the inverse and direct Fourier transform (respectively) 
... Or through the Laplace transform 
.
3. The transient function is the reaction of the chain to a single jump. This is the accumulation of the signal over time t.
^
Aperiodic amplifier
Equivalent circuit of the simplest aperiodic amplifier. The amplifying device is presented in the form of a current source SE 1 with internal conductivity G i = 1 / R i. Capacitance C includes the interelectrode capacitance of the active element and the capacitance of the external circuit shunting the load resistor R n.
The transfer function of such an amplifier
,
where S is the slope of the active element, E 1 is the voltage at the input.
Maximum gain (at) 
... From here 
, where is the delay time.
Transfer characteristic module 
–– AFC. That is, this amplifier only passes the signal in a certain frequency band. PFC –– 
.
Radio circuits and elements used to implement the signal and oscillation transformations listed in § 1.2 can be divided into the following main classes:
linear circuits with constant parameters;
linear circuits with variable parameters;
nonlinear circuits.
It should be pointed out immediately that in real radio devices, a clear selection of linear and non-linear circuits and elements is not always possible. The assignment of the same elements to linear or non-linear often depends on the level of the signals acting on them.
Nevertheless, the above classification of circuits is necessary for understanding the theory and technique of signal processing.
Let us formulate the main properties of these chains.
2. LINE CIRCUITS WITH CONSTANT PARAMETERS
You can proceed from the following definitions.
1. A circuit is linear if the elements included in it do not depend on the external force (voltage, current) acting on the circuit.
2. The linear chain obeys the principle of superposition (overlay).
In mathematical form, this principle is expressed by the following equality:
where L is an operator characterizing the effect of the circuit on the input signal.
The essence of the superposition principle can be formulated as follows: when several external forces act on a linear circuit, the behavior of the circuit (current, voltage) can be determined by superimposing (superposition) the solutions found for each force separately. You can also use the following formulation: in a linear chain, the sum of effects from individual influences coincides with the effect from the sum of influences. In this case, it is assumed that the chain is free from the initial energy reserves.
The superposition principle underlies the spectral and operator methods for analyzing transient processes in linear circuits, as well as the superposition integral method (Duhamel integral). Applying the principle of superposition, any complex signals when they are transmitted through linear circuits can be decomposed into simple, more convenient for analysis (for example, harmonic).
3. For any arbitrarily complex action in a linear circuit with constant parameters, no oscillations of new frequencies arise. This follows from the fact that when a linear circuit with constant parameters is harmonically influenced, the oscillation at the output also remains harmonic with the same frequency as at the input; only the amplitude and phase of the oscillation change. Having decomposed the signals into harmonic oscillations and substituting the results of the decomposition into (1.1), we will make sure that only oscillations with frequencies included in the input signal can exist at the output of the circuit.
This means that none of the transformations of signals, accompanied by the appearance of new frequencies (i.e., frequencies that are absent in the spectrum of the input signal), can, in principle, be carried out using a linear circuit with constant parameters. Such circuits are widely used for solving problems not related to spectrum transformation, such as linear amplification of signals, filtering (by frequency), etc.
3. LINE CIRCUITS WITH VARIABLE PARAMETERS
These are circuits, one or several parameters of which change over time (but do not depend on the input signal). These are often referred to as linear parametric circuits.
Properties 1 and 2 formulated in the previous subsection are also valid for linear parametric chains. However, in contrast to the previous case, even the simplest harmonic effect creates in a linear circuit with variable parameters a complex vibration with a frequency spectrum. This can be illustrated by the following simplest example. Let to a resistor, the resistance of which changes in time according to the law
harmonic EMF applied
Resistance current
As you can see, the current contains components with frequencies that are not present in. Even from this simplest model it is clear that by changing the resistance over time, it is possible to transform the spectrum of the input signal.
A similar result, albeit with more complex mathematical calculations, can be obtained for a circuit with variable parameters containing reactive elements - inductors and capacitors. This issue is discussed in chap. 10. Here we just note that the linear circuit with variable parameters transforms the frequency spectrum of the impact and, therefore, can be used for some signal transformations accompanied by the transformation of the spectrum. From what follows, it will also be seen that a periodic change in time of the inductance or capacitance of the oscillatory circuit allows, under certain conditions, to "pump" energy from an auxiliary device that changes this parameter ("parametric amplifiers" and "parametric generators", Ch. 10).
4. NON-LINEAR CHAINS
A radio circuit is nonlinear if it includes one or more elements, the parameters of which depend on the input signal level. The simplest nonlinear element is a diode with a current-voltage characteristic shown in Fig. 1.4.
Let's list the main properties of nonlinear circuits.
1. The principle of superposition is inapplicable to nonlinear circuits (and elements). This property of nonlinear circuits is closely related to the curvature of the current-voltage (or other similar) characteristics of nonlinear elements, which violates the proportionality between current and voltage. For example, for a diode, if the voltage corresponds to the current and the voltage corresponds to the current, then the total voltage will correspond to a current different from the sum (Fig. 1.4).
From this simple example, it is clear that when analyzing the effect of a complex signal on a nonlinear circuit, it cannot be decomposed into simpler ones; it is necessary to look for the response of the circuit to the resulting signal. The inapplicability of the principle of superposition for nonlinear circuits makes spectral and other methods of analysis based on the decomposition of a complex signal into components unsuitable.
2. An important property of a nonlinear circuit is the transformation of the signal spectrum. When a nonlinear circuit is exposed to the simplest harmonic signal in the circuit, in addition to oscillations of the fundamental frequency, harmonics with frequencies that are multiples of the fundamental frequency (and in some cases, a constant component of current or voltage) arise. In the future, it will be shown that with a complex signal shape in a nonlinear circuit, in addition to harmonics, there are also oscillations with combination frequencies, which are the result of the interaction of individual oscillations that make up the signal.
From the point of view of transforming the signal spectrum, it is necessary to emphasize the fundamental difference between linear parametric and non-linear circuits. In a nonlinear circuit, the structure of the spectrum at the output depends not only on the shape of the input signal, but also on its amplitude. In a linear parametric circuit, the structure of the spectrum does not depend on the signal amplitude.
Free oscillations in nonlinear circuits are of particular interest for radio engineering. Such oscillations are called self-oscillations, since they arise and can stably exist in the absence of external periodic influence. The power consumption is compensated by a DC power source.
The main radio engineering processes: generation, modulation, detection and frequency conversion are accompanied by the transformation of the frequency spectrum. Therefore, these processes can be carried out using either nonlinear or linear parametric circuits. In some cases, both non-linear and linear parametric circuits are used simultaneously. In addition, it should be emphasized that nonlinear elements work in combination with linear circuits that separate the useful components of the transformed spectrum. In this regard, as already noted at the beginning of this section, the division of circuits into linear, nonlinear and linear parametric is very arbitrary. Usually, to describe the behavior of various nodes of the same radio engineering device, it is necessary to use a variety of mathematical methods - linear and nonlinear.
Rice. 1.4. Current-voltage characteristic of a nonlinear element (diode)
The above basic properties of circuits of three classes - linear with constant parameters, linear parametric and nonlinear - are preserved for any form of circuit implementation: with lumped parameters, with distributed parameters (lines, radiating devices), etc. These properties also apply to devices digital signal processing.
However, it should be emphasized that the principle of superposition underlying the division of circuits into linear and nonlinear ones was formulated above for the operation of summing signals at the circuit input [see. (1.1). However, this operation does not exhaust the requirements for modern signal processing systems. It is important for practice, for example, the case when the signal at the input of the circuit is the product of two signals. It turns out that for such signals it is possible to carry out processing that obeys the principle of superposition, but this processing will be a combination of specially selected nonlinear and linear operations. Such processing is called homomorphic.
The synthesis of such devices is considered at the end of the course (see Chapter 16), after studying linear and nonlinear circuits, as well as digital signal processing, the development of which was the impetus for the widespread use of homomorphic processing.
"APPROVED"
Vice Rector for Academic Affairs
_____________ V. G. Prokoshev
"____" ______________ 2011
THE WORKING PROGRAM OF THE DISCIPLINE
"Radio circuits and signals"
(name of the discipline)
Direction of training 210400 "Radio Engineering"
Provisioning profiles "Radiotekhnika", "Radiophysics"
Qualification (degree) of the graduate Bachelor
Form of study full-time
| Semester | Labor intensity (credit units / hour) | Lectures (hours) | Practice. occupations (hour.) | Laborat. works (hour.) | Well. slave. (hour.) | CPC | form of control (copies / credit) |
| 4 | 4/144 | 34 | 17 | 17 | --- | 76 | Offset |
| 5 | 3/108 | 17 | 17 | 17 | 30 | 27 | Exam, pass (cr) |
| Total | 7/252 | 51 | 34 | 34 | 30 | 103 | Exam, pass (cr) |
Vladimir, 2011
Objectives of mastering the discipline
The purpose of mastering the discipline "Radio circuits and signals" is: instilling in students, firstly, a deep understanding of the properties of various radio signals and radio circuits, the essence and features of the processes occurring when signals pass through radio circuits; secondly, the ability to analytically describe, analyze and experimentally investigate processes in radio circuits on the basis of the methods and techniques emitted in the course, thereby laying the foundation for theoretical and practical knowledge and skills used in the study of special disciplines by students in the specialty "Radio Engineering". Training in the field of radio engineering for various areas of professional activity of a specialist:
design and engineering;
production and technological;
research;
organizational and managerial;
installation and commissioning;
service and operational.
The task of the discipline is to teach the student knowledge of
classification, fundamental properties and basic characteristics of radio signals and radio circuits in the time and frequency domains, the laws of signal transformation in various radio circuits;
methods for analyzing the transmission of deterministic and random oscillations through linear (with constant parameters), parametric, nonlinear and discrete circuits, the limits of applicability and properties of the methods;
methods of storing and extracting information from radio signals, principles of constructing devices for these purposes, sources and methods of reducing errors and distortions of the transmitted message;
the basics of chain synthesis;
methods of optimal filtering of signals;
The place of discipline in the structure of the PLO HPE
The discipline "Radio circuits and signals" refers to general disciplines:
The code of the educational center of the educational program of the educational cycle of the main educational program (section) - B3;
Professional cycle;
Basic (general education) part.
Relationship with other disciplines
The course "Radio circuits and signals" is based on the knowledge of "Mathematics", "Physics", "Electronics", "Digital devices and microprocessors", "Circuitry of analog electronic devices", "Fundamentals of circuit theory", "Electrodynamics and propagation of radio waves" and is the basis for the study of "Transmitters and Signal Forming Devices", "Signal Receiving and Processing Devices", "Radio Engineering Systems", "Radio Automation", etc.
Trainee competencies. Formed as a result of mastering the discipline
As a result of mastering the discipline, the student must have the following general cultural competencies (GC)
The ability to master the culture of thinking, the ability to generalize, analyze, perceive information, set a goal and choose ways to achieve it (OK-1)
The ability to logically correctly, reasonably and clearly build oral and written speech (OK-2)
The ability to cooperate with colleagues, work in a team (OK-3)
The ability to use the basic laws of natural sciences in professional activities, to apply the methods of mathematical analysis and modeling, theoretical and experimental research (OK-10),
The ability to present a scientific picture of the world adequate to the modern level of knowledge based on knowledge of the basic provisions, laws and methods of natural sciences and mathematics (PC-1)
The ability to identify the natural scientific essence of problems arising in the course of professional activity, to attract the appropriate physical and mathematical apparatus for their solution (PC-2)
Willingness to take into account modern trends in the development of electronics, measuring and computing technology, information technology in their professional activities (PC-3)
Ability to master methods for solving problems of analysis and calculating the characteristics of electrical circuits (PC-4)
Ability to master the basic techniques of processing and presenting experimental data (PC-5)
The ability to collect, process, analyze and systematize scientific and technical information on research topics, use the achievements of domestic and foreign science, technology and technology (PC-6)
The ability to collect and analyze initial data for the calculation and design of parts, assemblies and devices of radio engineering systems (PC-9)
Readiness to calculate and design parts, assemblies and devices of radio engineering systems in accordance with the terms of reference using design automation tools (PC-10)
Willingness to organize metrological support of production (PK-16)
The ability to collect and analyze scientific and technical information, generalize domestic and foreign experience in the field of radio engineering, analyze patent literature (PC-18)
The ability to implement programs of experimental research, including the choice of technical means and processing of results (PC-20)
The ability to perform tasks in the field of certification of technical means, systems, processes, equipment and materials (PC-25)
The ability to carry out verification, commissioning and adjustment of equipment and adjustment of software tools used for the development, production and adjustment of radio technical devices and systems (PK-27)
The ability to take part in the organization of maintenance and tuning of radio technical devices and systems (PC-29)
Willingness to check the technical condition and residual life of equipment, organize routine inspections and routine repairs (PK-30)
Ability to develop operating instructions for technical equipment and software (PC-32)
As a result of mastering the discipline, the student must:
Know:
the main types of active devices, their models and methods of their quantitative description when used in radio circuits and devices;
methods for analyzing DC and AC circuits in the time and frequency domains;
basic methods for measuring the characteristics of radio circuits and signals, assessing their reliability and accuracy;
the main types of deterministic and random signals in radio engineering and methods of their transformation;
standard packages of applied programs focused on solving scientific and design problems of radio electronics;
principles of construction of signal processing devices in radio systems and complexes for various purposes;
Be able to:
use standard software packages to solve practical problems;
to use computer systems and software packages for the design and research of radio engineering devices;
to apply statistical theories of detection and discrimination of signals, estimation of their parameters and filtering of information processes;
use the theory of optimal signal reception when designing radio systems for transmitting information;
Own:
methods and tools for the development and execution of technical documentation;
models of active devices used in radio engineering;
methods of analysis of electrical circuits in stationary and transient modes;
spectral methods of analysis of deterministic and random signals and their transformations in electrical circuits;
standard software for design automation and modeling of electronic circuits, devices and systems;
statistical methods of analysis and synthesis of radio engineering systems and devices.
STRUCTURE AND CONTENT OF THE DISCIPLINE
4.1. Theoretical course
4.1.1. Introduction
Requirements of the curriculum and work program for the discipline. Points of the rating system of attestation of students. Recommendations for the study of the course, the relationship with other disciplines.
Literature. Block diagram of the information transmission system. Basic radio engineering processes. Basic concepts, terms and definitions.
The subject and objectives of the discipline, its place in the knowledge system of an engineer. The role of radio engineering in scientific research and industrial production.
Requirements for term paper.
4.1.2. The main characteristics of the signals. Signal classification.
Typical radio circuits. Classification criteria. Deterministic and random, continuous, discrete, quantized and digital signals, control and modulated oscillations. Features of the propagation of radio waves of various bands.
4.1.3. Spectral analysis of periodic signals.
Generalized Fourier series. Harmonic analysis of periodic signals.
4.1.4. Spectral analysis of non-periodic signals.
Fourier transform and its properties.
4.1.5. Distribution of power in the spectrum of a periodic signal and energy in the spectrum of a non-periodic signal
Independence of the average power of a periodic signal from the phases of individual harmonics. Parseval's equality. The relationship between signal duration and spectrum width (Riemann's lemma). Examples.
4.1.6. Single impulse and single leap
The concept of a delta function (impulse) as a limiting expression of some impulses of a unit area. Delta-function in the time and frequency domains, its spectrum and properties. Single jump, methods of its introduction, connection with the delta function, spectrum. Conclusions.
4.1.7. Correlation analysis of deterministic fluctuations.
The concept of the correlation function of a deterministic signal, its properties, connection with the spectral characteristic. Cross correlation function. Coherence. Examples.
4.1.8. Discretization of signals. Kotelnikov's theorem and series.
Representation of signals with a limited frequency band in the form of a Kotelnikov series. The number of degrees of freedom of the signal. Frequency domain sampling theorem.
4.1.9. Linear radio circuits with constant parameters.
Definition and basic properties of linear circuits. Frequency response and phase response of aperiodic and resonant amplifiers. Methods for determining the frequency response and phase response. Examples. Ideal and real differentiating and integrating circuits, their frequency response and phase response, the use of operational amplifiers. Comparison of time characteristics of ideal and real circuits.
4.1.10. Linear feedback circuits.
Main characteristics of feedback systems. Stability criteria. Negative feedback. Systems with a delay in a loop with feedback. Impulse response of an ideal and real comb filter.
4.1.11. Radio signals, AM vibrations and their spectra.
Conditions for the slowness of changes in amplitude, phase, frequency. AM vibrations, basic concepts and definitions. Amplitude modulation. Spectrum and vector diagram of AM oscillations during modulation with a harmonic and complex signal. Examples.
4.1.12. Angle modulation. Oscillation spectrum with PA.
Phase and instantaneous frequency of oscillation. Oscillation spectrum at PA. Signal spectrum. Communication FM and FM. Radio pulse with chirp signal with a large base.
4.1.13. Oscillation spectrum with mixed amplitude-angular modulation.
General presentation of such fluctuations. Oscillation spectrum with mixed amplitude-phase modulation by a harmonic signal of one frequency (2 cases). Reasons for spectrum asymmetry.
4.1.14. Narrowband envelope, frequency and phase.
The ambiguity of determining the envelope and phase of a narrow-band oscillation. Establishment of ambiguity by introducing an additional, Hilbert-conjugate signal. Basic relationships. Envelope properties, determination of instantaneous frequency and phase of oscillation for a given signal. An example of a biharmonic vibration.
4.1.15. Analytical signal.
Generalization of the concept of complex amplitude. Complex envelope concept. Analytical (complex) signal and its relationship with a given physical signal, properties and relationship of the spectra of the original signal, envelope, complex envelope and analytical signal. Analytical signal properties and Hilbert transform.
4.1.16. Discretization of a narrow-band oscillation according to Kotelnikov.
Relationship of the period (frequency) of the samples with the envelope spectrum and the phase of the modulated oscillation. The difference in the information capacity of signals with different types of modulation.
4.1.17. Passage of deterministic oscillations through linear circuits with constant parameters.
Methods for analyzing the passage of oscillations in linear circuits. Spectral method. Example. Integral overlay method. Example.
4.1.18. Effects of radio signals on selective circuits.
Features of signal transmission through selective circuits. Approximate spectral method, simplified superposition integral method. Features of their application.
4.1.19. Distortion of modulated oscillations in selective circuits.
Distortion of AM signals. Distortion of FM and FM signals. Instantaneous frequency method on the example of a resonant amplifier.
4.1.20. Nonlinear circuits and methods of nonlinear theory. Non-linear elements, their characteristics and properties.
Non-linear elements. Approximation of nonlinear characteristics. Spectrum transformations in a circuit with a resistive nonlinear element under the action of one and two sinusoidal voltages. Combination frequency theory. Filtered non-linear circuit.
4.1.21. Receiving and detecting AM vibrations.
Getting AM_vibrations. Detection of AM oscillations. Conditions for undistorted detection of oscillations.
4.1.22. Frequency and phase detection, signal frequency conversion, synchronous detection.
Principles of construction of frequency and phase detectors, features of frequency converters, synchronous signal detection.
4.1.23. The structure of a self-oscillating system.
Definition of the oscillatory system. Oscillator structure. The mechanism of the occurrence of self-oscillations. Conditions for the balance of phases and amplitudes. The steady-state mode of the generator. Soft and hard generator mode. Soft and hard modes of self-excitation. Frequency stability. Oscillator nonlinear equation. Autogenerators with an oscillating circuit, with internal feedback, PC generators. Angular modulation in an oscillator.
4.1.24. Parametric chains.
Principles of implementation of parametric circuits and their basic properties. Passage of oscillations through parametric circuits. Transmission function.
4.1.25. Impulse response of a parametric circuit.
Obtaining an impulse response for a first-order circuit. Example. Differences from a chain with constant parameters.
4.1.26. The principle of parametric amplification.
The principle of parametric amplification. Obtaining the equivalent circuit of reactivity, changing according to the harmonic law. Single-loop parametric amplifier.
4.1.27. Application of parametric circuits.
Parametric modulators, detectors, frequency converters.
4.1.28. Characteristics of random fluctuations.
Classification of random processes. Distribution laws of random processes. Stationary stochastic processes. Ergodic property.
4.1.29. Description of random signals in the frequency and time domains.
Power spectral density and correlation function of a random process. Wiener-Khinchin theorem. Model of a random process in the form of "white noise". Examples.
4.1.30. Narrowband random processes.
Decomposition of the signal into quadrature independent components. Obtaining the distribution laws of the correlation function of the envelope, frequency and phase of narrow-band normal noise.
4.1.31. Markov processes.
Basic definitions. Generalized Markov equation. Areas of application of Markov processes.
4.1.32. Conversion of characteristics of a random process.
Determination of the spectral power density and the correlation function of the output signal. Effect of "white" noise on linear circuits.
4.1.33. Propagation of the sum of harmonic oscillations with random phases.
The method of characteristic functions and its application for estimating the distribution of the sum of harmonic oscillations with random phases.
4.1.34. Normalization of random processes in narrow-band circuits.
The effect of a sequence of identical pulses with a random phase on a narrow-band system, the effect of FM oscillations with a random modulation period on a narrow-band system. Conditions under which normalization will occur. Denormalization.
4.1.35. Effect of the sum of harmonic signal and noise on the amplitude detector.
Distribution law and correlation function of noise passed through the detector. Basic relations when passing through the detector of an additive mixture of a noise signal. Signal-to-Noise Ratio.
4.1.36. Effect of Signal and Noise on the Frequency Detector and the Amplitude Resonance Limiter.
Static characteristics of the signal at the output of the circuit. Signal-to-noise ratio at the output at different ratios at the output.
4.1.37. Transformation of the distribution law and energy spectrum in a non-inertial nonlinear element.
Transformation of the distribution law in a linear element with an unambiguous and ambiguous inverse characteristic. Methods for finding the energy characteristics of a process at the output of a nonlinear circuit.
4.1.38. Optimal filtering against background noise.
The concept of the main tasks of statistical radio engineering on the examples of various systems. Matched filtering of the target signal. Schwarz's inequality.
4.1.39. Frequency and time characteristics of the matched filter. Physical feasibility.
The frequency response of the filter and its relationship to the frequency spectrum of the input signal. Filter impulse response and its relationship to the input signal. Paley-Wiener criterion.
4.1.40. Signal and noise at the output of the matched filter.
The form of the useful signal at the output. Correlation functions of deterministic signals. Examples.
4.1.41. Examples of constructing consistent filters.
Synthesis and finding a signal at the output of matched filters, when a burst of identical pulses is at the input, a pulse with a chirp. Comb filter.
4.1.42. Formation of a signal coupled with a given filter.
The principle of shaping a signal matched to this filter.
4.1.43. Filtration of a given signal when there is no white noise.
Noise whitening procedure. Constructing a matched filter.
4.1.44. Barker codes.
M - positional codes. Block diagram of the matched filter for the Barker code.
4.2. Practical lessons
Practical lessons are focused on solving problems and examples corresponding to the theoretical course and serving to apply the knowledge gained to solving applied problems. Design assignments have been introduced for some sections with the involvement of computer technology in order to facilitate and accelerate computational work, the study of nonlinear problems that are not amenable to analytical solutions, and the modeling of processes and circuits.
Topic 1. Spectral analysis of periodic signals.
Purpose of the lesson: Application of Fourier series for spectral analysis of periodic signals of various shapes. In the classroom, students gain skills in determining signal spectra. The result of the lesson is the ability of students to determine the amplitude and phase spectrum of periodic signals.
Topic 2. Spectral analysis of non-periodic signals.
Purpose of the lesson: Application of integral Fourier transform for spectral analysis of non-periodic signals. When determining the signal spectra, students acquire the skills to analyze the spectrum of control signals, learn to determine the effective width of the signal spectrum.
Topic 3. Signal transmission through linear circuits with constant parameters.
Purpose of the lesson: Analysis of the passage of signals through linear circuits. Students learn to apply the spectral position integral method when analyzing signal transmission through linear circuits, and become familiar with the impulse response of various linear circuits with constant parameters.
Topic 4. Analysis of amplitude-modulated signals.
Purpose of the lesson: Study of the structure of the spectrum of AM vibrations. Students in the lesson define the spectra of AM vibrations with different envelopes, spectral and vector diagrams of AM signals.
Topic 5. Analysis of radio signals with angular modulation.
Purpose of the lesson: Study of the structure of the spectrum of oscillations with angular modulation. Students learn to distinguish between phase and frequency modulated radio signals, to determine the effective spectrum width of such radio signals.
Topic 6. Transmission of radio signals through electoral circuits.
Purpose of the lesson: Obtaining skills in applying methods of analyzing the transmission of radio signals through electoral circuits. The analysis is based on the approximate characteristics of the electoral circuits - amplitude-frequency and pulse. Comparison with exact methods is given.
Topic 7. Approximation of current-voltage characteristics of nonlinear circuits.
Purpose of the lesson: Study of possible modes of operation of nonlinear elements. Based on this, students acquire skills in the development of modulator circuits, detectors, mixers.
Topic 8. Modulation and demodulation.
Purpose of the lesson: calculation of modulator and demodulator circuits. Students get acquainted with practical circuits of non-linear elements, with the help of which signals are converted and methods for their calculation.
Topic 9. Random processes. Characteristics of stochastic processes.
Purpose of the lesson: Getting the skills to apply the theory of probability to the analysis of stochastic processes. Students get acquainted with the laws of probability distribution of radio signals, determine their numerical characteristics.
Topic 10. Transfer of random processes through linear chains.
Purpose of the lesson: Obtaining the skills of analyzing the characteristics of a random process when transmitting it through linear chains. Students learn and apply analytical methods for a variety of purposes.
Topic 11. Transfer of random processes through nonlinear circuits.
Purpose of the lesson: Studying the transmission of random processes through standard radio engineering units. Students should calculate the characteristics of random signals when they are transmitted through circuits - a non-linear element plus a load (typical nodes).
Topic 12. Consistent filters.
Purpose of the lesson: Mastering the techniques of the matched filter response to a given signal and the synthesis of the filter structure for some signals. Students calculate the correlation functions of various signals, synthesize matched filters for given signals, determine the signal-to-noise ratio at the input and output of the filter.
4.3. Laboratory works.
The laboratory practice on the course "Radio circuits and signals" is designed to consolidate theoretical knowledge, acquire skills and study experimental research methods, various signals, circuits and their characteristics, and provides for the implementation of 8 laboratory works for 4 academic hours (two are allocated for independent work on compiling the plan of experimental research on the topic proposed by the teachers). The work is carried out in two cycles, by teams of 2-3 students (taking into account the division of the academic group into 2 subgroups).
For the work performed, each student draws up a report of the AO in the established form. Timely defense of work is the basis for credit for laboratory practice.
Topic 1. Typical linear radio circuits.
Topic 2. Spectral analysis.
Topic 3. Modulation of signals.
Topic 4. Transistor autogenerators.
Topic 5. Passage of amplitude-modulated oscillations through selective circuits.
Topic 6. Laws of distribution of random processes.
Topic 7. Correlation analysis of signals.
Topic 8. Transformation of correlation functions in linear radio circuits.
4.4. Course work.
In a typical term paper, students calculate the signal and its spectrum at the output of a specific radio circuit or find the optimal filter option for a given signal and noise.
In the course project you must:
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