Basic radio engineering processes and their characteristics. Radio engineering signals

Basic radio engineering processes

1. 
   Converting the original message into an electrical signal.
2. 
   Generation of high-frequency oscillations.
3. 
   Oscillation control (modulation).
4. 
   Amplification of weak signals in the receiver.
5. 
   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:

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).

,

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.

1. 
   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:

1. 
   To non-linear circuits (and elements) superposition principle is not applicable.
2. 
   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:

1. 
   ^ Exact decomposition into simplest orthogonal functions (signal analytic model, signal behavior analysis).

This task is realized on trigonometric basis functions, since they have the simplest form and are the only functions that retain their shape when passing through linear chains; when using these functions, you can use the symbolic method ().

1. 
   ^ 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

1. 
   Rectangular wobble... A similar hesitation, often called meander(Meander is the Greek word for "ornament") is especially widely used in measuring technology.

^ Harmonic analysis of non-periodic signals

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

1. 
   Let s (t) be an even function with respect to time.

Then . Since the second integral of an odd function in symmetric limits is equal to zero. That is, the function S (W) is real and even with respect to W.

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.

1. 
   A (t) = even function + odd function, and q (t) is an even function.

Suppose that, where .

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

1. 
   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 –– .

From the preceding it is seen how various transformations the signal undergoes in the process of transmission over the communication channel. Some of these processes are mandatory for most radio engineering systems, regardless of their purpose, as well as the nature of the transmitted messages. Let us list these fundamental processes and, along the way, note their main features in relation to the generalized scheme of a radio engineering channel shown in Fig. 1.1.

Converting the original message into an electrical signal and encoding... When transmitting speech and music, such a transformation is carried out using a microphone, when transmitting images (television) - using transmitting tubes (for example, a superortikon). When transmitting a written message (radiotelegraphy), coding is first performed, which means that each letter of the text is replaced by a combination of standard characters (for example, dots, dashes and pauses in Morse code), which are then converted into standard electrical signals (for example, pulses of different durations or different polarity).

It should be noted that the circuit in Fig. 1.1 corresponds to the case when information is entered "at the beginning" of the communication channel, that is, directly at the transmitter. The situation is somewhat different, for example, in a radar channel, where information about a target (range, altitude, speed, etc.) is entered as a result of the reflection of a radio wave from a target in free space.

Generation of high frequency vibrations... The high frequency generator is the source of carrier frequency oscillations. Depending on the purpose of the radio communication channel, the oscillation power varies from thousandths of a watt to millions of watts. Naturally, the design forms and sizes of these generators are different - from the simplest small-sized element to a grandiose technical structure.

The main characteristics of a high-frequency generator are frequency and range (the ability to quickly change from one operating frequency to another), power and efficiency. The stability of the vibration frequency is especially important. Radio engineering is in an exceptional position in this respect. The propagation conditions of radio waves and the wide spectrum of signal frequencies dictate the use of very high carrier frequencies. The conditions of signal processing against the background of interference and the need to mitigate mutual interference between different radio channels make it necessary to achieve the maximum possible reduction in absolute frequency changes. This leads to extremely stringent requirements for relative frequency stability.

Oscillation control (modulation)... The modulation process consists in changing one or several parameters of the high-frequency oscillation according to the law of the transmitted message. The frequencies of the modulating signal, as a rule, are small in comparison with the carrier frequency of the generator. Various techniques are used to implement modulation, usually based on changing the potential of the electrodes of electronic devices included in the circuit of the radio transmitting device. The main characteristic of the modulation process is the degree of correspondence between the change in the high-frequency oscillation parameter and the modulating signal.

Strengthening Weak Signals at the Receiver... The receiver antenna captures a negligible fraction of the energy emitted by the transmitter antenna. Depending on the distance between the transmitting and receiving stations, the degree of directivity of the antenna radiation and the conditions of radio wave propagation, the power at the receiver input is 10 -10 ... 10 -14 W. At the output of the receiver, for reliable signal registration, a power of the order of milliwatts, units of watts or more is required. From this it can be seen that the gain in the receiver should reach 10 7 ... 10 14 in terms of power or 10 4 ... 10 7 in terms of voltage.

In modern receivers, reliable signal registration is provided at input voltages of the order of a microvolt. The solution to this complex problem is made possible by the achievements of modern electronics. An important role is also played by special methods for constructing receiver circuits, which provide high gain while maintaining the stability of the receiver. These methods include the conversion (lowering) of the oscillation frequency in the receiver path, carried out in such a way that the structure of the transmitted signal is preserved (in the diagram in Fig. 1.1, the frequency conversion process is not indicated). In addition to receiving devices, the frequency conversion process is widely used in various radio engineering and radio measuring devices.

The problem of gain in the receiver is inseparable from the problem of separating the signal from the background noise. Therefore, one of the main parameters of the receiver is selectivity, which means the ability to separate useful signals from the totality of the signal and extraneous influences (interference) that differ from the signal in frequency. Frequency selectivity is carried out using resonant oscillatory circuits.

Separation of a message from a high-frequency waveform (detection and decoding)... Detection is the reverse process of modulation. As a result of detection, a voltage (current) should be obtained that changes in time in the same way as one of the parameters (amplitude, frequency or phase) of the modulated oscillation changes. In other words, the transmitted message must be restored. The detector, as a rule, is switched on at the output of the receiver, therefore, a modulated oscillation is applied to it, already amplified by the previous steps of the receiver. The main requirement for a detector is an accurate reproduction of the waveform.

After detection, the signal is decoded, that is, the process is the reverse of the encoding. In a number of radio-technical channels, coding and decoding are not used.

In addition to the listed processes, one way or another related to the transformation of frequency spectra, amplification of oscillations without frequency transformation, carried out in various amplifiers, is widely used in radio engineering devices. These amplifiers include:

Low-frequency amplifiers of control signals used in front of the transmitter modulator, as well as at the output of the receiver;

Amplifiers of short impulses used in television and radar technology, as well as in impulse radio communication systems;

High frequency high power amplifiers used in radio transmitting devices;

High-frequency amplifiers of weak signals used in radio receiving and measuring devices.

In addition to the processes mentioned, which, as already noted, are inherent in any radio engineering line, in a number of special cases many other processes are widely used: frequency multiplication and division, generation of short pulses, various types of pulse modulation, etc.

Chapter 1 Elements of the General Theory of Radio Engineering Signals

The term "signal" is often found not only in scientific and technical issues, but also in everyday life. Sometimes, without thinking about the severity of terminology, we identify concepts such as signal, message, information. This usually does not lead to misunderstandings, since the word "signal" comes from the Latin term "signum" - "sign", which has a wide semantic range.

Nevertheless, starting a systematic study of theoretical radio engineering, it is necessary, if possible, to clarify the meaning of the concept of "signal". In accordance with the accepted tradition, a signal is called a process of changing in time the physical state of an object, which serves to display, register and transmit messages. In the practice of human activity, messages are inextricably linked with the information contained in them.

The range of issues based on the concepts of "message" and "information" is very wide. It is the object of close attention of engineers, mathematicians, linguists, philosophers. In the 40s, K. Shannon completed the initial stage of developing a deep scientific direction - information theory.

It should be said that the problems mentioned here, as a rule, go far beyond the scope of the course "Radio circuits and signals". Therefore, this book will not describe the relationship that exists between the physical appearance of the signal and the meaning of the message contained in it. Moreover, the question of the value of the information contained in the message and, ultimately, in the signal will not be discussed.

1.1. Classification of radio engineering signals

When starting to study any new objects or phenomena, science always strives to carry out their preliminary classification. Below, such an attempt is made in relation to signals.

The main goal is to develop classification criteria, as well as, which is very important for the subsequent one, to establish a certain terminology.

Description of signals by means of mathematical models.

Signals as physical processes can be studied using various instruments and devices - electronic oscilloscopes, voltmeters, receivers. This empirical method has a significant drawback. The phenomena observed by the experimenter always appear as particular, isolated manifestations, devoid of the degree of generalization that would make it possible to judge their fundamental properties, to predict the results under changed conditions.

In order to make signals objects of theoretical study and calculations, one should indicate the method of their mathematical description or, in the language of modern science, create a mathematical model of the signal under study.

A mathematical model of a signal can be, for example, a functional dependence, the argument of which is time. As a rule, in the future, such mathematical models of signals will be denoted by the symbols of the Latin alphabet s (t), u (t), f (t), etc.

The creation of a model (in this case, a physical signal) is the first essential step towards a systematic study of the properties of a phenomenon. First of all, the mathematical model allows one to abstract from the specific nature of the signal carrier. In radio engineering, the same mathematical model describes current, voltage, electromagnetic field strength, etc. with equal success.

The essential side of the abstract method, based on the concept of a mathematical model, lies in the fact that we get the opportunity to describe precisely those properties of signals that objectively appear as decisively important. At the same time, a large number of secondary signs are ignored. For example, in the overwhelming majority of cases it is extremely difficult to choose the exact functional dependences that would correspond to the electrical oscillations observed experimentally. Therefore, the researcher, guided by the entire set of information available to him, selects from the available arsenal of mathematical models of signals those that in a particular situation describe the physical process in the best and simplest way. So choosing a model is pretty much a creative process.

Functions describing signals can take both real and complex values. Therefore, in what follows we will often talk about real and complex signals. The use of this or that principle is a matter of mathematical convenience.

Knowing the mathematical models of signals, one can compare these signals with each other, establish their identity and difference, and carry out a classification.

One-dimensional and multidimensional signals.

A typical signal for radio engineering is the voltage at the terminals of a circuit or the current in a branch.

Such a signal, described by one function of time, is usually called one-dimensional. In this book, one-dimensional signals will most often be studied. However, it is sometimes convenient to introduce into consideration multidimensional, or vector, signals of the form

formed by some set of one-dimensional signals. An integer N is called the dimension of such a signal (the terminology is borrowed from linear algebra).

A multidimensional signal is, for example, a system of voltages at the terminals of a multipole.

Note that a multidimensional signal is an ordered collection of one-dimensional signals. Therefore, in the general case, signals with different order of components are not equal to each other:

Multivariate signal models are especially useful in cases where the functioning of complex systems is analyzed using a computer.

Deterministic and random signals.

Another principle of classification of radio-technical signals is based on the possibility or impossibility of accurately predicting their instantaneous values ​​at any time.

If the mathematical model of the signal allows such a prediction, then the signal is called deterministic. The methods of its assignment can be varied - a mathematical formula, a computational algorithm, and finally, a verbal description.

Strictly speaking, deterministic signals, as well as deterministic processes corresponding to them, do not exist. The inevitable interaction of the system with the surrounding physical objects, the presence of chaotic thermal fluctuations and simply incomplete knowledge about the initial state of the system - all this forces us to consider real signals as random functions of time.

In radio engineering, random signals often manifest themselves as interference, preventing the extraction of information from the received waveform. The problem of countering interference, increasing the noise immunity of radio reception is one of the central problems of radio engineering.

It may seem that the concept of "random signal" is controversial. However, it is not. For example, the signal at the output of a radio telescope receiver directed at a source of cosmic radiation is chaotic oscillations, which, however, carry a variety of information about a natural object.

There is no insurmountable boundary between deterministic and random signals.

Very often, in conditions where the level of interference is much less than the level of a useful signal with a known shape, a simpler deterministic model turns out to be quite adequate for the task at hand.

The methods of statistical radio engineering, developed in recent decades for the analysis of the properties of random signals, have many specific features and are based on the mathematical apparatus of the theory of probability and the theory of random processes. A number of chapters of this book will be entirely devoted to this range of questions.

Impulse signals.

A very important class of signals for radio engineering are impulses, that is, oscillations that exist only within a finite period of time. In this case, a distinction is made between video pulses (Fig. 1.1, a) and radio pulses (Fig. 1.1, b). The difference between these two main types of impulses is as follows. If - video pulse, then the corresponding radio pulse (frequency and initial are arbitrary). In this case, the function is called the envelope of the radio pulse, and the function is called its filling.

Rice. 1.1. Pulse signals and their characteristics: a - video pulse, b - radio pulse; c - determination of the numerical parameters of the pulse

In technical calculations, instead of a complete mathematical model, which takes into account the details of the "fine structure" of the pulse, they often use numerical parameters that give a simplified idea of ​​its shape. So, for a video pulse close in shape to a trapezoid (Fig.1.1, c), it is customary to determine its amplitude (height) A. From the time parameters indicate the pulse duration, the front duration and the cutoff duration

In radio engineering, they deal with voltage pulses, the amplitudes of which range from fractions of a microvolt to several kilovolts, and the durations reach fractions of a nanosecond.

Analog, discrete and digital signals.

Concluding a brief overview of the principles of classification of radio-technical signals, we note the following. Often the physical process that generates a signal develops in time in such a way that the signal values ​​can be measured in. any moments in time. Signals of this class are usually called analog (continuous).

The term "analog signal" emphasizes that such a signal is "analogous", completely similar to the physical process that generates it.

A one-dimensional analog signal is clearly represented by its graph (oscillogram), which can be either continuous or with break points.

Initially, signals of an exclusively analog type were used in radio engineering. Such signals made it possible to successfully solve relatively simple technical problems (radio communication, television, etc.). Analog signals were easy to generate, receive and process using the means available at the time.

The increased requirements for radio engineering systems, a variety of applications forced the search for new principles of their construction. In some cases, analogue systems have been replaced by pulse systems, the operation of which is based on the use of discrete signals. The simplest mathematical model of a discrete signal is a countable set of points - an integer) on the time axis, at each of which the reference value of the signal is determined. Typically, the sampling rate for each signal is constant.

One of the advantages of discrete signals over analog signals is that there is no need to reproduce the signal continuously at all times. Due to this, it becomes possible to transmit messages from different sources over the same radio link, organizing multichannel communication with time division of channels.

Intuitively, fast time-varying analog signals require small steps to sample. In ch. 5 this fundamentally important issue will be explored in detail.

A special kind of discrete signals are digital signals. They are characterized by the fact that the reading values ​​are presented in the form of numbers. For reasons of technical convenience of implementation and processing, binary numbers with a limited and usually not too large number of digits are usually used. Recently, there has been a trend towards widespread adoption of systems with digital signals. This is due to the significant advances made by microelectronics and integrated circuitry.

It should be borne in mind that in essence any discrete or digital signal (we are talking about a signal - a physical process, not a mathematical model) is an analog signal. So, a slowly changing analog signal can be compared with its discrete image, which has the form of a sequence of rectangular video pulses of the same duration (Fig. 1.2, a); the height of the ethnh impulses is proportional to the values ​​at the reference points. However, you can act differently, keeping the height of the pulses constant, but changing their duration in accordance with the current reading values ​​(Fig. 1.2, b).

Rice. 1.2. Discretization of the analog signal: a - at variable amplitude; b - with variable duration of the counting pulses

The two analog signal sampling methods presented here become equivalent if we assume that the analog signal values ​​at the sampling points are proportional to the area of ​​the individual video pulses.

Fixation of sample values ​​in the form of numbers is also carried out by displaying the latter in the form of a sequence of video pulses. The binary number system is ideally suited for this procedure. You can, for example, associate a high level with one, and a low potential level with zero, f Discrete signals and their properties will be studied in detail in Ch. 15.

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 (current of electric displacement) can be closed in the same way as the lines of force of a 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) laws of the 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 (310 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. Приl 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 EN 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.

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 of harmonic oscillations. 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 of electrical circuits" the modulator is a 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 radio engineering 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 diagram of the 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 assumes the presence of a 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 the case of representing the input signal in the form z (t) = k (t) · s (t), the interference 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.