Method of frequency modulation of a radio signal. Main characteristics of signals Types of signals used in radio electronics

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 rigor of terminology, we identify such concepts as signal, message, information. Usually this does not lead to misunderstandings, since the word "signal" comes from the Latin term "signum" - "sign", which has a wide semantic range.

Nevertheless, when embarking on a systematic study of theoretical radio engineering, one should, if possible, clarify the meaningful meaning of the concept of "signal". In accordance with the accepted tradition, a signal is the process of changing the physical state of an object over time, 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 1940s, 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 connection 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 signals

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

The main goal is to develop classification criteria, and also, which is very important for the future, 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. Phenomena observed by an experimenter always appear as particular, single manifestations, devoid of the degree of generalization that would allow one to judge their fundamental properties and predict results under changed conditions.

In order to make signals objects of theoretical study and calculations, one should indicate a method for 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 property 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 exactly those properties of signals that objectively act as decisively important. In this case, a large number of minor features are ignored. For example, in the overwhelming majority of cases it is extremely difficult to select exact functional dependences that would correspond to electrical oscillations observed experimentally. Therefore, the researcher, guided by the totality of information available to him, chooses 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, the choice of model is a largely creative process.

Functions describing signals can take both real and complex values. Therefore, in the future we will often talk about real and complex signals. The use of one principle or another 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 classify them.

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

formed by some set of one-dimensional signals. The 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 set of one-dimensional signals. Therefore, in the general case, signals with different component order are not equal to each other:

Multidimensional signal models are especially useful when the functioning of complex systems is analyzed using a computer.

Deterministic and random signals.

Another principle for the classification of radio 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 ways of setting it 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 physical objects surrounding it, the presence of chaotic thermal fluctuations, and simply the incompleteness of knowledge about the initial state of the system - all this makes us 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 combating 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 contradictory. 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 various 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 to the task.

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

impulse signals.

A very important class of signals for radio engineering are impulses, i.e., oscillations that exist only within a finite period of time. In this case, video pulses (Fig. 1.1, a) and radio pulses (Fig. 1.1, b) are distinguished. The difference between these two main types of impulses is as follows. If is a video pulse, then the radio pulse corresponding to it (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 impulse

In technical calculations, instead of a complete mathematical model that takes into account the details of the "fine structure" of the pulse, numerical parameters are often used to give a simplified idea of its shape. So, for a video pulse that is 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 duration of the pulse, the duration of the front and the duration of the cut

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

Analogue, discrete and digital signals.

Concluding a brief overview of the principles of classification of radio signals, we note the following. Often the physical process that generates the signal evolves over time in such a way that the signal values can be measured in. any points 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 visually represented by its graph (oscillogram), which can be either continuous or with break points.

Initially, only analog type signals were used in radio engineering. Such signals made it possible to successfully solve relatively simple technical problems (radio communications, 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, the variety of applications forced us to look for new principles for their construction. In a number of cases, analog systems were 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, in each of which the reference value of the signal is determined. As a rule, the sampling step for each signal is constant.

One of the advantages of discrete signals over analog signals is that they do not 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 multi-channel communication with channel separation in time.

It is intuitively clear that fast time-varying analog signals require a small step to be sampled. 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 reference values are presented in the form of numbers. For reasons of technical convenience of implementation and processing, binary numbers are usually used with a limited and, as a rule, not too large number of digits. Recently, there has been a trend towards the widespread introduction of systems with digital signals. This is due to the significant advances made in 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, and not a mathematical model) is an analog signal. Thus, an analog signal slowly changing in time 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 these pulses is proportional to the values at the reference points. However, it is possible to do otherwise, keeping the height of the pulses constant, but changing their duration in accordance with the current reference values (Fig. 1.2, b).

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

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

Recording of reference 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. It is possible, for example, to 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 Chap. 15.

Before proceeding to the study of any phenomena, processes or objects, science always strives to classify them according to as many features as possible. Let's make a similar attempt with regard to radio signals and interference.

The basic concepts, terms and definitions in the field of radio signals are established by the state standard “Radio signals. Terms and Definitions". Radio signals are very diverse. They can be classified according to a number of criteria.

1. It is convenient to consider radio engineering signals in the form of mathematical functions given in time and physical coordinates. From this point of view, the signals are divided into one-dimensional and multidimensional. In practice, one-dimensional signals are the most common. They are usually functions of time. Multidimensional signals consist of many one-dimensional signals, and in addition, reflect their position in n- dimensional space. For example, signals that carry information about the image of an object, nature, person or animal, are functions of both time and position on the plane.

2. According to the features of the structure of the temporal representation, all radio signals are divided into analog, discrete and digital. In lecture No. 1, their main features and differences from each other have already been considered.

3. According to the degree of availability of a priori information, the whole variety of radio signals is usually divided into two main groups: deterministic(regular) and random signals. Radio engineering signals are called deterministic, the instantaneous values of which are reliably known at any time. An example of a deterministic radio engineering signal is a harmonic (sinusoidal) oscillation, a sequence or burst of pulses, the shape, amplitude and temporal position of which is known in advance. In fact, a deterministic signal does not carry any information and almost all of its parameters can be transmitted over a radio channel with one or more code values. In other words, deterministic signals (messages) essentially contain no information, and there is no point in transmitting them. They are usually used to test communication systems, radio channels or individual devices.

Deterministic signals are divided into periodical and non-periodic (impulse). An impulse signal is a signal of finite energy, significantly different from zero for a limited time interval, commensurate with the time of completion of the transient process in the system for which this signal is intended to act. Periodic signals are harmonic, that is, containing only one harmonic, and polyharmonic, the spectrum of which consists of many harmonic components. Harmonic signals include signals described by a sine or cosine function. All other signals are called polyharmonic.

random signals are signals whose instantaneous values are unknown at any time and cannot be predicted with a probability equal to one. Paradoxical as it may seem at first glance, but a signal carrying useful information can only be a random signal. The information in it is embedded in a set of amplitude, frequency (phase) or code changes of the transmitted signal. In practice, any radio signal containing useful information should be considered as random.

4. In the process of transmitting information, signals can be subjected to one or another transformation. This is usually reflected in their name: signals modulated, demodulated(detected), coded (decoded), reinforced, detainees, discretized, quantized and etc.

5. According to the purpose that the signals have in the modulation process, they can be divided into modulating(primary signal that modulates the carrier wave) or modulated(carrier vibration).

6. By belonging to one or another type of information transmission systems, they distinguish telephone, telegraphic, broadcasting, television, radar, managers, measuring and other signals.

Consider now the classification of radio interference. Under radio interference understand a random signal, homogeneous with a useful one and acting simultaneously with it. For radio communication systems, interference is any random effect on a useful signal that degrades the fidelity of the reproduction of transmitted messages. Classification of radio interference is also possible on a number of grounds.

1. According to the place of occurrence of interference, they are divided into external and domestic. Their main types have already been discussed in lecture No. 1.

2. Depending on the nature of the interaction, interference with the signal is distinguished additive and multiplicative interference. Additive noise is the noise that is added to the signal. Multiplicative interference is called interference, which is multiplied with the signal. In real communication channels, both additive and multiplicative interference usually occur.

3. According to the main properties, additive noise can be divided into three classes: concentrated on the spectrum(narrowband interference), impulse noise(focused in time) and fluctuation noise(fluctuation noise), not limited in time or spectrum. Concentrated over the spectrum is called interference, the main part of the power of which is located in separate parts of the frequency range, smaller than the bandwidth of the radio engineering system. Impulse interference is a regular or chaotic sequence of impulse signals that are homogeneous with the useful signal. The sources of such interference are digital and switching elements of radio circuits or devices operating next to them. Impulsive and concentrated noise is often referred to as pickups.

There is no fundamental difference between signal and noise. Moreover, they exist in unity, although they are opposite in their action.

5. According to the purpose that the signals have in the modulation process, they can be divided into modulating(primary signal that modulates the carrier wave) or modulated(carrier vibration).

1. According to the place of occurrence of interference, they are divided into external and domestic. Their main types have already been discussed in lecture No. 1.

There is no fundamental difference between signal and noise. Moreover, they exist in unity, although they are opposite in their action.

random processes

As mentioned above, the distinguishing feature of a random signal is that its instantaneous values are not predictable in advance. Almost all real random signals and noises are chaotic functions of time, mathematical models of which are random processes studied in the discipline of statistical radio engineering. random process called the random function of the argument t, where t current time. A random process is denoted by capital letters of the Greek alphabet , , . Other designations are also allowed if it is agreed in advance. A specific type of random process that is observed during an experiment, for example, on an oscilloscope, is called implementation this random process. Type of specific implementation x(t) can be specified by a certain functional dependence of the argument t or chart.

Depending on whether continuous or discrete values take an argument t and implementation X, there are five main types of random processes. Let us explain these types with examples.

A continuous random process is characterized by the fact that t and X are continuous quantities (Fig. 2.1, a). Such a process, for example, is noise at the output of a radio receiver.

A discrete random process is characterized by the fact that t is a continuous value, and X- discrete (Fig. 2.1, b). The transition from to occurs at any time. An example of such a process is the process that characterizes the state of the queuing system when the system jumps at arbitrary times t goes from one state to another. Another example is the result of quantizing a continuous process only by level.

The random sequence is characterized by the fact that t is discrete, and X- continuous quantities (Fig. 2.1, c). As an example, one can point to time samples at specific times from a continuous process.

A discrete random sequence is characterized by the fact that t and X are discrete quantities (Fig. 2.1, d). Such a process can be obtained as a result of level quantization and time discretization. These are the signals in digital communication systems.

A random stream is a sequence of points, delta functions or events (Fig. 2.1, e, g) at random times. This process is widely used in reliability theory, when the flow of faults in electronic equipment is considered as a random process.

Thus, a signal is a physical process whose parameters contain information (message) and which is suitable for processing and transmission over a distance.

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 a single function of time, is usually called one-dimensional.

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.

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

Analogue, Discrete and Digital Signals. Concluding a brief review of the principles of classification of radio signals, we note the following. Often the physical process that generates the signal develops in time in such a way that the signal values can be measured at any time. Signals of this class are 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 visually represented by its graph (oscillogram), which can be either continuous or with break points.

Multidimensional signal models are especially useful when the functioning of complex systems is analyzed using a computer.

Deterministic and random signals. Another principle for the classification of radio signals is based on the possibility or impossibility of accurately predicting their instantaneous values at any time.

Analog (continuous), discrete and digital signals. Often the physical process that generates the signal develops in time in such a way that the signal values can be measured at any time. Signals of this class are 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 visually represented by its graph (oscillogram), which can be either continuous or with break points.

The increased requirements for radio engineering systems, the variety of applications forced us to look for new principles for their construction. In a number of cases, analog systems were 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, in each of which the reference value of the signal is determined. As a rule, the sampling step for each signal is constant.

It is intuitively clear that fast time-varying analog signals require a small step to be sampled.

It should be borne in mind that, in essence, any discrete or digital signal (we are talking about a signal - a physical process, and not a mathematical model) is an analog signal.

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 to the task.

As a carrier of messages, high-frequency electromagnetic oscillations (radio waves) of the appropriate range are used, which can propagate over long distances.

The carrier frequency oscillation emitted by the transmitter is characterized by: amplitude, frequency and initial phase. In general, it is presented in the form:

i = I m sin(ω 0 t + Ψ 0),

where: i is the instantaneous value of the current of the carrier oscillation;

I m is the amplitude of the current of the carrier oscillation;

ω 0 is the angular frequency of the carrier oscillation;

Ψ 0 – the initial phase of the carrier wave.

The primary signals (transmitted message, converted into electrical form) that control the operation of the transmitter can change one of these parameters.

The process of controlling high-frequency current parameters using a primary signal is called modulation (amplitude, frequency, phase). The term “manipulation” is used for telegraphic types of transmission.

In radio communications, radio signals are used to transmit information:

radiotelegraph;

radiotelephone;

phototelegraphic;

telecode;

complex types of signals.

Radio telegraph communication differs: by the method of telegraphy; according to the method of manipulation; on the use of telegraph codes; by way of using the radio channel.

Depending on the method and speed of transmission, radiotelegraph communications are divided into manual and automatic. With manual transmission, manipulation is carried out with a telegraph key using the MORSE code. The transmission speed (for auditory reception) is 60-100 characters per minute.

With automatic transmission, manipulation is carried out by electromechanical devices, and reception is carried out using printing machines. Transmission speed 900–1200 characters per minute.

According to the method of using the radio channel, telegraph transmissions are divided into single-channel and multi-channel.

According to the method of manipulation, the most common telegraph signals include signals with amplitude keying (AT - amplitude telegraph - A1), with frequency shift keying (FT and DFT - frequency telegraphy and double frequency telegraphy - F1 and F6), with relative phase shift keying (OFT - phase telegraphy - F9).

For the use of telegraph codes, telegraph systems with the MORSE code are used; start-stop systems with 5 and 6 digit codes and others.

Telegraph signals are a sequence of rectangular pulses (parcels) of the same or different duration. The parcel with the shortest duration is called elementary.

Basic parameters of telegraph signals: telegraphy speed (V); manipulation frequency (F);width of the spectrum (2D f).

telegraphy speed V equal to the number of chips transmitted in one second, measured in bauds. At a telegraphy rate of 1 baud, one chip is transmitted per 1 s.

Keying frequency F numerically equal to half the speed of telegraphy V and is measured in hertz: F=V/2 .

Amplitude-shift keyed telegraph signal has a spectrum (Fig.2.2.1.1), which, in addition to the carrier frequency, contains an infinite number of frequency components located on both sides of it, at intervals equal to the manipulation frequency F. three spectrum components located on either side of the carrier. Thus, the width of the spectrum of the amplitude-shift keyed telegraph RF signal is equal to 6F. The higher the keying frequency, the wider the spectrum of the RF telegraph signal.

Rice. 2.2.1.1. Temporal and spectral representation of the AT signal

At frequency shift keying the current in the antenna does not change in amplitude, but only the frequency changes in accordance with the change in the manipulating signal. The spectrum of the signal FT (DFT) (Fig. 2.2.1.2) is, as it were, the spectrum of two (four) independent amplitude-shift keyed oscillations with their own carrier frequencies. The difference between the frequency of "pressing" and the frequency of "squeezing" is called the frequency spacing, denoted ∆f and can be in the range of 50 - 2000 Hz (most often 400 - 900 Hz). The spectrum width of the FT signal is 2∆f+3F.

Fig.2.2.1.2. Temporal and spectral representation of the chirp signal

To increase the throughput of the radio link, multichannel radiotelegraph systems are used. In them, on one carrier frequency of the radio transmitter, two or more telegraph programs can be transmitted simultaneously. There are systems with frequency division multiplexing of channels, with time division of channels and combined systems.

The simplest two-channel system is the system of double frequency telegraphy (DFT). The signals manipulated in frequency in the DCT system are transmitted by changing the carrier frequency of the transmitter due to the simultaneous effect of the signals of two telegraph devices on it. This uses the fact that the signals of two devices operating simultaneously can have only four combinations of transmitted messages. With this method, at any time, a signal of one frequency is emitted, corresponding to a certain combination of manipulated voltages. The receiving device has a decoder, with the help of which telegraph sendings of constant voltage are formed through two channels. Frequency multiplexing consists in the fact that the frequencies of individual channels are located in different parts of the total frequency range and all channels are transmitted simultaneously.

With time division of channels, the radio link is provided to each telegraph device sequentially with the help of distributors (Fig. 2.2.1.3).

Fig.2.2.1.3. Multi-channel time division system

For the transmission of radiotelephone messages, mainly amplitude-modulated and frequency-modulated high-frequency signals are used. The modulating low-frequency signal is a collection of a large number of signals of different frequencies located in a certain band. The spectrum width of a standard low-frequency telephone signal, as a rule, occupies a band of 0.3-3.4 kHz.