A signal is a physical process that is a function of certain parameters and is used as an information carrier. In radio engineering, two groups of electrical signals are studied: deterministic and random.
The information contained in the signal is displayed by the law of its change in time S (t). If this law is known and predetermined in advance, then the signal is called deterministic (from the Latin determinatio - determination). An example of such a signal is a cosine oscillation described by the function
where S m is the signal amplitude; u=2рf - circular frequency of the signal; c - initial phase of the signal.
For deterministic signals, the value of s (t) is known in advance at any time t for given values of amplitude, angular frequency and initial phase.
If the law of signal change s (t) is not predetermined, then it is not known in advance what value it will have at one time or another. The values of such signals at different times are random. That's why they are called random.
Signals are classified based on essential features relevant mathematical models signals. All signals are divided into two independent groups: deterministic and random.
Deterministic signals are divided into periodic and non-periodic (pulse). A pulse signal is a signal of finite energy, significantly different from zero during a limited time interval commensurate with the time of completion of the transient process in the system on which this signal is intended to influence. Periodic signals can be 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 at any time are unknown and cannot be predicted with a probability equal to one. Paradoxical as it may seem at first glance, only a random signal can be a signal carrying useful information. The information in it is contained in a variety of amplitude, frequency (phase) or code changes in the transmitted signal. In practice, any radio signal containing useful information should be considered random.
Most radio signals used in practice are classified as random for two reasons. Firstly, any signal that carries information must be considered random. Secondly, in devices that “work” with signals, there is almost always noise or interference that is superimposed on the useful signal. Therefore, in any communication channel, the useful signal is distorted during transmission and the message on the receiving side is reproduced with some error.
There is no insurmountable boundary between deterministic and random signals. Under conditions of a large useful signal to noise ratio, i.e. in the case when the level of interference is significantly less than the level of the useful signal, the deterministic model of the signal is adequate to the real situation. In this case, it is possible to apply methods for analyzing non-random signals.
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), encoded (decoded), amplified, delayed, sampled, quantized, etc.
According to the purpose that signals have during the modulation process, they can be divided into modulating (the primary signal that modulates the carrier wave) or modulated (carrier wave).
Radio circuits
Radio engineering circuits are a set of passive and active elements connected in a certain way, ensuring the passage and functional conversion of signals.
An electrical circuit occurs if sufficiently narrow paths for electric current are created in space, placing conductors made of materials with high electrical conductivity along these paths, surrounded by a well-insulating environment. It is also possible to place circuit elements along the chain, i.e. conductive devices limited in volume (resistors, vacuum tubes, semiconductors), or similarly limited in volume devices with local concentrators of electric and magnetic fields (capacitors, inductors).
The main passive (i.e. those without energy sources inside) elements are:
a) Active resistance R - an element in which an irreversible loss of electrical energy occurs, i.e. Ohm's law also holds for alternating currents;
b) Capacitance - an element in which the flow of current is accompanied by the accumulation of charges on the plates, and the energy from EMF sources is converted into the energy of the electric field between the plates.
c) Inductance is an element in which the flow of current is accompanied by the transition of electrical energy into the energy of a magnetic field.
Based on the nature of signal conversion in them, circuits are divided into linear with constant parameters, linear-parametric and nonlinear circuits.
Linear circuits are circuits in which all elements are linear, i.e. parameters do not depend on voltage and current values. If these parameters do not change over time, then the circuits are called linear with constant parameters.
Linear-parametric - circuits that contain elements that depend on time due to control of external influences, but do not depend on current and voltage.
Nonlinear - circuits containing at least one nonlinear element, the parameters of which depend on the processes occurring in them (current and voltage levels). Nonlinear circuits are described by nonlinear differential equations.
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Preface | |
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SECTION I. TASKS AND EXERCISES |
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Topic 1. General theory of radio signals | |
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Topic 2. Spectral representations of signals | |
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Topic 3. Energy spectra of signals. Principles of correlation analysis | |
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Topic 4. Modulated signals | |
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Topic 5. Signals with limited spectrum | |
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Topic 6. Basics of the theory of random signals | |
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Topic 7. Correlation theory of random processes | |
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Topic 8. Impact of deterministic signals on linear stationary systems | |
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Topic 9. Impact of deterministic signals on frequency-selective systems | |
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Topic 10. Impact of random signals on linear stationary circuits | |
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Topic 11. Signal conversions in nonlinear radio circuits | |
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Topic 12. Signal conversion in linear parametric circuits | |
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Topic 13. Fundamentals of the theory of synthesis of linear radio circuits | |
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Topic 14. Active circuits with feedback and self-oscillating systems | |
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Topic 15. Discrete signals. Principles of digital filtering | |
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Topic 16. Optimal linear filtering of signals | |
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SECTION II. Directions | |
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SECTION III. Solutions | |
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SECTION IV. Answers | |
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Applications | |
PREFACE TO THE SECOND EDITION
"An example is sometimes more useful than a rule" I. Newton
From his own experience, the reader certainly knows that an integral part of the process of studying exact sciences - first of all, mathematics and physics, as well as many natural sciences - is problem solving. Having first encountered tasks during school years, we then become so accustomed to them that we do not bother ourselves with questions about what the task as such is, what its cognitive role is. Moreover, some students view tasks as a necessary evil that must simply be endured patiently. In this regard, it is useful to note that European science and pedagogy, whose history goes back more than one millennium, only by the end of the 17th century came to the conclusion that teaching based on rote memorization of theoretical principles was extremely ineffective. Newton's words from his textbook "Algebra", taken as an epigraph, successfully emphasize a principle that is unlikely to become outdated - the key to successful learning is the active cognitive creativity of the student, who gets the opportunity to see the theory in action through his own experience.
The educational tasks are, by their nature, close to chess etudes, or rather to those scales and arpeggios that no aspiring musician can do without. A well-written problem carries all the features of a small scientific and pedagogical essay - its scientific topic is strictly delineated and, most importantly, to successfully solve the problem, you need to independently construct the mental algorithm that is known in advance to the teacher and which the student must demonstrate.
Like everything in the world, the method of teaching through problem solving has its own internal limitation: the formulation of the problem is inevitably poorer than the reality to which this problem relates. This circumstance must certainly be taken into account when correlating the conclusions of theory with practice.
How to learn to solve problems? Many serious books have been written on this subject. Without in any way pretending to generalize, we emphasize the following.
Firstly, you should develop an attitude towards this activity as an exciting work that allows you to widely
reveal a person's intellectual abilities. The techniques are varied - having successfully solved a problem, think about what other similar problems can be solved using the method you found. Don't forget to praise yourself if your work is going well. And most importantly, do not become discouraged if the task stubbornly “does not want to be solved.” After resting, get to work again - persistence in achieving a goal is an indispensable personality trait of a true professional. If you were unable to cope with a difficulty on your own and have to turn to a teacher, do not prioritize the “prescription” side of the matter - after all, the goal is not just to get the right answer, but to understand as deeply as possible why you need to act this way and not otherwise.
Secondly, after opening a textbook, you should not reduce the matter to looking for a formula that will immediately give the desired answer. Formal knowledge of the theory is necessary, but by no means a sufficient condition for successfully solving a problem. The most important mental procedure has always been a certain guess, and this is, in fact, the beginning of any creativity. If it is immediately clear how to solve a particular problem, it still should not be neglected. Accurate completion of all calculations and calculations is very important for developing the skill of independent work.
I take this opportunity to express my gratitude to the reviewer of the book, Prof. M.P. Demina for useful tips and favorable criticism.
FROM THE PREFACE TO THE FIRST EDITION
This book contains material for exercises in the course “Radio Engineering Circuits and Signals”.
Basic radio engineering processes
Converting the original message into an electrical signal.
Generation of high-frequency oscillations.
Oscillation control (modulation).
Strengthening weak signals in the receiver.
Isolating a message from a high-frequency oscillation (detection and decoding).
Radio circuits and methods
their analysis
Circuit classification
And the elements used to carry out 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;
Nonlinear circuits.
^
Linear circuits with constant parameters
We can proceed from the following definitions:
A circuit is linear if its elements do not depend on the external force (voltage, current) acting on the circuit.
A linear circuit 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 superposing (superposition) the solutions found for each of the forces separately.
Otherwise: in a linear chain, the sum of the effects of individual influences coincides with the effect of the sum of influences.
For any, no matter how complex, influence in a linear circuit with constant parameters, no oscillations of new frequencies arise.
^ Linear circuits with variable parameters
This refers to circuits in which one or more parameters change over time (but do not depend on the input signal). Such circuits 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 in a linear circuit with variable parameters, which has a spectrum of frequencies.
^ Nonlinear circuits
A radio circuit is nonlinear if it includes one or more elements whose parameters depend on the level of the input signal. The simplest nonlinear element is a diode.
Basic properties of nonlinear circuits:
To nonlinear circuits (and elements) the superposition principle does not apply.
An important property of a nonlinear circuit is the transformation of the signal spectrum.
^ Signal classification
From an information point of view, signals can be divided into deterministic and random.
Deterministic call any signal whose instantaneous value at any time can be predicted with probability one.
TO random refer to signals whose instantaneous values are unknown in advance and can be predicted only with a certain probability less than one.
Along with useful random signals, in theory and practice we have to deal with random interference - noise. Useful random signals, as well as interference, are often combined under the term random fluctuations or random processes.
Signals in a radio communication channel are often divided into control signals and on radio signals; The former are understood as modulating, and the latter as modulated oscillations.
Signals used in modern radio electronics can be divided into the following classes:
Arbitrary in magnitude 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 a 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 over the interval t 2, t 1 is defined as the integral of the instantaneous power:
.
Attitude
Means the average signal power over the interval t 2, t 1.
^
Arbitrary Signal Representation
as a sum of elementary vibrations
For the theory of signals and their processing, the expansion of a given function f(x) into various orthogonal systems of functions j n (x) is important. Any signal can be represented as a generalized Fourier series:
,
Where C i are 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
Norm of the basis function.
If the function is not orthonormal, then it can be reduced in this way. As n increases, Cn decreases.
Let us assume that a set of basis functions (j n ) is given. When specifying a set of basis functions and a fixed number of terms in the generalized Fourier series, the Fourier series gives an approximation original function, which has a minimum root-mean-square error in determining the original function. The generalized Fourier series gives
Such a series gives a minimum on average error (error).
There are 2 problems of decomposing a signal into simple functions:
^ Exact decomposition into simplest orthogonal functions (analytical model of the signal, analysis of signal behavior).
^ Approximation of process signals and characteristics , when it is necessary to minimize the number of terms of a generalized series. These include: Chebyshev, Hermite, and Legendre polynomials.
^ Harmonic analysis of periodic signals
When expanding a periodic signal s(t) into a Fourier series in trigonometric functions, we take as the orthogonal system
The orthogonality interval is determined by the norm of the function
The average value of the function over the period.
- basic formula for
definitions of Fourier series
Modulus is an even function, phase is an odd function.
Consider a pair for the kth term
- Fourier series expansion
^
Examples of spectra of periodic signals
Square wave. This kind of fluctuation, often called meander(Meander is a Greek word meaning “ornament”) and is especially widely used in measuring technology.
Let the signal s(t) be given in the form of some function different from zero in the interval (t 1 ,t 2). This signal must be integrable.
Let's take an infinite period of time T, including the interval (t 1,t 2). Then . The spectrum of a non-periodic signal is continuous. A given signal can be represented as a Fourier series 
, Where
Based on this we get:
Since T®µ, the sum can be replaced by integration, and W 1 by dW and nW 1 by W. Thus we move on 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 a non-periodic signal and the envelope of the line spectrum of a periodic signal, we will see that they coincide in shape, but differ in scale 
.
Consequently, the spectral density S(W) has all the basic properties of the complex Fourier series. That is, we can write where
, A 
.
Spectral density module 
is an odd function and can be considered as an amplitude-frequency characteristic. Argument 
- odd function considered as a phase-frequency characteristic.
Based on this, the signal can be expressed as follows
From the evenness of the module and the oddness of the phase, it follows that the integrand in the first case is even, and in the second case it is odd with respect to W. Therefore, the second integral is equal to zero (an odd function in 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)
.
^
Properties of the Fourier transform
Signal time shift
Let a signal s 1 (t) of an arbitrary shape have a spectral density S 1 (W). When this signal is delayed for a time t 0, we obtain a new time function 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 
.
Each signal has its own spectral density. A shift of the signal along the time axis leads to a change in its phase, and the magnitude 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. New signal s 2 (t) is related to the original relation.
The pulse duration s 2 (t) is n times less than the initial one. Spectral density of compressed pulse 
. Let's introduce a new variable. We'll get it.
When a signal is compressed n times, its spectrum expands by the same amount. The modulus of the spectral density will decrease by n times. When the signal is stretched in time, the spectrum narrows and the spectral density modulus increases.
^ Vibration 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
Let's split it into 2 integrals.
The resulting relationship can be written in the following form
Thus, multiplying the function s(t) by a harmonic oscillation leads to splitting the spectrum into 2 parts, shifted by ±w 0.
^ Signal differentiation and integration
Let a signal s 1 (t) with spectral density S 1 (W) be given. Differentiation of this signal 
gives the ratio 
. Integration 
leads to the expression 
.
^ Signal addition
When adding signals s 1 (t) and s 2 (t) having 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 . This signal corresponds to the spectrum
Let's 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 time functions 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 Fourier transform
Let s(t) be an even function with respect to time.
Assuming that s(t) is an even function. Let us write s(t) in the form
. Let's replace W by t and t by W, we get 
. If the spectrum has the shape of a 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 the expression in which f(t)=g(t)=s(t). In this case, this integral is equal to . This relation is called Parseval's equality.
Energy calculation of bandwidth: 
, Where 
, A 
.
^
Examples of spectra of non-periodic signals
Square pulse
Defined by the expression
Let's find the spectral density
.
As the pulse lengthens (stretches), the distance between the zeros decreases, and the value of S(0) increases. The modulus 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 change takes into account the phase increment by p.
When counting 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 shift of the pulse by time (the resulting phase response is shown by the dotted line).
Bell-shaped (Gaussian) pulse
Determined by the expression . The constant a has the meaning of half the pulse duration, determined at the level e -1/2 of the pulse amplitude. Thus, the total pulse duration is .
Signal spectral density 
.
For convenience, we add the exponent to the square of the sum 
, where the value d is determined from the condition 
, where . Thus, the expression for the spectral density can be reduced to the form 
.
Moving to a new variable 
we get 
. Considering that the integral included in this expression is equal to , we finally obtain 
, Where 
.
Pulse spectrum width
The Gaussian pulse and its spectrum are expressed by identical functions and have the property of symmetry. For it, the ratio of pulse duration and bandwidth is optimal, i.e., for a given pulse duration, a Gaussian pulse has a minimum bandwidth.
delta pulse (single pulse)
The signal is given by the relation 
. It can be obtained from the above impulses by tending t and to zero.
It is known that, therefore, the spectrum of such a signal will be constant (this is the pulse area equal to unity).
To create such a pulse, all harmonics are needed.
Exponential momentum
Signal of the form , c>0.
The signal spectrum is found as follows
Let's write the signal in another 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 which A(t) is amplitude modulation, w(t) is frequency modulation, j(t) is phase modulation. The last two form angular modulation. The frequency w must be large compared to the highest frequency of the signal spectrum W (spectrum width occupied by the message).
A modulated oscillation has a spectrum, the structure of which depends both on the spectrum of the transmitted message and on the type of modulation.
There are several types of modulation possible: continuous, pulse, pulse code.
^
Amplitude modulation
The general expression for amplitude modulated oscillation is as follows
The nature of the envelope A(t) is determined by the type of message being transmitted.
If the signal is a message, then the envelope of the modulated oscillation can be represented as . Where W is the modulation frequency, g is the initial phase of the envelope, k is the proportionality coefficient, DA m is the absolute change in amplitude. Attitude 
- modulation coefficient. Based on this, we 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 peak power. The average power over the modulation period is .
The power for transmitting an amplitude-modulated signal is greater than for transmitting a simple signal.
Spectrum of amplitude-modulated signal
Let the modulated oscillation be defined by the expression
Let's transform this expression
The first term is the original unmodulated oscillation. The second and third are oscillations that appear during the modulation process. The frequencies of these oscillations (w 0 ±W) are called side modulation frequencies. Spectrum width 2W.
In the case when the signal is a sum 
, where , a . Moreover, where 
.
From here we get
Each of the components of the modulating signal spectrum independently forms two side frequencies (left and right). The spectrum width in this case is 2W 2 = 2W max 2 maximum frequency of the modulating signal.
In a vector diagram, the time axis rotates clockwise with an angular frequency w 0 (counting from the horizontal axis). The amplitudes and phases of the side lobes are always equal to each other, so their resulting vector DF will always be directed along the OD line. The final vector OF changes only in amplitude without changing its angular position.
Let there be a signal. Let's write it in another form.
The signal corresponds to the spectrum 
, where , and S A is the spectral density of the envelope. This gives us the final expression for the spectrum
This is explained by the gating effect of the d-function, i.e. 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 an oscillation with frequency modulation. However, frequency is a derivative of phase. If you change the phase, the current frequency will also change.
Frequency modulation
,
Where represents 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; - angular modulation index.
Let's assume where 
.
,
Where m is the modulation coefficient.
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 changing the modulation frequency.
At the World Cup deviation W.
With FM the value proportional to the amplitude of the modulating voltage and does not depend on the modulation frequencyW.
For a monochromatic modulating signal, phase and frequency modulation are indistinguishable.
^
Signal spectrum with angle modulation
Let the oscillation be given
There are two amplitude modulated signals. Such components that differ in are called quadrature components.
Let . This coincides with . 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 with angular modulation is infinitely large, in contrast to the spectrum with amplitude modulation.
With angular modulation, the spectrum of a frequency-modulated oscillation, even when modulated by 1 frequency, consists of an innumerable number of harmonics grouped around the carrier frequency.
Flaws: the spectrum is very wide.
Advantages: most noise resistant.
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 the 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.
Spectral width at m very large
ShS=2mW=2w d
If the modulation coefficient is significantly less than unity, then such modulation is called fast, then w d<< W.
If m >> 1, then this slow modulation, then w d >> W.
^
Spectrum of a frequency-modulated radio pulse
filling
, Where
Where , 
The main parameter of a linearly frequency modulated signal (chirp) or the base of the chirp signal.
B can be both positive and negative.
Let's assume that b>0
The signal spectrum consists of 2 components:
1 - burst near frequency w o;
2 - surge near frequency -w o.
When determining the spectral density in the region of positive frequencies, the second term can be discarded.
Let's add the exponential to a complete square
, where C(x) and S(x) are Fresnel integrals
Chirp signal spectral density module
Phase of the spectral density of the chirp signal
The larger m, the closer the spectrum shape is to rectangular with spectrum width . The phase dependence is quadratic.
As m tends to large values, the shape of the frequency response tends to be rectangular, and the phase consists of two parts:
1). gives a parabola
2). strives for
For large m and : 
Then the module value is: .
Mixed amplitude-frequency modulation
Spectral density of cosine quadrature wave 
at =0 it will be
When determining the spectrum of a sine quadrature oscillation 
the phase angle should be equal to -90°. Hence,
Thus, the final spectral density of vibration 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 type of functions A(t) and q(t).
With frequency modulation, the phases of odd harmonics change by 180°. Simultaneous modulation of both frequency and amplitude at certain 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 asymmetrical.
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 asymmetrical, but with respect to w = 0 it is symmetrical. The same result can be obtained with an odd function A(t). In this case, the spectrum is purely imaginary and odd.
For symmetry of the output spectrum, parity of 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 chirp has an even phase and even amplitude. 
Moreover 
The output spectrum turned out to be symmetrical.
A(t) = even function + odd function, and q(t) is an even function.
.
The spectrum turned out to be asymmetrical.
Narrowband signal
It is understood as 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 vibration 
can be represented in the form 
, Where . In this expression, the envelope A(t), unlike A o, is a function of time, which can be determined from the condition of preserving the given function a(t)
From this expression it is clear that new feature A(t) is not essentially an “envelope” in the conventional sense, since it may intersect the a(t) curve (instead of touching at the points where A(t) is at its maximum value). That is, we did not correctly determine the envelope and frequency. There is a method of instantaneous frequency - Hilbert's method for determining frequency.
If there is a signal, then
Total signal phase 
, and the instantaneous frequency 
Physical envelope 
.
Let us assume that we have chosen the reference frequency not w o, but w o + 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 magnitude of the signal s(t) is always less than or equal to u s (t). Equality occurs when cos w o t = 1. At these moments, the derivative of the signal and the derivative of the envelope are equal.
The physical envelope coincides with maximum value 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 
, 
. Hence the amplitude will be 
.
^
Analytical signal
Let there be a signal s(t) defined as 
. Let's divide it into two components 
.
In that expression 
–– analytical signal. If you enter a variable then . That is, we received 
. There is a real signal 
, Hilbert conjugate signal 
. There is an analytical signal 
.
, 
–– direct and inverse Hilbert transforms.
Determination of carrier and envelope using Hilbert's method
Signal amplitude 
, its phase 
. Instantaneous frequency value 
.
Example: . .
–– precise definition of the envelope. Using the Hilbert method allows you to give unambiguous and absolutely reliable values of the envelope and instantaneous frequency of the signal.
–– any signal can be expanded into a Fourier series.
– Hilbert conjugate signal.
If the signal is represented not by a Fourier series, but by a Fourier integral, then the following relations are valid: 
, 
.
^
Analytical Signal Properties
The product of the analytical signal z s (t) and its associated 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
––Hilbert transform, where H() is the transformation operator. 
Example. Signal s(t) is an ideal low-frequency signal.
Frequency and time characteristics
radio circuits
Let there be a linear active four-port network.
1. Transfer function 
. Characterizes the change in the output signal relative to the input signal. The module is called amplitude-frequency response or simply frequency response. The argument is the phase-frequency characteristic or simply phase.
2. Impulse response 
–– the reaction of the circuit to a single impulse. Characterizes the change in 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. Transition function – the reaction of the circuit to a single step. This is the accumulation of a 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 that shunts 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 input voltage.
Maximum gain (at ) 
. From here 
, where is the delay time.
Transfer characteristic module 
–– frequency response. That is, this amplifier passes a signal only in a certain frequency band. FCHH –– 
.
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NEW. IN AND. Kaganov. Radio engineering circuits and signals. Laboratory computerized workshop. 2004 164 pp. djvu. 3.5 MB.
Listed 22 application programs based on the universal mathematical package “Mathcad” and the operation of 29 radio-electronic circuits is analyzed using a software package (Electronics Workbench). The programs allow computer analysis of signals used in radio engineering; use a computer to simulate linear circuits of concentrated and distributed types and consider the processes occurring in them; simulate and calculate transistor amplifiers, self-oscillators, modulators and demodulators. With the help of this textbook, the student will be able to master practical skills in modeling, analysis and calculation using a computer of the main types of radio circuits that underlie the construction of radio electronic devices.
For students of secondary vocational educational institutions.
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NEW. Baskakov S.I. Radio engineering circuits and signals. Guide to problem solving. 2002 214 pp. djvu. 2.2 MB.
The manual contains tasks for all sections of the course of the same name. It contains the conditions of the problems, examples of solutions, guidelines and answers. When working with the manual, it is recommended to use S. I. Baskakov’s textbook “Radio Engineering Circuits and Signals” (Moscow: Vyssh. shk., 2000). The second edition added tasks on wavelet analysis of signals and methods for assessing the information characteristics of a radio channel. Problems related to computer analysis of circuits and signals using MathCAD and Electronics Workbench software products are proposed.
For university students studying radio engineering specialties.
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G.V. Belokopytov and others. Fundamentals of radiophysics. 1996 256 pp. djvu. 2.8 MB.
Contents:
Signals and spectra. Signals and information. Linear lumped radiophysical circuits. Nonlinear active and passive elements. Signal conversion in nonlinear systems and systems with variable parameters. Amplifiers of electrical and optical signals. Generators of electrical oscillations. Noises. Distributed systems. Introduction to Digital Electronics.
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Baskakov S.I. Radio engineering circuits and signals. Textbook. 3rd ed. reworked additional year 2000. 462 pp. PDF. 53.5 MB.
The textbook is intended for active independent acquisition of knowledge in the field of theoretical radio engineering; it contains an extensive methodological apparatus, including a list of results, test questions, tasks of medium and increased levels of complexity. Issues of classical synthesis and problems of analysis of transient processes in circuits, the theory and technology of digital signal processing and the method of noise-resistant radio reception are considered. The third edition (2nd - 1988) added material on the fundamentals of information theory using wavelet analysis methods, which have gained recognition in the last decade.
For university students studying radio engineering specialties. It will be useful for those improving their qualifications in the field of theoretical radio engineering.
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Vinogradova, Rudenko, Sukhorukov. Wave theory. 1979 384 pp. djvu. 3.8 MB.
Set out general issues theories of waves of various physical natures (electromagnetic, sound, etc.). The laws of wave propagation in linear and nonlinear media are considered. Much attention is paid to the presentation of various mathematical methods for analyzing wave equations. The book includes a number of issues of modern wave theory, which have so far been presented only in specialized scientific literature.
Quite accessible when studying general physics. The calculations are quite detailed.
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V.F. Vpasov. Radio engineering course. Uch. allowance. 1962 932 pp. djvu. 17.2 MB.
The book is intended as a teaching aid for students of technical universities and engineering academies. It may be useful when self-study radio engineering students correspondence departments universities The contents of the book cover all the main sections of radio engineering. The presentation is illustrated with computational examples and problems.
I can't say what's missing from this book. In my opinion there is everything.
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I.S. Gonorovsky. Radio engineering circuits and signals. Textbook. 3rd ed. add. reworked 1977 608 pp. djvu. 6.8 MB.
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Govorkov V.A. Electrical and magnetic fields, ed. 3rd, revised and additional 1968 488 pp. djvu. 6.6 MB.
The book outlines the theory of the electromagnetic field to the extent necessary for the practical calculation of most stationary and alternating magnetic fields encountered in electrical communications technology, radio engineering, electronic engineering, energy, automation devices, etc. Particular attention is paid to graphical constructions of pictures of fields, very useful for mastering complex physical laws and being the first and necessary step in applying theory to practice. A significant place in the book is devoted to approximate calculations of electric and magnetic fields using the grid method. Their mastery frees the calculator from the thankless task of finding not always sufficiently justified approximations to the boundary conditions under which the differential equations of mathematical physics allow so-called “exact” solutions.
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L.D. Goldstein, N.V. Zernov. Electromagnetic fields and waves. 1971 665 pp. djvu. 5.1 MB.
The fundamentals of the theory of the electromagnetic field are outlined. The main attention is paid to the consideration of rapidly varying fields and the analysis of the properties of radio engineering elements, the theory of which is based on the equations of electrodynamics (for example, waveguides, cavity resonators, etc.). The issues of interaction of the electromagnetic field with matter, which form the theoretical basis of quantum electronics, are also considered.
The book is intended for graduate students and engineers working in the field of applied electrodynamics; it can also be used as a textbook for university students with radio engineering specialties.
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I.S. Gonorovsky. Radio engineering circuits and signals. Textbook. 3rd ed. add. I'll change it. 1977 608 pp. djvu. 6.8 MB.
The book is a textbook for the course “Radio Engineering Circuits and Signals” for universities specializing in radio engineering. In connection with the introduction new program of this course, this edition has been radically revised and supplemented with the following new sections: discrete and digital signal processing; approximation of processes and characteristics by Walsh functions; synthesis of radio circuits.
Particular attention is paid to sections devoted to statistical phenomena in radio circuits. The sections on spectral and correlation analysis of deterministic and random signals, as well as on the theory of their transformation in linear, parametric and nonlinear devices, have been methodically revised.
Although the book is intended for students of radio engineering departments of universities, it can also be useful to a wide range of specialists working in the field of radio electronics and related fields of science and technology.
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Ivanov, Sergienkko, Ushakov. Theoretical foundations of radio engineering. Uch. allowance. 2002 308 pp. djvu. 2.0 MB.
The manual outlines the fundamentals of the theory of deterministic and random signals, linear and nonlinear circuits with constant parameters, optimal and discrete signal filtering, as well as self-oscillators. The examination of theoretical material is completed with test questions and detailed solutions to problems.
For university students enrolled in bachelor's and engineer training programs in the areas of "Radio Engineering" and "Telecommunications" May be useful for graduate students and engineering and technical workers.
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Kaganov V.I. Radio engineering + computer + Mathcad. year 2001. 416 pp. djvu. 5.9 MB.
The theoretical foundations of radio engineering and its interaction with computer computing are outlined. The solution of various problems on the theory of radio signals, linear and nonlinear radio engineering devices, optimization problems, methods of generating, amplifying, forming, receiving and processing radio signals is carried out using the mathematical software package "Mathcad". A total of 50 programs are given. The principles of constructing satellite-space and ground-based radio communication systems and the use of computers in them are considered. The book was written based on the author's teaching experience at MIREA.
For specialists in the field of radio electronics and students of radio engineering universities.
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Kravchenko V.F. Electrodynamics of superconducting structures. Theory, algorithms and methods of calculations. 2006 271 pp. djvu. 2.6 MB.
The monograph presents and generalizes theoretical data on the surface impedance of superconductors. Various impedance boundary conditions are considered and the boundaries of their use in boundary value problems of electrodynamics are determined. Researched a large number of physical models of various superconducting structures for internal and external boundary value problems. New algorithms have been obtained, and methods for their calculations have been developed. The monograph is intended for scientists, engineers dealing with issues of radiophysics and electronics, problems of mathematical modeling of physical processes occurring in various superconducting structures, as well as for undergraduate and graduate students of universities specializing in applied physics and computational mathematics.
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B.R. Levin. Theoretical foundations of statistical radio engineering. 3rd ed. reworked add. 1989 656 pp. djvu. 14.3 MB.
The revised edition of the three-volume A974-1976) consists of two parts corresponding to two main tasks of statistical radio engineering: probabilistic analysis of the passage of stochastic signals through a standard system and statistical synthesis of systems for detecting, distinguishing signals and estimating their parameters against the background of interference with complete a priori information and in conditions of a priori uncertainty. The structure and logical sequence of material arrangement remain the same. Some sections of the three-volume book that are of interest to a narrower circle of specialists are not included, but a number of new chapters and new results have been added along with a modern interpretation of well-known provisions.
For researchers specializing in the field of radio engineering and communications, as well as for graduate students and university teachers.
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Logginov et al. Fundamentals of radiophysics. Fundamentals of radiophysics. 1996 250 pp. djvu. Size 2.9 MB.
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G.T. Markov, B.M. Petrov, G.P. Grudinskaya. Electrodynamics and radio wave propagation. Uch. allowance. 1969 376 pp. djvu. 7.8 MB.
The book consists of two parts. Part I examines the basic equations of electrodynamics. The issues of excitation of radio waves by various sources are studied in free space, in media in the presence of bodies, as well as in waveguides, resonators and other guiding systems. The solution of problems of excitation and diffraction of radio waves is carried out from a unified methodological position, which allows focusing on physical processes. Rigorous and asymptotic methods for solving boundary value problems of electrodynamics are considered, and the possibilities of using computers for solving them are shown. Part II describes the propagation of radio waves of various ranges in natural environments, such as the surface layers of the Earth, the troposphere, the ionosphere, and outer space, as well as methods for studying these environments. Most chapters of the book contain control tasks.
Intended for students of radio engineering and radiophysics specialties at universities and will be useful for engineers and scientists in the same specialties.
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Mazor, Machussky, Pravda and others. Radio engineering. Encyclopedia. 2002 948 pp. djvu. 20.4 MB.
The encyclopedia contains material, the terminological composition of which is mainly related to the materials of courses in radio engineering disciplines taught at universities. Approximately 2,500 dictionary entries provide interpretations of approximately 4,000 of the most frequently used radio engineering terms. The book can be used in two ways, as an encyclopedia on radio engineering and as a collection of 33 short textbooks on basic radio engineering disciplines.
For students of radio engineering specialties at universities, as well as for students of related specialties, graduate students, radio engineers, radio amateurs.
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R.M. Marston. Popular audio chips. 2007 381 pp. djvu. 10.4 MB.
This publication is an encyclopedia of microcircuits often used to create audio equipment of various classes. A detailed description of the operating principle of the IC is given, and optimal circuit solutions are proposed. Detailed and accessible explanations are accompanied by diagrams and graphs; many examples of practical diagrams are given with comments and useful general information. The ICs covered in the book include output and preamplifiers, compressor expanders, ICs for tone and volume control, noise attenuation, and analog and digital delay lines, bar meters, and power supplies.
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E.I. Nefedov. Open coaxial resonant structures. 1982 111 pp. djvu. 3.1 MB.
The monograph represents the first systematic presentation in domestic and world literature of the theory of open coaxial resonant structures, which have found wide application in antenna-waveguide technology, quantum and diffraction electronics, diagnostics of plasma and electron flows, measuring technology, microwave electronics and, in particular, relativistic electronics, as well as in a number of other areas of modern physics and technology related to the development of the ranges of millimeter, submillimeter and light waves. A classification of open coaxial resonant structures is given, and the theory and algorithms for calculating coaxial and disk resonators are outlined. The properties of higher types of waves of coaxial circular and elliptical waveguides and a biconical horn are studied in detail. A number of interesting physical effects have been discovered that are realized in coaxial cylindrical and disk open structures.
The book is intended for scientific workers and design engineers of radio-electronic equipment of new ranges of electromagnetic waves. It will be useful and is recommended for graduate and senior students of radio physical and radio engineering specialties.
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V.V. Nikolsky. Electromagnetic field theory. 1961 188 pp. djvu. 3.7 MB.
The content of the book meets the usual requirements for the course of the same name for the radio engineering specialty of colleges, and the example compiled by Acad. V. A. Kotelnikov program 070J/J4. It determines the sequence of presentation of the material and the titles of the chapters. However, the content of the book is somewhat broader than what is regulated by this program. The reason for this is the ongoing development of technology and theory of microwave devices in recent years, as well as their further penetration into radio engineering practice. The nature of the presentation was determined to a certain extent on the basis of the author’s lectures on this course at the Faculty of Radio Engineering and in the course “Applied Electrodynamics and Microwave Engineering” at the Faculty of Advanced Training for Engineers of the VZEI.
Old books are useful because they discuss the basics in much more detail. They have a much greater relationship between text and formulas and therefore are more understandable.
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Nikolsky, Nikolskaya. Electrodynamics and radio wave propagation. Textbook manual for universities. 3rd ed., revised. add. 1989. 544 pp. djvu. 6.8 MB.
The theory of electromagnetism is presented with an emphasis on radio engineering electrodynamics and the analysis of wave processes. The reflection and refraction of waves, radiation, diffraction, processes in hollow and dielectric waveguides, resonators, periodic, quasi-poptic and other structures, in microwave integrated circuits, etc. are discussed. Methods of mathematical modeling in electrodynamics, based on the use of a computer, are discussed. A distinctive feature of the book is big number pictures of electromagnetic fields calculated and constructed on a computer. For students of radio engineering specialties, as well as radio engineers and radio physicists.
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Potemkin V.V. Radiophysics. Textbook allowance. 1988 264 pp. djvu. 4.8 MB.
The textbook, written in accordance with the program for the course “Fundamentals of Radiophysics” taught at universities across the country, gives the theory of basic physical processes widely used in radiophysical equipment and radiophysical research methods. The operation of operational, differential and parametric amplifiers, synchronous detection, elements of digital electronics and integrated circuits, noise of electronic devices and other issues are discussed in detail. The presentation is characterized by a clear physical interpretation and clarity and is not overloaded with mathematical calculations and complex calculations. For students of physical specialties of universities.
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K. Rothhammel. A. Krischke. Antennas. In 2 volumes. 11th ed. reworked additional 2007 djvu.
Volume 1. Propagation of electromagnetic waves. Balancing and matching of antennas. Shortwave antenna. 411 pp. 8.3 MB.
The first volume contains the theoretical foundations necessary for the design and operation of antennas, issues of their balancing and matching, as well as the necessary descriptions of the designs of various short-wave antennas.
Volume 2. Frame and active systems. Antennas for meter = and decimiter waves. Methodology of aethene measurements. 411 pp. 10.3 MB.
The content of the book compared to the previous edition has been expanded and supplemented with the latest technical developments; At the same time, the previous division in three main areas is preserved: basic concepts, types of antennas and their designs.
For many years now, radio amateurs have consistently turned to Karl Rothhammel's reference manual, which has become a standard in technical literature. Concise theoretical information combined with detailed description technical solutions allow you to successfully build the antennas listed in the book even for those who have little knowledge of technology. The contents of this publication have again been expanded and supplemented due to the latest technical developments. The chapters on antenna types, baluns and blocking links have been rewritten. Outdated information has been omitted, and established views and data have been brought into line with new information; At the same time, the previous division in three main areas is preserved: basic concepts, types of antennas and their designs.
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Ed E. Reference manual on high-frequency circuitry. In 2 parts. 1990 doc. two files in one archive 6.4 MB.
We bring to the attention of readers the book by E. Red, “A Reference Guide to High-Frequency Circuitry,” which covers the main issues in the development of high-frequency transceiver equipment. It describes the principles of operation of various elements and functional units, provides a large number of practical circuits of receivers, transmitters, as well as digital frequency synthesizers that make up modern radio stations (transceivers). The book discusses in-phase and anti-phase hybrid connections (couplers), which are widely used in communications technology for dividing and summing power. An analysis of various filters (bandpass, low-pass filters, high-pass filters with various approximations) and their characteristics are also given: Chebyshev, Butterworth, Cauer, etc. filters are considered. Depending on the specific task for which a particular filter is intended, recommendations are given on the correct choice of type filter in different places of the tract. In this case, the calculation procedure is given, which is brought to the level of nomograms, which makes it possible to easily and quickly select the required frequency response (amplitude-frequency response) and ensure the necessary suppression of unwanted frequencies. Recommendations for filter design that are important from a practical point of view are presented in a concentrated form. The book also pays considerable attention to quartz filters in the form of both grating and ladder structures. Recommendations for choosing filters and calculation formulas for their design are given (depending on the purpose). The issues of designing diode mixers of different types are considered in sufficient detail: balanced, ring, etc. At the same time, mixers are analyzed for various values of input power. Much attention is paid to amplifiers. Different types of amplifiers in different operating modes are considered. The given characteristics allow you to quickly evaluate required parameters amplifiers over a wide frequency range. Specific cascade schemes for both bipolar and field effect transistors indicating the nominal values of the elements simplify the design. Similar devices are discussed to one degree or another in the works, but in them individual functional units (amplifiers, filters, etc.) are usually “considered in theoretical terms and in most cases are analyzed in isolation without connection with specific devices in which they are used. The book is presented from a practical perspective, taking into account the role of this device depending on the requirements for the receiver as a whole.
The second part discusses the circuits and circuit elements of professional receivers, transmitters and transceivers. Among the complex and rather difficult to manufacture circuits presented, there are those typical for amateur radio and measuring equipment.
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R. A Svoren. Electronics step by step. Practical encyclopedia of a young radio amateur. 4th ed. reworked add. year 2001. 549 pp. djvu. 21.9 MB.
The radio amateur's practical encyclopedia includes popular stories about the basics of electrical, electronics and radio engineering, sound recording, television, radio reception, electronic music, automation and computer technology. The book contains many practical diagrams and descriptions of designs for self-production. The reference material in the book will be of great help to the radio amateur in his practical work. Leaving the main (educational) part of the book almost unchanged, the author added 128 short stories about modern devices, methods and applications of electronics, and also developed 200 new illustrations for the book, combining them into a “Funny Note”
For a wide range of radio amateurs, it may be useful for students of schools and technical schools.
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Tkachenko F.A. Technical electronics. 2002 351 pp. djvu. 16.5 MB.
The devices, characteristics and parameters of passive elements in discrete and integrated versions are considered.
The physical basis of the operation of semiconductor devices, structure, operating principle, parameters, characteristics and methods of including semiconductor diodes and transistors in an electrical circuit are given.
There is information about the operation of amplifiers of alternating and direct signals, operational amplifiers, logic circuits and the construction of triggers, comparators, analog-to-digital and digital-to-analog converters based on them.
For students of radio engineering specialties of universities, engineering and technical workers.
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Tikhonov V.I. Statistical radio engineering. 2nd ed., revised. and additional 1982 624 pp. 30.9 MB.
The necessary information from probability theory and mathematical statistics is provided, and applied theory is presented in detail. different types random processes and their influence on the operation of nonlinear and linear systems is considered. On the base theoretical information Various meaningful radio engineering problems are considered in detail. The book includes questions from minimum programs for candidate exams in several radio engineering specialties.
For scientists, engineers, graduate students and students specializing in the field of radio engineering and automatic control.
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A. Ya. Usikov, E. A. Kaner, I. D. Truten and others. Electronics and radiophysics of millimeter and submillimeter radio waves. 1988 388 pp. djvu. 5.1 MB.
The book shows the formation of ideas and the development of research in the field of electrical science and radiophysics of millimeter and submillimeter radio waves, carried out at the Institute of Radiophysics and Electrical Science of the Academy of Sciences of the Ukrainian SSR over the past 30 years. The creation of pulsed and continuous magnetrons, magnetron triodes and tetrodes, clinotroes, reflective klystrons, measuring equipment of waveguide and beamline types, high-pervence electron optics and lasers for radiophysical research is considered. Theoretical studies of electronic resonances and waves in metals, high-frequency properties of semiconductors and plasma instabilities, experimental studies of hypersonic waves, quantum radio physics and paramagnetic masers are presented. The problems of radio vision and digital image processing, synthesis of color stereo images and visualization of radar data are covered.
For specialists working in the field of electronics and radiophysics, graduate students and students of radiophysics faculties of universities and radio engineering faculties of technical universities.
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Volume 1. 1. Circuits and components of radio engineering and electronic devices. 2. Audio broadcast receivers. 3. Television reception. 4. Electro-acoustic equipment. 5. Magnetic sound recording. 6. Equipment for amateur radio communications. 7. Automatic devices. 8. Power supply for radio equipment.
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N.I. Chistyakov editor. Reference book for amateur radio designer. In 2 volumes. 2nd ed. reworked add. 1993 366 pp. djvu. 5.7 MB.
Volume 2. 1. Measuring instruments and amateur radio measurements. 2. Design and manufacture of amateur radio equipment. 3. Components and elements of radio equipment. 4. Antennas. 5. Satellite television broadcasting.
Ministry of Education and Science of the Russian Federation
Federal State Budgetary Educational Institution
higher professional education
National Mineral Resources University "Mining"
S. I. Malinin Radio engineering circuits and signals
lecture notes
ST. PETERSBURG
UDC 621.396.6:681.3
BBK z 844.1я73-5
Lecture notes have been developed in accordance with the requirements of the state educational standard for higher professional education.
The purpose of studying the discipline is to equip students with knowledge in the field of synthesis and analysis of various radio circuits and mastering the principles of ensuring noise immunity when transmitting, receiving and reproducing signals.
The main objective of the discipline is to study the principles of generation, amplification, radiation and reception of electromagnetic waves related to the radio range; practical use of these waves for the purposes of transmitting, storing and converting information.
Lecture notes are intended for students of specialty 210601.65 - radio-electronic systems and complexes.
Malinin S.I.
D 33. Radio engineering circuits and signals/. National Mineral Resources University "Mining". St. Petersburg, 2013, 226 p.
UDC 621396.6:681.3.
BBK z 844.1я73-5
© National Mineral Resources
University "Mining", 2013
Introduction
The purpose of studying the discipline is to equip students with knowledge in the field of synthesis and analysis of various radio circuits and mastering the principles of ensuring noise immunity when transmitting, receiving and reproducing signals, the principles of generation, amplification, emission and reception of electromagnetic waves related to the radio range; practical use of these waves for the purposes of transmitting, storing and converting information.
The discipline “Radio Engineering Circuits and Signals” fully complies with the curriculum, belongs to the OPD.F.07 cycle and is studied by students of specialty 210302.65 of all forms of study in two semesters.
Improving lectures on the discipline “Radio Engineering Circuits and Signals” has been and remains an urgent task in connection with the development of radio engineering in general. The novelty of the proposed text of lectures lies in the updated methodology for presenting the material, associated with a deeper coverage of those issues that, in the author’s opinion, were not sufficiently covered in previous editions, and have become relevant to the present time.
This text of lectures does not replace the classical textbooks given in the list of references, but allows you to systematize the material being studied and makes it possible to more freely navigate a large volume of literature.
1. Deterministic radio signals
1.1. The main tasks solved by radio engineering
Radio engineering is a field of science and technology that deals with the study and application of electromagnetic oscillations and radio frequency waves. The radio range includes frequencies below the infrared range (3 THz, which is equal to 3 × 10 12 Hz).
Radio engineering solves many problems, the main one of which is transmitting information over a distance using radio waves.
Radio waves are electromagnetic waves with frequencies up to 3 THz, propagating in space without artificial guide lines. The development of radio engineering began with the invention of a device for receiving electromagnetic waves (Popov, Marconi).
Radio communication is communication between objects via radio waves. Radio communication happens:
one-sided,
double-sided,
between two objects
between several objects,
between moving or stationary objects
The range of applications of radio technology is constantly expanding. Currently, radio technology provides not only the transmission, but also the receipt of information about the environment. Radio engineering provides impact on natural or technical objects:
radar,
radio navigation,
radio control,
radiotelemetry, etc.
Radar solves the problem of detecting and recognizing various objects, as well as determining their coordinates and movement parameters using radio waves (ships, planes, missiles, structures on the ground, clouds, precipitation, etc.). Radar allows you to accurately measure the distance from the Earth to the Moon and other planets.
Radio navigation solves problems of control and movement along optimal trajectories of various objects. The main tasks solved by radio navigation are determining the optimal course and geographic coordinates of the object.
Radio control provides automatic control of objects at a distance using radio waves, radio engineering methods and means. Ensures the movement of aircraft in automatic mode (artificial earth satellites, weather probes, etc.).
Radiotelemetry solves problems of measuring at a distance using radio waves, for example, on hard-to-reach objects - radiosondes, earth satellites, etc.
Radio engineering is widely used in medicine; radio engineering methods and devices are widely used in all areas of science and technology.
Information is a collection of information about events, phenomena, objects, intended for transmission, reception, storage, and use. All applications of radio engineering are related to the transmission of information.
To convey information you need to present it in some form. Information presented in this form is called message . There are audio messages, text messages and
A message (information) can be transmitted over a distance using a specific material medium. Various signals act as carriers.
Signals – these are physical processes whose parameter values reflect transmitted messages (electrical oscillations and electromagnetic oscillations and waves).
Radio channel ensures the transmission of a message from one point to another. Basic elements of a radio channel:
transmitter,
receiver,
the physical environment in which radio waves propagate.
Processes that ensure the functioning of a radio channel using the example of a radio communication channel:
1 – Source of message (person, audio cassette...).
2 – Converter of a message into an electrical signal (microphone, tape recorder...). The output of the converter receives message signals. These signals are generally low frequency, and they are not used to excite radio waves, since the size of the antenna must be commensurate with the wavelength. To transmit information, it is modulated. Modulation consists of changing the parameters of high-frequency (secondary signal) oscillations in accordance with the low-frequency (primary) signal. A high frequency signal modified to match a low frequency signal is called a modulated signal.
3 – Radio transmitter (modulator).
High frequency vibrations are emitted by the transmitting antenna. The radio wave becomes the material carrier of the message. Some of the energy is captured by the receiving antenna.
4 – Radio receiver. It is used to receive signals and convert them to their original form (the process of converting a high-frequency modulated signal into a low-frequency signal is called demodulation, or detection). At the output of receiver 4 a low-frequency signal appears, close to the transmitted signal. The low-frequency signal is partially distorted by interference, etc. The receiver is designed in such a way that it attenuates interference as much as possible.
5 – Converter of electrical signal into message.
6 – Recipient of the message.
Basically, all these processes are associated with various signal transformations. The conversion is carried out through radio circuits.