Brief information about the technological testing of the material. Carrying out technological tests. Optical and physical testing
The textbook outlines the fundamentals of the theory of deterministic and random signals, linear and nonlinear circuits with constant parameters, optimal and discrete filtering of signals, as well as self-oscillators. In addition to theoretical material, control questions are given. detailed examples of problem solving, as well as tasks for independent solution (with answers).
Recommended by the Educational and Methodological Association of Universities Russian Federation on education in the field of radio engineering, electronics, biomedical engineering and automation as a textbook for students of higher educational institutions students in the direction 210400 "Radio engineering".
Trigonometric Fourier series.
The trigonometric, harmonic series, which is most often called simply the Fourier series, occupies a special place among radio engineering applications of functional series: the importance of signal decomposition in an orthogonal harmonic system of functions is determined, in particular, by the nature of the transformation that the signal undergoes when passing through a stationary linear circuit.
The output signal in this case is a harmonic signal with the same circular frequency ω, which differs from the input in amplitude and phase shift. If the expansion of the input signal in terms of a system of trigonometric functions is known, then the output signal can be obtained as the sum of input harmonics independently transformed by the circuit. In addition, it is possible to use in the calculations the so-called symbolic method (the method of complex amplitudes), well known from the circuit theory course.
Table of contents
Foreword
1. Main characteristics of deterministic signals
1.1. Signals, signal models
1.2. Generalized Fourier Series
1.3. Trigonometric Fourier series
1.4. Spectra of some periodic signals
1.5. Fourier transform and its properties
1.6. Fourier transform of some signals
1.7. Spectra theorems
1.8. Spectral functions of product and convolution of signals
1.9. Fourier transform of some non-integrable absolutely signals
1.10. Energy Relations in Spectral Analysis
1.11. Correlation analysis of deterministic signals
1.12. Convolution of signals
1.13. Correlation-spectral analysis of deterministic signals
Tasks
2. Modulated radio signals
2.1. Modulation. Basic concepts
2.2. AM radio signals
2.3. Angle modulated radio signals
2.4. Fourier analysis of modulated radio signals
2.5. Pulse-amplitude modulation
2.6. Intrapulse modulation
2.7. The complex envelope of the radio signal. Cross-correlation function of modulated signals
2.8. Analytical Signal and Hilbert Transform
test questions and tasks
Tasks
3. Fundamentals of the theory of random processes
3.1. Implementation Ensemble
3.2. Probabilistic characteristics of random processes
3.3. Correlation functions of random processes
3.4. Stationary and ergodic random processes
3.5. Spectral characteristics of random processes
3.6. Wiener-Khinchin theorem
3.7. Narrow band random process
Control questions and tasks
Tasks
4. Linear circuits with constant parameters
4.1. Frequency and time characteristics of linear circuits. Methods for analyzing the passage of deterministic signals
4.2. Calculation of transient and impulse responses of a linear circuit
4.3. Transformation of the characteristics of a random process in a linear circuit
4.4. RC low and high pass filters and their characteristics
4.5. Passing Signals Through Simple RC Circuits
4.6. Single oscillatory circuit and its main characteristics
4.7. Linear feedback circuits
4.8. Linear circuit stability conditions
Control questions and tasks
Tasks
5. Principles of optimal linear filtering of signals against the background of noise
5.1. Matched filtering of deterministic signals
5.2. Signal-to-noise ratio at the input and output of the matched filter
5.3. Applying Matched Filters
5.4. Optimal filtering for non-white noise
5.5. Quasi-optimal filtering of deterministic signals
5.6. Optimal filtering of random signals
Control questions and tasks
Tasks
6. Fundamentals of discrete signal filtering
6.1. Analogue, Discrete and Digital Signals
6.2. Quantization noise
6.3. Kotelnikov's theorem
6.4. Spectrum of the sampled signal
6.5. Discrete Fourier Transform
6.6. Fast Fourier Transform
6.7. Z-transform method
6.8. Discrete Filtering Algorithm
6.9. Discrete filter system function
6.10. Recursive and non-recursive discrete filters
6.11. Implementation forms of digital filters
6.12. Discrete Filter Synthesis Methods
6.13. Digital Filter Synthesis Examples
6.14. Discrete random signals
Control questions and tasks
Tasks
7. Conversion of radio signals in non-linear radio circuits
7.1. Nonlinear Elements
7.2. Approximation of non-linear characteristics
7.3. Impact of a harmonic pinal on a non-inertia non-linear element
7.4. Bi- and polyharmonic action on a non-inertia non-linear element. Signal frequency conversion
7.5. Nonlinear resonant amplification and frequency multiplication
7.6. Getting amplitude-modulated oscillations
7.7. Amplitude detection
7.8. Frequency and phase detection
7.9. Impact of a random stationary signal on a non-inertia non-linear element
Control questions and tasks
Tasks
8. Generation of harmonic oscillations
8.1. Self-oscillating system
8.2. Amplitude balance and phase balance
8.3. Occurrence of oscillations in the oscillator
8.4. Stationary mode of operation of the oscillator
8.5. Soft and hard self-excitation modes
8.6. Nonlinear oscillator equation
8.7. Analysis of LC oscillator circuits
8.8. RC oscillators and oscillators with internal feedback
Control questions and tasks
Tasks
Application. Answers to tasks
Answers to the problems of chapter 1
Answers to the problems of chapter 2
Answers to the problems of chapter 3
Answers to the problems of chapter 4
Answers to the problems of chapter 5
Answers to the problems of chapter 6
Answers to the problems of chapter 7
Answers to the problems of chapter 8
Bibliography
Alphabetical index.
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Textbooks and study guides
1. I.S. Gonorovsky. Radio engineering circuits and signals. - M .: Radio and communication, 1986
Download: DjVu (10.8M)
2. Popov V.P. Fundamentals of the theory of circuits. – M.: graduate School, 1985.
Download: DjVu (3.9M)
3. Baskakov S.I. Radio engineering circuits and signals. - M .: Higher school, 1998.
Download: DjVu (5.7 M)
4. Sibert U.M. Chains, signals, systems. In two parts. – M.: Mir, 1988.
Download: Volume 1. DjVu (2.2 M) Volume 2. DjVu (2.6 M)
5. Kuznetsov Yu.V., Tronin Yu.V. Fundamentals of the analysis of linear radio-electronic circuits (temporal analysis). Textbook, - M .: MAI, 1992.
Download: PDF (1.8 M) DjVu (672 K)
6. Kuznetsov Yu.V., Tronin Yu.V. Fundamentals of the analysis of linear electronic circuits (frequency analysis). Tutorial. – M.: MAI, 1992.
Download: PDF (1.5 M) DjVu (680 K)
7. Kuznetsov Yu.V., Tronin Yu.V. Linear radio electronic circuits and signals. Exercises and tasks ( tutorial). – M.: MAI, 1994.
Download: PDF (3.3 M) DjVu (487 K)
9. Latyshev V.V. Ruchev M.K., Selin V.Ya., Sotskov B.M. Transient processes in linear circuits. – M.: MAI, 1992.
10. Latyshev V.V. Ruchev M.K., Selin V.Ya., Sotskov B.M. Spectral analysis of signals (tutorial). – M.: MAI, 1988.
11. Latyshev V.V. Ruchev M.K., Selin V.Ya., Sotskov B.M. Spectral analysis of narrow-band signals (tutorial). – M.: MAI, 1989.
12. Latyshev V.V. Ruchev M.K., Selin V.Ya., Sotskov B.M., Methods for analyzing the passage of signals through radio engineering devices (textbook). – M.: MAI, 1991.
13. Latyshev V.V., Ruchyev M.K., Selin V.Ya., Sotskov B.M., Signal conversion in nonlinear circuits (textbook). – M.: MAI, 1994.
Exercise 1. Analysis of time and frequency characteristics of impulse signals.
Download: PDF (243 K) DjVu (53 K)
Task 2. Analysis of time and frequency characteristics of periodic signals.
Download: PDF (257 K) DjVu (54 K)
Task 3. Analysis of the passage of pulsed and periodic signals through linear circuits.
Download: PDF (256 K) DjVu (56 K)
Methodical materials
1. Synthesis and analysis of digital filters using the MatLab software package
Download: PDF (457 K) DjVu (248 K)
The proposed materials contain a course of lectures, a set of homework assignments and term paper on the synthesis of frequency-selective filters.
Compiler: associate professor of department 405 Ruchev Mikhail Konstantinovich.
Lecture 1 . Active linear circuits. Basic equivalent circuits for linear, active circuits. Main methods of analysis of linear circuits. PDF
Lecture 2 . Low frequency amplifier. The main characteristics of ULF. PDF
Lecture 3 . resonant amplifier. Passage of radio signals. Demodulation effect. PDF
Lecture 4 . Feedback in linear circuits. Positive and negative OS. PDF
Lecture 5 . The concept of nonlinear distortion. Stability of feedback circuits. PDF
Lecture 6 . Matched and frequency selective filters (CHF). Statement of the problem of synthesis of CHIF. PDF
Lecture 7 . Chebyshev filters. Synthesis of filters of other types. PDF
Lecture 8 . CHIF implementation: ladder, cascade, ARC implementation. PDF
Lecture 9 . 9. Statement of the problem of analysis of nonlinear circuits. Approximation of the nonlinear CVC: polynomial, linear-polyline. PDF
Lecture 10 . Spectral analysis of output current in cutoff mode. PDF
Lecture 11 . Amplitude modulator and amplitude detector. PDF
Lecture 12 . diode detector. Frequency, phase detectors. PDF
Lecture 13 . Nonlinear resonant amplification. Frequency multiplication. Frequency conversion. PDF
Lecture 14 . Discrete signals and their processing. Kotelnikov's theorem. PDF
Lecture 15 . Mathematical description of discrete signals. PDF
Lecture 16 . Discrete Fourier transform. Direct Z-transform. PDF
Lecture 17 . Inverse Z-transform. Digital filters. PDF
Lecture 18 . Analysis of digital filters. PDF
Compiler: associate professor of department 405 Ruchev Mikhail Konstantinovich.
Lesson plan .
To assess the ability of the material to perceive certain under conditions as close as possible to production, technological tests are used. Such assessments are of a qualitative nature. They are necessary to determine the suitability of the material for the manufacture of products using a technology that involves a significant and complex.
To determine the ability of sheet material up to 2 mm thick to withstand operations (drawings), the method of testing for drawing a spherical hole using special punches having a spherical surface (GOST 10510) is used.
Figure 1 - Scheme of the test for drawing a spherical hole according to Eriksen
During the test, the pulling force is fixed. The design of the device provides for automatic termination of the drawing process at the moment when the force begins to decrease (the first cracks appear in the material). A measure of the ability of a material to draw is the depth of the elongated hole.
A sheet or tape less than 4 mm thick is tested for kink (GOST 13813). The test is carried out using the fixture shown in figure 2.
Figure 2 - Scheme of the kink test
1 - lever; 2 - replaceable leash; 3 - sample; 4 - rollers; 5 - sponges; 6 - vice
The sample is first bent to the left or right by 90 0, and then each time by 180 0 in the opposite direction. The criterion for the end of the test is the destruction of the sample or the achievement of a given number of kinks without destruction.
Wire made of non-ferrous and ferrous metals is tested for twisting (GOST 1545) with the determination of the number of full revolutions before the destruction of samples, the length of which is usually 100 * d (where d is the wire diameter). The kink test (GOST 1579) is also used according to a scheme similar to the sheet material test. Carry out a winding test (GOST 10447). The wire is wound in tightly fitting turns on a cylindrical rod of a certain diameter.
Figure 3 - Wire winding test
The number of turns should be within 5 ... 10. An indication that the sample has passed the test is the absence of delamination, peeling, cracks or tears in both the base material of the sample and its coating after winding.
For pipes with an outer diameter of not more than 114 mm, a bend test (GOST 3728) is used. The test consists in a smooth bending of a pipe section in any way at an angle of 90 0 (Figure 4, position a) so that its outer diameter in no place becomes less than 85% of the initial one. GOST sets the value of the bend radius R depending on pipe diameter D and wall thickness S. The sample is considered to have passed the test if no metal discontinuities are found on it after bending. Samples of welded pipes shall withstand the test in any position of the weld.
The beading test (GOST 8693) is used to determine the ability of the pipe material to form a flange of a given diameter D (Figure 4, item b). A sign that the sample passed the test is the absence of cracks or tears after flanging. Flanging with preliminary distribution on the mandrel is allowed.
The expansion test (GOST 8694) reveals the ability of the pipe material to withstand deformation during expansion into a cone up to a certain diameter D with a given taper angle α (Figure 4, item c). If, after distribution, the sample does not have cracks or tears, then it is considered to have passed the test.
For pipes, a test for flattening to a certain size H (figure, position d) is provided, and for welded pipes, GOST 8685 provides for the position of the seam (figure, position e), hydraulic pressure test.
To test wire or rods of round and square section intended for the manufacture of bolts, nuts and other fasteners by the method, a draft test (GOST 8817) is used. The standard recommends a certain degree of deformation. The criterion of validity is the absence of cracks, tears, delaminations on the side surface of the sample.
Figure 4 - Pipe test schemes
a - on the bend; b - on board; c - for distribution; d, e - for flattening
For bar materials, a bending test is widely used: bending to a certain angle (Figure 5, position a), bending until the sides are parallel (Figure 5, position b), bending until the sides touch (Figure 5, position c).
Figure 5 - Schemes of bending tests
a - bend to a certain angle; b - bend until the sides are parallel; c - until the sides touch
The ability of a metal to undergo various types deformations are usually detected during technological testing of samples. The results of technological tests of metals are judged by the state of their surface. If, after testing, no external defects, cracks, tears, delaminations or breaks are found on the surface of the sample, then the metal passed the test.
The extrusion test is used to determine the ability sheet metal be cold-formed and drawn. I put the sample] 'in a special device in which a hole is squeezed out with a punch with a spherical surface until the first crack appears in the metal.
A characteristic of the plasticity of a metal is the depth of the hole before the destruction of the metal.
Bending test welds carried out to determine the viscosity of a butt-welded joint. The sample is freely mounted on two cylindrical supports and subjected to bending until the first crack appears. The toughness characteristic is the magnitude of the bending angle.
A cold or hot bend test is carried out to determine the ability of a sheet metal to accept a bend given in size and shape. Test specimens are cut from the sheet without surface treatment.
For sheet metal thicknesses greater than 30 mm, a bend test is usually not carried out. A press or vise is used to carry out a bend test.
The cold settling test is used to determine the ability of a metal to accept a compressive strain of a given size and shape. The tests are carried out on rods directed into the dig and intended for the manufacture of bolts, rivets, etc. The sample must have a diameter equal to the diameter of the tested rod and a height equal to two rod diameters. In this test, the sample is upset by blows of a sledgehammer to a height specified by the technical conditions.
The flattening test is necessary to determine the ability of strip, bar or sheet metal to accept a given flattening.
A wire winding test with a diameter of up to 6 mm is designed to determine the ability of a metal to withstand a given number of turns. The wire is wound on a mandrel of a certain diameter. After winding, the wire should not have surface defects.
A wire bend test is used to determine the ability of a metal to withstand repeated bending and unbending. The test is subjected to round wire and rods with a diameter of 0.8-7 mm at a speed of about 60 kinks per minute until the sample breaks. Sample length 100-150 mm.
The test for a double roof lock is designed to determine the ability of sheet metal with a thickness of less than 0.8 mm to accept deformation given in size and shape. During the test, two sheets are connected with a double lock. The bend angle, the number of bends and bends of the lock are indicated in the technical specifications.
A pipe bend test with a diameter of not more than 115 mm in a cold or hot state is needed to determine the ability of the metal to take a bend of a given size and shape. A pipe sample not less than 200 mm long, filled with dry sand or filled with rosin, is bent 90 ° around the mandrel, the radius of which is indicated in the specifications.
A pipe flattening test is necessary to determine the ability of the metal to undergo flattening deformation. A sample with a length approximately equal to the outer diameter of the pipe is flattened by blows of a hammer (hammer, sledgehammer) or under a press to the dimensions specified in the technical specifications.
