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Signals and Systems 1

A tantárgy neve magyarul / Name of the subject in Hungarian: Jelek és rendszerek 1

Last updated: 2019. november 19.

Dept. of Broadband Infocommunications and Electromagnetic Theory

Mathematics: differential and integral calculus, linear algebra and matrix calculus, complex numbers, first order differential equations. The credit of Mathematics A1 is mandatory

A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

A kötelező előtanulmányi rendek grafikus formában itt láthatók.

The objective of the two semester Signals and Systems classes is to introduce the basic concepts of signal and system, and to provide computational methodologies to continuous and discrete time systems. The first semester (Signals and Systems I) presents the time domain and the sinusoidal steady state analysis. The examples refer to continuous systems represented by Kirchoff type electric circuits. The principles to formulate the models and the methods to solve the resulting equations are discussed.

The students fulfilling the requirements of this class will be able to apply the methodologies of system and network analysis in the time domain and in the frequency domain in case of sinusoidal excitation.

1-2. classes (1. week)

Basic concepts: signals, systems and circuits. System properties: linearity, causality and time – invariance. Input – output relationship. Systems represented with electric circuits. Two poles. Kirchhoff type systems.

3-4. classes (2. week)

The full set of circuit equations. Series resistors and voltage division. Parallel resistors and current division. The principle of superposition. Node voltage analysis. Mesh current analysis. Source transformations. Maximum power transfer.

5-6. classes (3. week)

Coupled two poles: ideal transformer, controlled sources, ideal operational amplifier and gyrator.

7-8. classes (4. week)

Two-Port Resistive Networks. Equations of the Two-Port Networks. Reciprocity, symmetry and passivity of the Two-Ports. Equivalent circuits of reciprocal and nonreciprocal Two-Ports. Two-Ports terminated with Two-Poles. Calculation of the input and transfer characteristics.

9-10. classes (5. week)

Dynamic circuits. Capacitors, inductors, coupled capacitors and coupled inductors. Circuit equations. Regularity. Initial conditions. State variables. The normal form of the continuous time state equations. Generation of the continuous time state equations from the full set of circuit equations.

11-13. classes (6-7. week)

Solution of the continuous time state equations. The natural response and the forced response. First-order circuits. The time constant of first-order circuits. Sequential switching. Second and higher order dynamic systems and circuits. Higher order dynamic circuits with complex or equal eigenvalues. The concept of stability.

14-16. classes (7-8. week)

Step function and Dirac delta function. Generalized derivatives. The Step response and Impulse response of dynamic systems. Calculation of linear time invariant dynamic systems response to arbitrary input with convolution. The concept of bounded-input, bounded-output (BIBO) stability.

17-20. classes (9-10. week)

Sinusoidal steady state analysis. Phasor notation. The concept of impedances. The methods of circuit analysis with phasors (node voltage and mesh current analysis, source transformations). Resonant circuits, quality factor, Wheatstone-bridge. Coupled inductors (the model of a transformer). Phasor diagrams. AC Steady state power analysis: averaged power, reactive power, complex power, apparent power, power factor. Maximum power transfer.

21-22. classes (11. week)

The concept of the Network Function. Logarithmic units and quantities. The Bode- and the Nyquist- diagram. Two-Port Network equations in frequency domain. The scattering parameters of Two-Ports. Interconnection of Two-Ports and equivalent equations.

23-26. classes (12-13. week)

Periodic steady state analysis. Fourier series of periodic signals. The trigonometric, the engineering and the complex Fourier series. Calculation of systems response to periodic excitation. Properties of periodic waveforms: definitions and relations to Fourier series. Periodic steady state power analysis. Averaged power calculations based on Fourier series.

27-28. classes (14. week)

Summary, auxiliary.

During the term:

(1) Every participant obtains a 3-part homework assignment on the third week. The homework must be completed without assistance. Turn-in weeks are as indicated on the cover page. The solutions will be graded 0...5 points for each part. Zero points will be awarded for late turn-in or missed turn-in.

(2) Three small written tests are held for 0...5 points each. Missed tests cannot be supplemented.

(3) One midterm test is held, where 0...25 points can be earned.(4) The general university rules apply for course attendance.The participant will be admitted to the exam iff the following achievements are completed:

Sum the point values of the two best small tests (test1, test2), the average value of the two best homework parts (hw) and the midterm points (md): pv = (test1 + test2 + hw + md). The student obtains the signature for admission to the exam if pv is at least 20 AND at least 10 points were obtained for the midterm test.

Exam:(1) Admission the the exam is only possible if the signature has been obtained during the semester.(2) The exam consist of written and oral parts. A maximum of 60 points can be awarded in the written test (pe). The written part is graded as follows: up to 29 points: 1, from 30 points: 2, from 39 points: 3, from 45 points: 4, from 51 points: 5.

Participants who have obtained at least a grade of 2 participate in the oral exam part. The final exam grade is being decided by the examiner, taking into account the grade obtained during the written part (in most cases, a +/- 1 grade correction is customary, however, deviations are possible in some cases). Preliminary exam: N/A

Dr. Fodor György: Hálózatok és rendszerek. (55064)

Dr. Fodor György (szerk.): Villamosságtan példatár. (TKV 44555)

Recommended:

Simonyi Károly: Villamosságtan. Akadémiai Kiadó, 1983

Dr. Bokor Árpád (szerk.) Hálózatok és rendszerek. Számítógépes gyakorlatok (55042)