Circuits and systems I

Objectives:

Master the study of simple electrical circuits: fundamental laws, 1st-order circuits, ideal AOP in linear and non-linear regimes
Understand the various quantities involved in a system: quantities that act on the system (inputs) and quantities characterizing the state of the system (outputs or system responses).
Establish relationships between the inputs and outputs of a linear system, and deduce the system's properties: frequency and time behavior, dominant modes, etc.
Understand the study of an electrical circuit in the form of a system represented by the association of quadripoles, and discover the notion of matching.
Know how to manipulate tools adapted to the study of linear systems: transfer function or transmittance, representation diagrams, in particular the BODE diagram, Laplace transform, characteristic matrices
Learn about the filter function and associated templates, and the implementation of filters using passive and active elements
Methodology for synthesizing analog filter functions
Elements concerning the limitations of filter implementations
Examples of applications
Apply the knowledge acquired to a CAD environment by designing and simulating an active filter.

Contents:
This course begins with the study of simple electrical circuits: fundamental laws governing circuits (Kirchoff's laws, Thévenin and Norton's equivalent models...), study of first-order circuits.), study of first-order circuits (time constant, harmonic response, Bode diagram, sinusoidal and indexed time response), study of the ideal AOP in linear and non-linear regimes.
After a general introduction to physical systems, the focus is on the notion of transmittance or transfer function of generalized linear systems. The study of harmonic frequency response is associated with the BODE representation, widely used in electronics. The use of the Laplace transform, introduced in parallel in mathematics, then allows us to generalize the notion of transmittance and use it to study the temporal response in transient conditions (impulse, index and ramp responses). The knowledge model and behavior model aspects are thus addressed. The notion of stability is barely touched upon, paving the way for the servo systems presented in automatic control in the following semester.
This introduction to linear systems is completed by an introduction to the study of quadrupoles, with a presentation of the main representative matrices (impedance, admittance, hybrid, transfer), their properties and associations, characteristic quantities: input impedance, output impedance, no-load, on-load, gains, iterative impedance, ending with the notion of power matching, which will be detailed in the following semester.
Finally, the synthesis of filters is covered, enabling the previous concepts to be implemented. The principles, applications and limitations of these functions are presented, before a CAD synthesis example is produced.

Physics for preparatory classes or applied physics degree L1 and L2

I/ General information on linear electronic circuits 1. Basic laws: Kirchoff's laws, equivalent Thévenin and Norton models 2. 1st-order circuits: determination of the time constant, harmonic response with the Bode diagram, sinusoidal and index time response 3. The ideal linear OP amplifier: voltage amplifiers, block diagram, calculation of amplification, input impedance, main OP amplifier circuits (integrator, filters, etc.) 4. The ideal OP amplifier in non-linear operation: study of comparators and their applications (astable, etc.), study of some diode circuits (ideal diodes) II/ Generalized Linear Systems Analysis 1. Notions of systems and Transfer Function or Generalized Transmittance 2. Harmonic response and BODE representation 3. Transfer function and LAPLACE transform 4. Transient time response III/ Quadrupoles 1. Representative matrices: impedance, admittance, hybrid, transfer 2. Properties: symmetries, associations 5. Characteristic quantities: input impedance, output impedance, no-load, load, voltage and current gains, notion of power matching
IV/ Analog filters1. General information on the "filtering" function2. Filter types: passive filter, active filter3. Filter functions and associated templates: Low-pass and high-pass filters, Band-pass filter4. Filter families and response shapes5. Summary and comparison6. Filter synthesis7. Limitations8. Applications

Analog electronics
Linear circuits and systems - Analysis methods
Passive and active analog filters - Synthesis methodology

Handout - General works on linear systems and quadripoles