Network analysis (electrical circuits)

Basic Concepts and Analysis Techniques
– Component: A device with two or more terminals for current flow.
– Node: A point where terminals of multiple components are connected.
– Branch: The connection between two nodes.
– Mesh: A group of branches forming a complete loop.
– Port: Two terminals with identical currents.
– Simplification: Replacing components with equivalent ones.
– Resistive circuit: Contains resistors and ideal sources.
– Equivalence: Two circuits with the same voltage and current relationship.
– One-port network: Equivalence with respect to a pair of terminals.
– Multi-port network: Equivalence with respect to all corresponding ports.
– Series impedances: Sum of individual impedances.
– Parallel impedances: Reciprocal sum of individual impedances.
– Delta-wye transformation: Impedance reduction for multi-terminal networks.
– Simple networks: Analysis without systematic approaches.
– Nodal analysis: An alternative approach using node voltage as unknown variable.
– Mesh Analysis: Analysis using mesh currents and KVL equations.
– Superposition: Calculating the effect of each generator individually.

Advanced Concepts and Techniques
– Choice of Method: Ad-hoc application of simple equivalent circuits, nodal analysis, mesh analysis, and superposition.
– Transfer Function: Expresses the relationship between input and output of a network.
– Two Terminal Component Transfer Functions: Impedance relationship for resistors, inductors, and capacitors.
– Direct Discretization Method for DAEs: Adapting ODE solution methods to DAEs in circuit simulation.
– Simulation-based Methods for Time-based Network Analysis: Solving a circuit as an initial value problem using temporal discretization.
– Non-linear Networks: Analysis of circuits with non-linear components.
– Constitutive Equations: Describing the relationship between voltage and current in non-linear components.
– Existence, Uniqueness, and Stability: Considerations for non-linear circuit analysis.
– Methods for Network Analysis: Different approaches for analyzing linear and non-linear aspects of a circuit.

Biasing and Small Signal Analysis of Non-Linear Devices
– Biasing of Non-Linear Devices: Choosing the operating point of a non-linear device.
– Small Signal Equivalent Circuit: Representing non-linear devices with an equivalent linear network.
– Piecewise Linear Method: Approximating the transfer function of a non-linear device using straight lines.
– Time-Varying Components: Representing non-linear components with periodically varying linear components.
– Vector Circuit Theory: Generalization of circuit theory for circuits like spin circuits.

Specialized Techniques and Applications
– Delta-wye transformation: Impedance reduction for multi-terminal networks.
– Extension to star-polygon transformations: Expanding the delta-wye transformation to more complex networks.
– Representation of non-ideal generators: Modeling non-ideal generators in circuit analysis.
– Superposition of powers: Limitations of superposition in finding total power consumed in linear circuits.
– Effective medium approximations for high-density random resistors: Approximations for analyzing circuits with many resistors.

Advanced Topics and Emerging Technologies
– Laplace transform: Converting differential equations to the s-domain for control theory applications.
– Methods for analyzing linear and non-linear aspects of a circuit: Different approaches for analyzing circuit behavior.
– Graphical methods: Load line analysis for determining the quiescent operating point of non-linear devices.
– Transistor [h] parameters: Two-port network parameters used for analyzing transistor behavior.
– Piecewise Linear Method for diodes: Approximating the transfer function of a diode using straight lines.
– Vector Circuit Theory for spin circuits: Generalization of circuit theory for circuits in spintronics. Source:  https://en.wikipedia.org/wiki/Circuit_Analysis