Subject Overview

An advanced study of electrical network analysis and synthesis, integrating classical circuit theory, graph-based formulations, transform methods, network functions, passive and active synthesis, filter design, computational simulation, optimization and contemporary data-driven modelling. Emphasis is placed on rigorous analysis, realizability, engineering trade-offs and validated design practice.

Learning Goal

Students will be able to formulate and solve complex electrical networks; evaluate stability, passivity and realizability; synthesize one-port, two-port and filter networks from specifications; apply computational and optimization tools; and make technically sound, ethical and standards-aware design decisions for modern electrical systems.

Syllabus

1. Network Foundations and Mathematical Preliminaries

Learning Objective: Review circuit variables, lumped-network assumptions, linearity, time invariance, causality, reciprocity, passivity, Kirchhoff’s laws, complex frequency, impedance, admittance and initial-condition conventions.

Category: foundation

2. Network Topology and Graph-Theoretic Formulation

Learning Objective: Apply graphs, trees, links, cut sets, tie sets, incidence matrices and network topology to derive systematic nodal, mesh and modified nodal equations.

Category: foundation

3. Network Theorems and Equivalent Circuits

Learning Objective: Critically apply superposition, substitution, reciprocity, compensation, Tellegen, Thévenin, Norton and maximum-power-transfer theorems to analysis, sensitivity and design decisions.

Category: core

4. Transient and Transform-Domain Analysis

Learning Objective: Analyse first- and higher-order network responses using differential equations, Laplace transforms, convolution, initial and final value theorems, natural response, forced response and switching conditions.

Category: core

5. Sinusoidal Steady State, Resonance and Frequency Response

Learning Objective: Evaluate phasor-domain networks, power and power factor, series and parallel resonance, quality factor, bandwidth, selectivity, Bode characteristics and frequency-dependent performance.

Category: core

6. Two-Port and Multiport Networks

Learning Objective: Derive and convert Z, Y, h, g, ABCD and scattering parameters; assess reciprocity, symmetry, passivity, termination, interconnection, impedance matching and power gain.

Category: core

7. State-Space and Generalized Network Models

Learning Objective: Construct state-variable models, identify independent energy-storage states, compute transition and transfer matrices, and evaluate controllability, observability, stability and descriptor formulations.

Category: advanced

8. Network Functions, Poles, Zeros and Stability

Learning Objective: Develop driving-point and transfer functions; interpret poles, zeros, residues and natural frequencies; and apply Hurwitz criteria, Routh analysis and pole-zero geometry to stability assessment.

Category: core

9. Realizability and Positive-Real Functions

Learning Objective: Determine whether prescribed immittance functions are physically realizable using positive-real conditions, Hurwitz polynomials, reactance-function properties and residue tests.

Category: advanced

10. Passive One-Port Network Synthesis

Learning Objective: Synthesize LC, RC and RL networks using Foster and Cauer forms; perform continued-fraction and partial-fraction expansions; and understand minimum-function, Brune and Bott–Duffin RLC synthesis principles.

Category: advanced

11. Two-Port, Ladder and Terminated Network Synthesis

Learning Objective: Synthesize reciprocal two-ports, ladder structures, constant-resistance networks, impedance transformers and terminated networks while balancing realizability, sensitivity and component count.

Category: advanced

12. Filter Approximation and Realization

Learning Objective: Translate specifications into Butterworth, Chebyshev, inverse-Chebyshev, elliptic and Bessel approximations; perform frequency and impedance transformations; and realize passive, active and switched-capacitor filters.

Category: application

13. Distributed, High-Frequency and Power Networks

Learning Objective: Extend network methods to transmission lines, S-parameter models, matching networks, RF/microwave interconnects, power-electronic networks and stability interactions in converter-dominated systems.

Category: application

14. Computational Network Analysis and Design Optimization

Learning Objective: Use sparse matrix methods, modified nodal analysis, SPICE, symbolic computation, numerical integration, sensitivity analysis, Monte Carlo methods, tolerance design, optimization and passivity-preserving model-order reduction.

Category: contemporary

15. Data-Driven Modelling, Governance and Emerging Practice

Learning Objective: Evaluate vector fitting, measurement-based macromodels, digital twins and AI-assisted topology or parameter optimization; validate models, manage uncertainty and reproducibility, protect data and intellectual property, and address safety, standards, sustainability and responsible engineering governance.

Category: strategic