Circuit theory for Electrical Engineers

Contents

• 1 Graph theory in circuits
  • 1.1 Preliminaries
    • 1.1.1 Cut-sets
    • 1.1.2 Loops
  • 1.2 Device properties
  • 1.3 The node-voltage method
    • 1.3.1 The incidence matrix
    • 1.3.2 The datum node
    • 1.3.3 Independent KVLs
    • 1.3.4 Tellegen’s theorem
    • 1.3.5 Circuit examples for node-voltage analysis
  • 1.4 The mesh method
  • 1.5 Important concepts
• 2 Network theorems
  • 2.1 Tableau analysis
  • 2.2 Superposition theorem
  • 2.3 Thévenin and Norton theorems
  • 2.4 Source transformations
  • 2.5 Reciprocity theorem
  • 2.6 Maximum power transfer theorem
  • 2.7 Important concepts
• 3 Sinusoidal steady-state analysis
  • 3.1 Preliminaries
  • 3.2 The phasor
  • 3.3 Inductors, capacitors, mutual inductances
    • 3.3.1 Inductor
    • 3.3.2 Capacitor
    • 3.3.3 Mutual inductance
  • 3.4 Circuit Analysis
  • 3.5 Network theorems
  • 3.6 Power computations with phasors
    • 3.6.1 Maximum power transfer theorem
    • 3.6.2 Reactive power
    • 3.6.3 Driving point impedance
  • 3.7 Three phase circuits
    • 3.7.1 Star-connected load
    • 3.7.2 Delta-connected load
    • 3.7.3 Symmetrical components
  • 3.8 Important concepts
• 4 Transient analysis
  • 4.1 Modified node analysis for general dynamic circuits
  • 4.2 First order circuits
  • 4.3 Second order circuits
  • 4.4 Higher order systems
  • 4.5 The matrix exponential
  • 4.6 The Laplace transform
    • 4.6.1 Important properties of the Laplace transform
    • 4.6.2 A few important Laplace transforms
    • 4.6.3 Partial fraction expansions for inverse Laplace transforms
    • 4.6.4 Solving a differential equation using Laplace transforms
    • 4.6.5 Directly solving a circuit using Laplace transforms
    • 4.6.6 Solving the state-space equation using Laplace transforms
• 5 Numerical transient analysis
  • 5.1 Forward Euler
  • 5.2 Backward Euler
  • 5.3 Trapezoidal
  • 5.4 Gear’s formula
  • 5.5 Numerical examples
  • 5.6 Numerical stability
    • 5.6.1 Stability of forward Euler
    • 5.6.2 Stability of backward Euler
    • 5.6.3 Stability of trapezoidal method
    • 5.6.4 Stability of Gear’s equations
  • 5.7 Other techniques
  • 5.8 Choice of algorithm
  • 5.9 Periodic steady state
    • 5.9.1 First order periodic steady state analysis
    • 5.9.2 Second order circuit with periodic switching
    • 5.9.3 Shooting method
  • 5.10 Important concepts
• 6 Two port networks
  • 6.1 General idea behind two-port analyses
  • 6.2 Impedance (Z) parameters
  • 6.3 Conductance (Y) parameters
  • 6.4 Star-Delta and Delta-Star conversion
  • 6.5 Hybrid (H) parameters
  • 6.6 Inverse hybrid (G) parameters
  • 6.7 Input and output impedance
  • 6.8 Transfer function
  • 6.9 Circuit configurations
    • 6.9.1 Series-series
    • 6.9.2 Series-shunt
    • 6.9.3 Shunt-series
    • 6.9.4 Shunt-shunt
  • 6.10 Multi-port networks
  • 6.11 Transmission parameters
  • 6.12 Important concepts
• 7 Transmission lines
  • 7.1 The general distributed circuit
  • 7.2 Analysis technique
  • 7.3 The wave equation
  • 7.4 Putting it all together
  • 7.5 Interpretation of the solution
  • 7.6 Reflection coefficient
  • 7.7 The response to a pulse
  • 7.8 Numerical simulation
  • 7.9 Steady-state sinusoid stimulation
  • 7.10 Quarter-wavelength lines
  • 7.11 Lossy transmission lines
    • 7.11.1 Loading coils
  • 7.12 Smith charts
  • 7.13 Important concepts
• 8 The scattering matrix
  • 8.1 Voltage and current waves
  • 8.2 Termination
  • 8.3 Impedance looking into a port
  • 8.4 Transmission
  • 8.5 Voltage and current gain
  • 8.6 Power
  • 8.7 Lossless passive two-port networks
  • 8.8 Reciprocity
  • 8.9 Important concepts
• 9 Complex Analysis in Circuit Theory
  • 9.1 Differentiation in the complex plane
  • 9.2 Integration in the complex plane
  • 9.3 Residue integration
  • 9.4 The inverse Fourier transform
  • 9.5 Cauchy’s Argument Principle
  • 9.6 Hurwitz polynomials
• 10 Elements of circuit synthesis
  • 10.1 P.r. functions
  • 10.2 General impedance synthesis
  • 10.3 Brune synthesis
  • 10.4 Transfer function synthesis
  • 10.5 Butterworth low-pass filter
  • 10.6 Chebyshev low-pass filter
  • 10.7 Minimum sensitivity realization
  • 10.8 Frequency transformations
    • 10.8.1 Low-pass to low-pass
    • 10.8.2 Low-pass to high-pass
    • 10.8.3 Low-pass to band-pass
    • 10.8.4 Low-pass to band-stop
  • 10.9 Modern electronic design
• A Z-transforms