EGR 224/Spring 2022/Sandbox

This is a page to collect some thoughts about what we are doing in class. The parts will likely be placed into a variety of different pages but for now, things are here.

The Goals

The goals for the middle and latter parts of EGR 224 are:

• To determine a consistent set of differential equations to model systems and
• To solve for the responses of those systems to a variety of input signals.

The Progression

The general progression for EGR 224 is:

• Defining fundamental quantities (charge, current, voltage, power, energy)
• Defining fundamental components / terminology (element, path, branch, essential branch, node, essential node, mesh, loop)
• Modelling basic elements (independent voltage and current sources, switches, resistors (and Ohm's Law), dependent voltage and current sources)
• Applying conservation equations (Kirchhoff's Current and Voltage Laws, conservation of Power)
• Using different frameworks for finding model equations (Node Voltage Method, Mesh Current Method, Branch Current Method, Superposition) and then solving them
• Using different frameworks for simplifying circuits (equivalent resistance, equivalent sources, Thevenin / Norton transformations)
• Using different processes for finding voltages and currents in equivalent networks (voltage division, current division)
• Introducing reactive elements, their model equations, and system constraints resulting from those elements
  • The conservation equations and frameworks from purely resistive networks still apply
• Solving different classes of reactive systems depending on the system itself and the input(s)
  • Long-term behavior of systems with constant sources (DC steady state)
  • Behavior of first-order systems with known initial conditions and constant forcing functions
  • Long-term behavior of systems with single-frequency sources (AC steady state)
    • This will include using linearity to get a system's response to sources with several single-frequency components - we can use superposition to get the response at each frequency and then add those responses together
  • Behavior of higher-order systems with known initial conditions and physically-realizable forcing functions.