Lecture Notes: Thevenin and Norton Equivalent Circuits

Introduction

• Topic: Finding Thevenin and Norton equivalent circuits in complex circuits.
• Complex circuits: Have multiple power supplies, making basic analysis challenging.
• Objective: Reduce complex circuits to their Thevenin or Norton equivalents.

Thevenin's Theorem

• Goal: Find the Thevenin equivalent voltage (VTH) and resistance (RTH).
• Steps:
  1. Remove the load resistor (identified between output terminals, labeled RL).
  2. Find open circuit voltage (VTH) across terminals (VAB).
  3. Determine equivalent resistance (RTH) from these terminals after short-circuiting voltage sources and open-circuiting current sources.

Finding VTH

• Open Circuit Voltage: Voltage across the terminals with load resistor removed.
• If no current flows through a component, like the 1-ohm resistor here, it doesn’t contribute to VTH.
• VTH is equal to the voltage across the current source, which is in parallel with the 12-ohm resistor.
• Use nodal analysis to find VTH by setting up equations using Kirchhoff's Current Law (KCL) and Ohm's Law.

Finding RTH

• Equivalent Resistance: Seen from the terminals after sources are turned off (voltage sources shorted, current sources open-circuited).
• Consider all resistances between terminals, including those inactive during VTH calculation.
• Calculate using parallel and series resistor combinations.

Norton's Theorem

• Goal: Find the Norton equivalent current (IN) and resistance (RN, same as RTH).
• Steps:
  1. Remove the load resistor.
  2. Short-circuit the terminals where the load was connected.
  3. Analyze circuit to find short-circuit current (IN).

Finding IN

• Use mesh or nodal analysis to determine current through the short-circuit path.
• Often involves simplifying the circuit by ignoring bypassed components due to short circuits.

Finding RN

• Same process as finding RTH; calculate equivalent resistance with sources turned off.

Analysis Methods

• Nodal Analysis: Use KCL, define current directions, and apply Ohm's Law.
• Mesh Analysis: Define mesh currents, apply Kirchhoff’s Voltage Law (KVL).
• Superposition Theorem: Consider one source at a time, sum contributions.
• Choose method based on circuit complexity and personal preference.

Conclusion

• Practice different methods for circuit analysis to understand their implications and results.
• Understanding Thevenin and Norton equivalents helps simplify analysis of complex circuits.
• The lecture included examples and explanations for each step in the analysis.