Lec 05 - Superposition (2)

Principle of Superposition

Overview

  • The principle of superposition applies to linear circuits where the impact of each energy source can be considered independently.

  • The net result is the algebraic sum of the effects from each energy source.

Key Points

  • Electric current is a vector quantity; hence it has both magnitude and direction.

  • Superposition allows for the analysis of circuits with multiple energy sources effectively by isolating each source's influence on the circuit.

Circuit Analysis with Multiple Energy Sources

Challenges with Multiple Sources

  • In circuit analysis, multiple energy sources introduce complexity:

    • How do the energy sources impact each other?

    • What are the assigned directions of the currents?

Linear Circuit Behavior

  • The circuits being studied in this module are linear, meaning they adhere to linear operations and rules. This characteristic allows the principle of superposition to be applicable.

Steps for Applying the Principle of Superposition

Example Application Steps

  1. Isolation of Sources:

    • For each energy source (e.g., V1, V2):

      • Replace other voltage sources with short circuits.

  2. Calculating Effects:

    • Calculate voltages and currents for each isolated scenario.

  3. Sum the Effects:

    • Use algebra to find the overall voltage and current values for the circuit by summing the results from each scenario.

Terminology

  • Constructive Interference: Occurs when currents flow in the same direction.

  • Destructive Interference: Occurs when currents flow in opposing directions.

Example 5.1: Circuit Analysis Using Superposition

Circuit Configuration

  • Circuit composed of resistors and multiple voltage sources.

Calculation Steps for V1

  1. Replace V2 with a short circuit.

  2. Analyze circuit:

    • Determine the effective resistance (R(1)) and currents (I1(1), I2(1)).

  3. Find voltage outputs (VA(1), VB(1), VC(1)).

Results for V1

  • Voltage and Current Calculations:

    • VA(1) = 6V, VB(1) = 0V, VC(1) = 619.05mV

Calculation Steps for V2

  1. Replace V1 with a short circuit.

  2. Analyze the circuit again:

    • Repeat resistance and current calculations for V2.

Results for V2

  • Voltage and Current:

    • VA(2) = 0V, VB(2) = 6V, VC(2) = -619.05mV

Final Voltage and Current Calculations

  • Combine results from both sources:

    • VA = VA(1) + VA(2) = 6V

    • VB = VB(1) + VB(2) = 6V

    • VC = VC(1) + VC(2) = 0V

  • Overall currents can also be calculated similarly.

  • Note: Ensure that the direction of resulting currents is consistent with the larger values.

Summary and Exercises

Summary of Superposition Principle

  • Each energy source is evaluated independently.

  • The resulting voltages and currents are summed algebraically.

  • Placing emphasis on vector direction allows correct interpretation of resultant currents.

Exercises

  1. Exercise 5.1: Calculate voltages and currents for a new circuit setup.

  2. Exercise 5.2: Repeat using different configurations and observations.

  3. Exercise 5.3: Analyze further configuration setups using superposition principles.

  4. Exercise 5.4 - 5.9: Continue applying the principles to progressively complex circuits to reinforce understanding.