Lesson 9

Super Position Theorem (SPT) Overview

  • The methodology of Ohm’s law is limited to single source circuits.

  • Complexity increases with multiple sources, causing difficulties in total resistance calculations.

  • SPT allows for the analysis of circuits with multiple voltage (or current) sources by evaluating them independently.

  • For every source, the remaining sources are turned off (terminated).

  • Once a single source is active, Ohm’s law can be applied effectively.

  • The number of procedures under SPT corresponds to the number of sources in the circuit.

Comparison of Circuit Analysis Methods

  • Kirchhoff’s Law (KL):

    • Relies on equations that depend on the number of branches in the circuit.

  • Maxwell’s Equations (ME):

    • Equations depend on the number of meshes in the circuit.

  • Nodal Analysis (NA):

    • Based on equations dependent on the number of nodes in the circuit.

  • Super Position Theorem (SPT):

    • Procedural rather than equation-dependent for dealing with multi-source networks.

Power Calculation Example

  • Given Component Values:

    • R1 = 20 Ohms, R2 = 30 Ohms, R3 = 12 Ohms

    • Voltage Sources: V1 = 24V, V2 = 9V, V3 = 6V

  • Task: Solve for power consumed by R3 using SPT.

SPT Procedures

  1. Determine Number of Sources:

    • The number of sources dictates the SPT process.

  2. Activate one Source at a Time:

    • Operate the source voltages individually while shutting down others.

  3. Apply Ohm’s Law:

    • Once a single source is active, calculate parameters using Ohm’s law.

  4. Sum Currents and Voltages:

    • Total currents and voltages are summed based on the number of active sources.

Activation of Sources in SPT

  • Example Steps:

    • Activate V1 while V2 and V3 are shorted.

    • Calculate total resistance (RT1) with respect to V1.

    • Determine total current (IT1) due to V1, keeping other sources shorted.

  • Repeat the process for each source (V2 and V3), using the same procedure.

Summary of Current Calculations

  • For each source activation:

    • Calculate individual currents (I11, I21 for V1; I12, I22 for V2; I13, I23 for V3).

  • Sum all corresponding currents to find the total current through R3.

  • Final Power through R3 calculated as:

    • P = I^2 * R

  • Conclude with power calculation based on composite current results.

Key Terms and Concepts to Remember

  1. Limitations of Ohm’s law in multi-source circuits.

  2. Composite currents and voltages in circuit analysis.

  3. Existence of composite powers across circuit components.

  4. Differences between single source and multi-source circuits.

  5. General procedures and steps of SPT analysis.

  6. Advantages of SPT over Kirchhoff’s Law, Maxwell’s Equations, and Nodal Analysis.

  7. Limitations of SPT when applied to complex multi-source circuits.