How to Calculate Thevenin Equivalent Resistance

To calculate the Thevenin equivalent resistance (R_th), follow these clear steps.

Method 1: Turning Off Independent Sources (Most Common)

Step 1: Identify the Output Terminals

Choose the two terminals where you want the Thevenin equivalent.

Step 2: Turn Off All Independent Sources

• Voltage sources → Replace with a short circuit
• Current sources → Replace with an open circuit

Note: Do not turn off dependent sources.

Step 3: Simplify the Circuit

• Combine resistors in series and parallel
• Use circuit-reduction techniques

The remaining resistance between the terminals is R_th.

Method 2: Using Open-Circuit Voltage and Short-Circuit Current

• Open-circuit voltage (V_oc)
• Short-circuit current (I_sc)

R_th = V_oc / I_sc

Method 3: Using a Test Source (For Dependent Sources)

1. Turn off independent sources
2. Apply a test voltage source (V_test) across the terminals
3. Measure the resulting current (I_test)

R_th = V_test / I_test

Quick Summary

Source Type	What to Do
Voltage source	Replace with short
Current source	Replace with open
Dependent source	Keep active
Final step	Combine resistors

If you have a specific circuit, you can calculate its Thevenin resistance step by step.

Circuit Diagram Example

Figure: Circuit for Thevenin equivalent calculation.

Simplified Passive Circuit After Turning Off Independent Sources

Equivalent circuit as seen from terminal A:

       A
       |
      4Ω
       |
       +------------------+
       |                  |
      2Ω                 2Ω
       |                  |
      GND                 1Ω
                           |
                          GND
    

Interpretation

• From terminal A:
  • 4Ω resistor in series
  • Parallel combination of:
    • 2Ω resistor to ground
    • Series connection: 2Ω + 1Ω to ground

The resulting Thevenin resistance is:

Rth = 5.2 Ω

Further Reading