Thevenin's Theorem

Thevenin's theorem is a theorem in electrical network theory.  This theorem states that any linear electrical network with voltage and current sources and resistances can be replaced by an equivalent circuit consisting of a single voltage source in series with a single resistor, called the Thevenin resistance.

• The Thevenin voltage is the open circuit voltage at the terminals of the network when all the internal sources are removed.
• The Thevenin resistance​ is the equivalent resistance of the network when all the internal voltage sources are replaced by short circuits and all the internal current sources are replaced by open circuits.
• Voltage Source to Current Source Transformation
  
  • Given a voltage source \(V_s\)​ in series with a resistor \(R_s\)​​, you can convert this to an equivalent current source \(I_s\) in parallel with a resistor \(R_s\).
  • The current source \(V_s\) is calculated using Ohm's Law  -  \(V_s = I_s \; R_s\)
  • The resistor \(R_s\) remains unchanged.
• Current Source to Voltage Source Transformation
  
  • Given a current source \(I_s\) in parallel with a resistor \(R_s\), you can convert this to an equivalent voltage source \(V_s\) in series with a resistor \(R_s\).
  • The voltage source \(V_s\) is calculated using Ohm's Law  -  \(V_s = I_s \; R_s\)
  • The resistor \(R_s\) remains unchanged.

These theorems are basic tools in circuit analysis, aiding engineers and designers in understanding and optimizing electrical circuits.

Steps to Apply Thevenin's Theorem

Identify the portion of the circuit for which you want to find the Thevenin equivalent.  This portion typically consists of a load resistor connected to a more complex network.
Remove the load resistor from the circuit temporarily.  This leaves the rest of the circuit, which we will simplify.
Find the Thevenin voltage (\(V_{th}\))  -  This is the open-circuit voltage at the terminals where the load resistor was connected.  Calculate the voltage across these terminals.
Find the Thevenin resistance (\(R_{th}\))  -  Deactivate all independent voltage sources (replace them with short circuits) and all independent current sources (replace them with open circuits).  Calculate the equivalent resistance seen from the terminals where the load resistor was connected.
Reattach the load resistor to the Thevenin equivalent circuit.  The circuit is now simplified to a single voltage source \(V_{th}\) in series with a resistor \(R_{th}\)​ and the load resistor.