SUPERPOSITION THEOREM

Definition: A linear network which contains two or more independent source can be analyzed to obtain the various voltages and branch currents by allowing the source to act one at a time, then superposition one at the time.

The principles apply of the linear relationship between current and voltages are:

1.      The Superposition Theorem states that a circuit can be analyzed with only one source of power at a time, the corresponding component voltages and currents algebraically added to find out what they'll do with all power sources in effect.

2.      To negate all but one power source for analysis, replace any source of voltage (batteries) with a wire; replace any current source with an open (break).

NORTON THEOREM

Definition: Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load.

Norton equivalent circuit

Four steps to follow for Norton’s Theorem:

1.    Find the Norton source current by removing the load resistor from the original circuit.

2.    Find the Norton current (I_N) through a short wire jumping across the open connection points where the load resistor used to be.

3.    Find the Norton resistance by removing all power sources in the original circuit (voltage sources shorted and current sources open) and calculating total resistance between the open connection points.

4.    Draw the Norton equivalent circuit, with the Norton current source in parallel with the Norton resistance. The load resistor re-attaches between the two open points of the equivalent circuit.

 

MAXIMUM POWER TRANSFER

Definition: The Maximum Power Transfer Theorem states that the maximum amount of power will be dissipated by a load resistance if it is equal to the Thevenin or Norton resistance of the network supplying power.

For example, Thevenin equivalent circuit show the Maximum Power Transfer Theorem tells us that the load resistance (R_L) resulting in greatest power dissipation is equal in value to the Thevenin resistance (R_TH) , in this case, 0.8 Ω:

The formula of the Power maximum;

THEVENIN THEOREM

Definition:  Thevenin’s Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.

Four steps to follow for Thevenin’s Theorem:

1.    Find the Thevenin source by removing the load resistor in the original circuit.

2.    Find the Thevenin resistor (R_TH) by removing all power sources in the original circuit (voltage sources shorted and current sources open) and calculating total resistance between the open points of the equivalent circuit.

3.    Find Thevenin voltage (V_TH) across the open connection points where the load resistor used to be.

4.    Draw the Thevenin equivalent circuit, with the Thevenin Voltage (V_TH) source in series with the Thevenin resistance (R_TH). The load resistor (R_L) re-attaches between the two open points of the equivalent circuit.