Thevenin and Norton Theorem

Thevenin and Norton Theorem

Thevenin's Theorem

      Thevenin’s theorem for linear electrical networks states that any combination of voltage sources, current sources and resistors with two terminals is electrically equivalent to a single voltage source and a single series resistor.It mean that it is possible to simplify any electrical circuit, no matter how complex it is. For Example:

Method 1

Step 1:  Find the open circuit voltage that will be  which is

Step 2: Take out the voltage source and make a short circuit in source connection

Method 2:  Use source transformation

Voltage source transformation

2 parallel resistances

Current source transformation

2 serial resistances

Norton's Theorem

       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. In Norton theorem, we just replace the circuit connected to a particular branch by equivalent current source . In this theorem, the circuit network is reduced into a single constant current source in which, the equivalent internal resistance is connected in parallel with it. Every voltage source can be converted into equivalent current source .It mean that this  theorem is just alternative of Thevenin theorem.

Mesh Analysis

Mesh Analysis

       Another way of simplifying the complete set of Kirchhoff’s equations is the mesh or loop current method. Note: Mesh current method is only applicable for “planar” circuits.
       There are 3 steps to consider in mesh analysis:
1.) Assign a mesh current to each mesh.
2.) Apply Kirchhoff’s voltage law (KVL) around each mesh, in the same direction as the mesh current so loop every mesh in the circuit .For example:

 

There are five mesh in this circuit.

3.) Solve the resulting loop equations for the mesh currents.

Example:

 

    Solve for the current through the 5 ohm resistor and the current through the 18V source using Mesh-Current Analysis.

Now write KVL equations for each loop.
KVL for i1:
-18V + 5(i1-i2) + 4(i1-i3) + 1(i1) = 0
then gather terms:
10i1 - 5i2 - 4 i3 -18V = 0
Note that the i1 term is positive, and all other current terms are negative (because they are all clockwise, all other panes will contribute a negative term). Let's do the other two panes with terms gathered up directly (write the total resistance of the loop multiplied by the mesh current that goes through that total resistance):
KVL for i2:
-5i1 + 10i2 - 3i3 - 12 = 0
KVL for i3:
-4i1 -3i2 +9i3 = 0
Now solve the three equations in three unknowns:
i1 = 7.02A
i2 = 6.28A
i3 = 5.21A     The current through the 5 ohm resistor is just i1 - i2, or 0.74A. The current through the 18V is i1, or 7.02A.

 

 

Circuit Theorem

Circuit Theorem

Linear Property

        Linear property is the linear relationship between cause and effect of an element. This property gives linear and nonlinear circuit definition. The property can be applied in various circuit elements.

The homogeneity (scaling) property and the additivity property are combination of linearity property.

Superposition  Property

      Suppose a branch of an electrical circuit is connected to numbers of voltage and current source s. As we can consider electrical current as electrical quantity, it can be easily assumed that total current flows through the branch is nothing but the summation of all individual currents, contributed by the each individual voltage or current source .

Source Transformation

     The source transformation of a circuit is the transformation of a power source from a voltage source to a current source, or a current source to a voltage source. In other words, we transform the power source from either voltage to current, or current to voltage.

      In voltage source transformation  just divide the voltage source to the resistor parallel or series for example:

       The other one is current source transformation just multiply the current source to the resistor parallel or series for example: