MESH AND NODAL ANALYSIS

Mesh  and  nodal  analysis

mesh analysis:

     Mesh analysis  is also called as loop analysis .

      The mesh current method is a method that is used to solve planar circuits for the currents (and indirectly the voltages) at any place in the 

     This method of analysis is specially useful for the circuits they have many nodes and loops.

     The difference between the loop and kirchoffs law is in loop analysis instead of branch currents the loop currents are considered for writing the equations.

     The advantages of this method is that for complex networks the no of unknown reduces which greatly simplify calculation work.

·        While assuming loop currents,considered the loops such that each elements of the network will be included atleast once in any of the loops.

Important points to remember for loop analysis:

1.         While assuming loop currents make sure that atleast one loop currents links with every element.
2.         No two loops should identical.
3.         Choose minimum number of loop currents.
4.         Convert current source if present,into their equivalent voltage sources for loop analysis ,whenever possible.
5.         If current is particular branch is required ,then try to choose loop currents in such a way that only one loop current links with that branch.

Super mesh analysis:

      A super mesh occurs when a current source is contained between two essential meshes. The circuit is first treated as if the current source is not there. This leads to one equation that incorporates two mesh currents. Once this equation is formed, an equation is needed that relates the two mesh currents with the current source. This will be an equation where the current source is equal to one of the mesh currents minus the other.

Summary of Supermesh Analysis

·        Evaluate if the circuit is a planer circuit. if yes, apply Supermesh. If no, perform nodal analysis instead.

·        Redraw the circuit if necessary and count the number of meshes in the circuit.

·        Label each of mesh currents in the circuit. As a rule of thumb, defining all the mesh currents to flow clockwise result in a simpler circuit analysis.

·        Form a supermesh if the circuit contains current sources by two meshes. So that, the supermesh would enclose both meshes.

·        Write a KVL (Kirchoff’s Voltage Law) around each mesh and supermesh in the circuit. Begin with an easy and will fitted one node. Now proceed in the direction of the mesh current. Take the “-“ sign in the account while writing KVL equations and solving the circuit. No KVL equation is needed if a current source lies on the periphery of a mesh. So, the mesh current is determined and evaluated by inspection.

·        One KCL (Kirchhoff’s Current Law) is needed for each supermesh defined and can be accomplished by simple application of KCL. in simple words, relate the current flowing from each current source to mesh currents.

·        An additional case can be occurred if the circuit contains on further dependent sources. In this case, express any additional unknown values and qantitis like currents ir voltages other than the mesh currents in terms of suitable mesh currents.

·        Arrange and organize the system of equations.

• At last, solve the system of equations for the Nodal voltages such as V1, V2, and V3 etc. there will be Mesh of them

Nodal analysis

         In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

        In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, I_branch = V_branch * G, where G (=1/R) is the admittance (conductance) of the resistor.

      Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs (e.g. SPICE) use nodal analysis as a basis. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis, can be used.

Important points to remember for nodal analysis:

·        Note all connected wire segments in the circuit. These are the nodes of nodal analysis.

·        Select one node as the ground reference. The choice does not affect the result and is just a matter of convention. Choosing the node with the most connections can simplify the analysis. For a circuit of N nodes the number of nodal equations is N−1.

·        Assign a variable for each node whose voltage is unknown. If the voltage is already known, it is not necessary to assign a variable.

·        For each unknown voltage, form an equation based on Kirchhoff's current law. Basically, add together all currents leaving from the node and mark the sum equal to zero. Finding the current between two nodes is nothing more than "the node with the higher potential, minus the node with the lower potential, divided by the resistance between the two nodes."

·        If there are voltage sources between two unknown voltages, join the two nodes as a supernode. The currents of the two nodes are combined in a single equation, and a new equation for the voltages is formed.

·        Solve the system of simultaneous equations for each unknown voltage.