FPGA Based Digital World - Basic Analysis Techniques for DC Circuit

Basic Analysis Techniques for DC Circuit

Two circuit analysis techniques are developed from the basic laws: one is nodal anlysis, which is based on a systematic appliation of KCL; another is mesh analysis, which is based on a systematic application of KVL.

The basic idea behind is to take node or mesh as a special element to decrease the number of equations, and as a result, simplifies the analysis.

Nodal Analysis

Nodal analysis is a general procedure used to find the node voltages as circuit variables.

A node is the point of connection between two or more branches.

The steps to determine the node voltages are:

1. Select a node as the reference node(called as ground, with zero potential)

2. Assign voltages v1,v2,... to the remaining n-1nodes (n-1 variables)

3. Apply KCL to the n-1 noreference nodes, and n-1 equations are established as a result;

4. Apply Ohm's law to each branch, to express the branch current in terms of node voltages;

And substiute the currents in the equations in step 2 with node voltages;

5. Solve the resulting simulatneous n-1 equations, and the n-1 node voltages are obtained.

In step 4, the equations are usually expressed in matrix to be solved easily.

Mesh Anlaysis

Mesh analysis is a general procedure to find the mesh currents as circuit variables.

A mesh is a loop which doesn't contain any other loops within it.

The steps to determine the mesh currents are:

1.Assign mesh currents to i1, i2,... the n meshes(n variables)

2.Apply KVL to each of the meshes, and as a result, n equations are established

3.Apply Ohm's law to each mesh, and express the voltage of the each mesh in the form of current.

As a result, the equations in steps 2 are n simutaneous equations with n mesh current variables.

4.Solve the equations in step 3 to get the mesh currents.

In step 3, the equations are usually expressed in matrix to be solved easily.

Nodal Analysis or Mesh Analysis?

When to decide using Nodal or Mesh technique, below factors are to be considered.

1 Nature of the network

The basic idea is to decrease the number of variables or resulting equations.

Mesh technique: network with many series-connected elements, voltage sources or supermeshes ->more number of nodes, less number of meshes

Nodal technique: network with parallel-connected elements,voltage sources or supernodes -> more number of meshes, less number of nodes

2 Required variables

Mesh technique: mesh currents required

Nodal technique: node voltages required.

Analysis with Matlab or Mathcad or Simetrix

The equations established with the above circuit analysis techniques are usaually much complex for a complex network, and it's hardly possible to solve it with hand, so CAD tools are usually employed.

Mathcad can be used to solve the equations in formulasm, and Matlab is good at the numerical solutions to the equations established during the circuit analysis.

Simetrix on Windows can simulate the whole circuit, with the voltages, currents and even the transfer function to be obtained.

An Eaxmple

[Problem]For below BJT circuit, calculate the output voltage Vo.Suppose VBE=0.7V, and β=250.

Example_Problem