Brief Lecture for MEL products

★Analysis method of simulators★

Why can the circuit simulator analyze any given circuit?

As for circuit analysis, we are initially taught to obtain the current and voltage of the resistor according to Ohm’s law at school.  As we learn more at school, we are taught to obtain current by defining the mesh current for the circuit and setting up the simultaneous equation using the Kirchhoff's law.  At this time, we are requested to “analyze a certain circuit” in the question.  In other words, in order to analyze any given circuit by manual programming, simultaneous equation is set up according to the circuit in the problem.
As you might already know, what we is necessary in order to analyze any given circuit is to examine the regularity to set up the simultaneous equation according the circuit diagram.

There are some methods which are used to analyze any given circuit.  However, we will explain the “nodal point analysis method” that is most commonly used here.  This analysis method is used also in S･NAP.

＜Nodal point analysis method(Nodal analysis)＞

In the nodal point analysis method, the nodal point equation is set up at each nodal point according to Kirchhoff's law that defines “summation of current flows into one point is 0”.
As for the nodal point, the section with the identical potential is considered to be one point.  For example, as for the bridge circuit shown at left, the sections that have different potential are (1), (2), (3), and GND.  Next, Kirchhoff's law that defines “summation of current flow into one point is 0” is applied to these three nodal points.  Then,

In (1), V1Gs+(V1-V2)G1+(V1-V3)G2=Is
In (2), (V2-V1)G1+V2G3+(V2-V3)G5=0
In (3), (V3-V1)G2+(V3-V2)G5+V3G4=0

the three above equations hold.  The following equations are led when the three equations above are organized for V1, V2, and V3 and represented in the form of the matrix..


When we closely examine the section of the coefficient matrix, the section ‘�@−�@’ is ’G1+G2+Gs’, the section ‘�A−�A’is ‘G1+G3+G5’, and the section ‘�B−�B’is ‘G2+G4+G5’. These are all the sum of the elements hanging onto the nodal points. Furthermore, the element of (2) – (1) refers to ‘-G1’ that is the element value connected between (1) and (2) with the minus added. The same thing is applicable to (2) – (1). The same phenomenon can be confirmed with other elements (i.e., (1) –(3)). In other words, ‘regularity’ leading to the simultaneous equation is as follows;

·  The element of Gij(i＝j) becomes the sum of the element values (admittance) connected to the nodal point.

·  The element of Gij(i≠j) becomes the sum of the element values (admittance) connected between their nodal points that are multiplied by –1.

·  Moreover, when considering only the current element, the matrix becomes symmetric and the size of the matrix becomes equal to the number of nodes.

Thus, the regularity is found and only the simultaneous equation is to be solved.  The procedure to analyze any given circuit is as follows;

·  Number the sections with the same potential.

·  Create the admittance matrix according to the rule above.

·  Solve the simultaneous equation.

This is the principle of the nodal point analysis method.

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