## Saturday, 16 August 2008

### How Can Graph Be Used As An Analytical Tool

Graph can be used in many ways. It can be used to show the trend of an event, it can solve unknowns as in simultaneous equations, it can identify the value of minimum or maximum points, and many more usages.

One important purpose of graph, however, is its ability to reflect the constraints of an equation or function. This function can come from a system under the Math Model.

Here, graph can analyse the weakness or strength of the system, or locate the value of a certain parameter that endangers its operation.

Let's show an example of the usefulness of Graph as an analytical tool.

Take the negative feedback amplifier as case-study.

The function or mathematical modelling expression of this amplifier is A / (1 + XA),
where the A is the amplification factor (or gain) of the amplifier and X is the feedback factor.

Let us plot the math equation and see the feature of this amplifier from the graph plotted.

In diagram 1, the math model equation is plotted with A = 1.

From this graph, let us analyse the features it exposes.

1. When the feedback factor (X) increases, the overall gain (y) decreases. This is so since more output signal is feedback resulting in reduction of actual input.

2. At the point when X = -1, the gain (y) becomes infinite! This is a dangerous value in that the amplifier will not operate as normal.

The 2 key features of the amplifier can therefore be revealed through proper analysis of the graph plotted using its model equation. The weakness of the system (amplifier) can then be exposed for caution and care in designing and usage.

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