Average Value Determination for Non-Sinusoidal Waves

The average value of a waveform over a period is the constant value that would enclose the same area over that period as the waveform itself. For simple sinusoidal waves, this can often be calculated using integration. However, many waveforms in electrical engineering are non-sinusoidal, meaning they do not follow a simple sine or cosine function. Determining the average value for these complex waveforms can be challenging.

Methods for Finding Average Value

Several methods exist to find the average value of a waveform:

• Method of Integration: This method involves finding a mathematical function that describes the waveform and then integrating it over one period, dividing by the period length. This is suitable for waveforms with simple mathematical descriptions.
• Graphical Methods (like Mid-ordinate method, Trapezoidal method): These methods approximate the area under the curve by dividing the period into several strips.
• Numerical Methods: These involve sampling the waveform at specific points and using numerical techniques to estimate the average.

Mid-ordinate Method Convenience for Non-Sinusoidal Waves

The Mid-ordinate method is particularly convenient for non-sinusoidal waves, especially when the waveform does not have a simple mathematical equation or is obtained experimentally (e.g., from an oscilloscope trace). Here's how the Mid-ordinate method works:

1. Divide the time period (T) of the waveform into a number of equal width strips, say 'n' strips. The width of each strip is \(\Delta t = T/n\).
2. At the midpoint of each strip, measure the instantaneous value of the waveform (the ordinate). Let these values be \(y_1, y_2, y_3, \ldots, y_n\).
3. The average value of the waveform is approximated by the average of these mid-ordinates: \[ \text{Average Value} \approx \frac{1}{n} \sum_{i=1}^{n} y_i \]

This method is convenient because:

• It can be applied to any waveform, regardless of its mathematical complexity or if it's only available graphically.
• It does not require finding a mathematical function for the waveform.
• The accuracy increases as the number of strips (n) increases.

For complex or irregularly shaped non-sinusoidal waves, the Mid-ordinate method provides a practical way to estimate the average value without resorting to complex integration techniques that might not even be possible if the function is unknown. The method of integration, while precise, is only practical when the waveform can be easily expressed as a mathematical function. Other methods like "Infinite method" or a generic "n-strips method" (which could encompass various numerical techniques) lack the specific definition and graphical convenience associated with the well-known Mid-ordinate method for graphical analysis.