Form factor of a pure sinusoidal waveform is:

Explanation:

Form Factor of a Pure Sinusoidal Waveform

Definition: The form factor of a waveform is defined as the ratio of the RMS (Root Mean Square) value to the average value (mean of the absolute values) of the waveform. It is a measure that provides insight into the shape and characteristics of the waveform.

Mathematical Expression: For a pure sinusoidal waveform, the form factor (FF) is given by the formula:

FF = (RMS Value) / (Average Value)

Calculation of RMS Value:

The RMS value of a pure sinusoidal waveform can be derived from its peak value (V_peak). For a sinusoidal waveform:

V_RMS = V_peak / √2

Calculation of Average Value:

The average value of a pure sinusoidal waveform, which is the mean of the absolute values over one complete cycle, is given by:

V_avg = 2V_peak / π

Derivation of Form Factor:

Using the values derived above, the form factor for a pure sinusoidal waveform can be calculated as follows:

FF = (V_peak / √2) / (2V_peak / π)

By simplifying this expression, we get:

FF = (π / 2√2)

By evaluating the numerical value of π / 2√2, we obtain:

FF ≈ 1.11

Correct Option Analysis:

The correct option for the form factor of a pure sinusoidal waveform is:

Option 1: 1.11

This option correctly represents the calculated form factor for a pure sinusoidal waveform. The form factor value of 1.11 indicates that the RMS value is slightly higher than the average value, reflecting the shape and nature of the sinusoidal waveform.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 1.414

This value represents the RMS to Peak value ratio for a sinusoidal waveform, not the form factor. The value 1.414 (√2) is the factor by which the peak value is divided to obtain the RMS value, not the average value.

Option 3: 0.707

This value is the reciprocal of the value in Option 2. It represents the RMS value as a fraction of the peak value of a sinusoidal waveform. This is not the form factor but rather the scaling factor between the RMS and peak values.

Option 4: 3.1415

This value is an approximation of π and does not relate to the form factor of a sinusoidal waveform. It is irrelevant to the context of form factors and waveforms.

Conclusion:

Understanding the form factor of a waveform is essential for analyzing and characterizing electrical signals. For a pure sinusoidal waveform, the form factor is a specific ratio that helps in understanding the relationship between its RMS and average values. The correct form factor for a pure sinusoidal waveform is 1.11, derived from the mathematical relationship between its RMS and average values. This knowledge is crucial in various applications, including electrical engineering and signal processing, where accurate waveform analysis is necessary.