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Question

What is the relationship between Em (average voltage) and Eo (peak voltage)?


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Solution

Step 1: Definition

  1. Peak voltage would be defined as a function's greatest instantaneous measurements obtained from zero volts. Denoted by Eo, it would be the most volatile point in whatsoever voltage waveform. This same resultant peak voltage is determined by the switching frequency as well as cable length.
  2. Average voltage was calculated by summing a sequence of instantaneous alternating measurements and afterward dividing the summation by the number of impulse responses utilized. It is denoted by Em.

Step 2: Finding the relationship between Em and Eo

We know,

E(t)=Eosinωt

The area under a positive half cycle with a period of T can be calculated as,
Area=0πEosinωtdt

The instantaneous voltage of a sinusoidal wave is given as

Em=1π0πEosinθdθ

As peak voltage is constantly taking out it as a constant term we will get,

Em=Eoπ0πsinθdθ

By integrating sinθ we will get cosθ

Now,

Em=Eoπ[cosθ]0π

By applying the limits we will get,

Em=2Eoπ

The mean or average value is approximately 0.637 times greater than the peak value.

Therefore, the relationship between Em and Eo is Em=0.637Eo.


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