Average and RMS value of Electrical Signals

To calculate average and RMS value of electrical signal and verification using MATLAB programming

At the end of this experiment students are able to

LO1: Derive average and RMS values of different signals 

LO2: Calculate average and RMS values of different signals with different combinations

LO3: Write MATLAB program for average and RMS values of different signals using symbolic math toolbox.

MATLAB Software with Symbolic toolbox

Average Value:

Definition:

The average voltage (or current) of a periodic waveform whether it is a sine wave, square wave or triangular waveform is defined as: “the quotient of the area under the waveform with respect to time”. In other words, the averaging of all the instantaneous values along time axis with time being one full period, (T).

For a periodic waveform, the area above the horizontal axis is positive while the area below the horizontal axis is negative. The result is that the average or mean value of a symmetrical alternating quantity is therefore zero, (0) because the area above the horizontal axis (the positive half cycle) is the same as the area below the axis (the negative half cycle) and thus cancel each other out. This is because when we do the maths of the two areas, the negative area cancels out the positive area producing zero average voltage.

Then the average or mean value of a symmetrical alternating quantity, such as a sine wave, is the average value measured over only one half of a cycle, since as we have just stated, the average value over one complete cycle is zero regardless of the peak amplitude.

The electrical terms Average Voltage and Mean Voltage or or even average current, can be used in both an AC and DC circuit analysis or calculations. The symbols used for representing an average value are defined as: Vavg or Iavg.

Root Mean Square Value:

The root mean square value of a quantity is the square root of the mean value of the squared values of the quantity taken over an interval. 

The value of an AC voltage is continually changing from zero up to the positive peak, through zero to the negative peak and back to zero again. Clearly, for most of the time it is less than the peak voltage, so this is not a good measure of its real effect.

The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. For example, a lamp connected to a 6V RMS AC supply will shine with the same brightness when connected to a steady 6V DC supply. However, the lamp will be dimmer if connected to a 6V peak AC supply because the RMS value of this is only 4.2V (it is equivalent to a steady 4.2V DC). 

For details see video given below

You have to solve problem assigned to your group:

This is sample program for calculation of average and RMS value

Here are questions and answers in quiz form which will be counted for your grades. Solve following quiz.