Sine Wave measurements vs equations

[Yarnzorrr]

I have the equation E(t)=7*sin(11000t+∏/3) and I measured the following:

E(.22ms) = .422V
Frequency = 1.751kHz
Period = 572.0 μs
Peak = 7V
Peak-Peak = 14V
E(rms) = 4.8V
E(average) = 105mV

I've calculated the following to compare
E(.22ms) = .422V
Frequecy = 1.75 kHz
Period = 571.4μs
Peak = 7v
Peak - Peak = 14v
E(rms) = 4.95v
E(average)=4.459V--------------------This value is no where near the measured value.


I'm using the formula Peak*0.637. Is this wrong? I'm not really sure. please help!

 

[Windadct]

Looks like you do not have a pure sine or not measuring TRUE RMS - and the measured "Average" includes the + and - side of the wave form ...~ 0v. Also "measured" RMS and Average totally depend on the instrument being used to measure with.

 

[yungman]

I have the equation E(t)=7*sin(11000t+∏/3) and I measured the following:

E(.22ms) = .422V
Frequency = 1.751kHz
Period = 572.0 μs
Peak = 7V
Peak-Peak = 14V
E(rms) = 4.8V
E(average) = 105mV

I've calculated the following to compare
E(.22ms) = .422V
Frequecy = 1.75 kHz
Period = 571.4μs
Peak = 7v
Peak - Peak = 14v
E(rms) = 4.95v
E(average)=4.459V--------------------This value is no where near the measured value.


I'm using the formula Peak*0.637. Is this wrong? I'm not really sure. please help!

Average is average value over time. For a sine wave with no offset, the top half is equal and opposite to the bottom half. So if you average out over time, it should be zero. Your assumption is not correct of Peak*0.637.

Then fact you measure 105mV average might due to the sine wave is not pure, containing even harmonic that create DC offset when averaging out.

 

[uart]

As yungman said, the average should be zero (or close to it). The value of 0.637 times the peak is for the (ideal) full wave rectified sine wave.

BTW. 0.637 is a numerical approximation of [itex]2/\pi[/itex], the theoretically exact value.

[tex]\frac{1}{\pi} \int_0^\pi \sin(x) dx = \frac{2}{\pi}[/tex]

 

[alphysicist]

I would like to point out that there are a few factors that could contribute to the discrepancy between the calculated and measured values. First, it is important to ensure that the measurement equipment used is accurate and properly calibrated. Additionally, external factors such as noise or interference could affect the measurements.

Furthermore, when dealing with sine waves, it is important to consider the phase angle. The equation given only provides the amplitude and frequency of the wave, but not the phase angle. This could also contribute to the difference between the calculated and measured values.

In terms of the formula used to calculate the RMS value, it is correct to use Peak*0.637 for a sine wave. However, it is important to note that this formula assumes a perfect sine wave, which may not always be the case in real-world measurements.

In conclusion, when comparing calculated values to measured values, it is important to consider the accuracy and calibration of the measurement equipment, external factors that may affect the measurements, and the limitations of the equations used. It may also be helpful to take multiple measurements and average them to improve accuracy.