Asymmetric Clipped Waveform - find RMS

In summary, the conversation discusses finding the root mean square of an asymmetrical clipped repeating waveform with the function y(t) = ((exp(sin(t)*b)-exp(-sin(t)*b*r))/(exp(sin(t)*b)+exp(-sin(t)*b)))*(1/b). It is suggested to use either a Fourier transform or numerical calculations for simpler results. It is also mentioned that for convergence, |b|<1 must be satisfied.
  • #1
pdelaney
1
0
I have an asymmetrical clipped repeating waveform and I want to be able to find the root mean square.

The function is as follows, with r and b constants:

y(t) = ((exp(sin(t)*b)-exp(-sin(t)*b*r))/(exp(sin(t)*b)+exp(-sin(t)*b)))*(1/b)

This is pretty computationally heavy. What are some approaches to use to get to a simpler root mean square? Should I use a Fourier transform?
 
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  • #2
This simplifies to y=1/b * tanh(bsin(t)). If b is small, tanh is approximately linear and you can expand the function to calculate the rms. Alternately, you can calculate the result numerically for various values of b. Note that you must have |b|<1 for convergence.
 

1. How is the RMS value calculated for an asymmetric clipped waveform?

The RMS (Root Mean Square) value of an asymmetric clipped waveform is calculated by taking the square root of the average of the squared values of the waveform. This is also known as the effective or DC equivalent value.

2. Why is the RMS value important for an asymmetric clipped waveform?

The RMS value is important because it represents the real power of the waveform and is used to calculate the average power dissipation in a circuit. It is also used to determine the equivalent heating effect of the waveform.

3. What factors can affect the accuracy of the RMS value for an asymmetric clipped waveform?

The accuracy of the RMS value can be affected by the shape and amplitude of the waveform, as well as the sampling rate and quantization error of the measuring instrument. Noise and distortion in the waveform can also impact the accuracy of the RMS value.

4. How does an asymmetric clipped waveform differ from a symmetrical waveform in terms of RMS value?

An asymmetric clipped waveform will have a different RMS value compared to a symmetrical waveform with the same peak amplitude. This is because the RMS value takes into account the negative values of the waveform, which are typically different in an asymmetric waveform.

5. Can the RMS value be used to compare different types of asymmetric clipped waveforms?

Yes, the RMS value can be used to compare the power of different types of asymmetric clipped waveforms. However, it is important to note that the RMS value alone may not provide a complete understanding of the waveform and other factors such as peak amplitude and frequency should also be considered.

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