What is the 3dB frequency of an RC filter and how can it be calculated?

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In summary, the conversation discusses calculating the 3dB frequency of an RC filter using results from a lab experiment. The individual is unsure if they should plot the results on a graph and look for the 3dB point, and is also questioning the accuracy of their second table of log frequencies and output voltages. Suggestions are given, including not taking the log of the frequency and using 20log() for the voltage transfer function plot. It is determined that the 3dB frequency is around 100Hz based on the results provided.
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vg19
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Homework Statement



Using your results, calculate the 3dB frequency of the RC filter.


The Attempt at a Solution



Basically in our lab, we made a simple series RC low pass filter. We put in a 16V peak to peak signal at varying frequencies below, and measured the output voltage at the capacitor (again peak to peak) on the scope. Now if I want to calc the 3dB frequency from my results, would I plot this on a graph and look for the 3dB point? I have tried this, but I think I am going wrong somewhere. The second table would be what I am trying to plot. I took first column is just the log of the frequency. The second column is 10log(Vout/Vin). It just doesn't seem right.

fin (Hz) Vo (V)
50 13.8
100 11.4
150 9.6
200 8.2
250 7.2
300 6.4




1.698970004 -0.749974923
2.000000000 -1.579527115
2.176091259 -2.326214759
3.301029996 -3.010299957
2.397940009 -3.665315444
2.477121255 -4.087127349

sorry for the formatting!
 
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  • #2
It looks OK to me, except log 200 is not 3.301029996
 
  • #3
I don't understand why you are taking the log of the frequency, but whatever. Keep in mind that the 3dB concept in this context is for the voltage transfer function plot (not power), so you should use 20log(), not 10log(). The 3dB point is basically where the output voltage amplitude is down by SQRT(2) compared to the input amplitude. I see one frequency on your first list that is darned close to this number...
 
  • #4
Firstly, you don't really have to log the frequencies. Secondly, 3dB below 16V is 16 times 10^(-3/20) which is 11.327V. Looking at the table of figures you obtained, I would say that this is roughly around the 100Hz mark.
 

1. What is the significance of the 3dB frequency in signal processing?

The 3dB frequency is significant because it marks the point at which the signal's power is reduced by half or 3 decibels. This is important in signal processing as it indicates the bandwidth or range of frequencies that the signal can accurately transmit or receive.

2. How is the 3dB frequency calculated?

The 3dB frequency is calculated using the equation f = 1/(2πRC), where f is the 3dB frequency, R is the resistance, and C is the capacitance of the circuit. This equation is derived from the transfer function of a first-order low-pass filter.

3. Can the 3dB frequency be different for different types of filters?

Yes, the 3dB frequency can vary depending on the type of filter being used. For example, a high-pass filter will have a different 3dB frequency than a low-pass filter. This is because different filters have different transfer functions and cut-off points.

4. How does the 3dB frequency affect the frequency response of a circuit?

The 3dB frequency determines the frequency response of a circuit by indicating the point at which the signal's power starts to decrease. This means that frequencies below the 3dB frequency will be attenuated or reduced, while frequencies above it will pass through relatively unaffected.

5. Why is the 3dB frequency often used as a reference point in signal processing?

The 3dB frequency is commonly used as a reference point because it is a standard measure of bandwidth and signal power. It allows for easy comparison between different signals and circuits, and is also a practical cut-off point for filtering out unwanted frequencies.

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