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10th June 2018, 22:51 #1
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lowpass RC filter design with attenuation known
Hello,
I want to ask this question stated in my textbook:
Can an lowpass RC filter be used to provide 1dB attenuation at 21 kHz and at least 22 dB attenuation at 820 kHz?
It is written in the solution that the 3 dB frequency is 41,27 kHz. I don't know where this comes from?
Can you please help m? Thank you.

10th June 2018, 23:56 #2
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Re: lowpass RC filter design with attenuation known
Hi,
What informations about filters do you have?
Do you know how they are defined?
Can you draw a frequency response chart? And insert the given informations as points and lines.
KlausPlease don´t contact me via PM, because there is no time to respond to them. No friend requests. Thank you.
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10th June 2018, 23:56

11th June 2018, 06:36 #3
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Re: lowpass RC filter design with attenuation known
The attenuation is easy enough to calc: Xc/SQRT((Xc)^2+(R)^2), 20log Answer for deciBell, where Xc = 1/( 2.pi.F.C)
at 820kHz the L of the cap and the wiring must be taken into consideration  as well as any L in the R.

11th June 2018, 07:08 #4
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Re: lowpass RC filter design with attenuation known
The combination of capacitor and resistor create a time constant (R x C). This is associated with a phase change. The phase difference results in reducing the amplitude. A given frequency is attenuated according to a formula.
To see the relationships it is helpful to draw the parallelogram angles. That might be the means to determine what time constant is suitable, and what R & C values will solve the exercise.

11th June 2018, 07:34 #5
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Re: lowpass RC filter design with attenuation known
The ratio of R/C is dependent on the value of any load R... heavy loading = large C, and vice versa ....
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11th June 2018, 07:34

11th June 2018, 22:06 #6
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Re: lowpass RC filter design with attenuation known
I applied this equation for the 1dB attenuation:
20xlog(Xc/sqrt(R^2+Xc^2)=1 dB
At the end I got RC=3.79x10^6 which is for 21kHz
Then I computed f3dB=1/(2*pi*RC)= 41993 Hz
which is quite similar to the textbook solution: 41270 Hz
Then I computed the attenuation for 820kHz and got 25.81 dB which is again similar to the textbook solution 25.97 dB.
Does that make sense? Because I did many other computations maybe with better accuracy but I lost them as there were many of meaningful and meaningless computations :)

12th June 2018, 02:40 #7
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Re: lowpass RC filter design with attenuation known
Your home work is really your concern, not to clog up message boards like this one ...
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12th June 2018, 03:23 #8
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12th June 2018, 06:08 #9
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Re: lowpass RC filter design with attenuation known
Hi,
I did not calculate the values...
But regarding the accuracy:
With low frequencies you are in an about horizontal line. This means a small error in attenuation causes a big error in frequency.
With higher frequencues you are in an steap area of the curve, then an error in attenuation causes a much smaller error in frequency.
Thus I assume, if you start your calculations from the higher frequencies you get more exact results.
I'd do such test calculations with Excel, because it's just repeating the same formula with different input values.
And you easily can calculate 50 points (or so) and draw a chart to visualize the results.
KlausPlease don´t contact me via PM, because there is no time to respond to them. No friend requests. Thank you.
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12th June 2018, 06:08

12th June 2018, 07:27 #10
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Re: lowpass RC filter design with attenuation known
Graph of ordinary RC lowpass filter (first order). The rolloff curve occupies a comparatively narrow range of the frequency spectrum. At low frequencies there is slight attenuation. At high frequencies there is extreme attenuation.
By convention, 3 dB attenuation designates the cutoff frequency. Your task is to calculate RC values which produce the desired frequencies for dB attenuation. A suitable R value to start with is 1k. This assumes the exercise can be solved for a firstorder filter. If you cannot then a secondorder filter might be needed.
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12th June 2018, 08:00 #11
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Re: lowpass RC filter design with attenuation known
The numbers in calculated in post #6 are correct, but not very accurate. Pocket calculator gives me RC = 3.8565e6.

12th June 2018, 22:01 #12
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Re: lowpass RC filter design with attenuation known
I have tried the 820 kHz and got RC=2.42e6 so it's better than the previous value gotten by 21kHz.
Anyway I don't have my own PC. I use public computer. Can you please suggest an online application that can help me with this? I think, however, that my calculations are not too bad as they are done manually.
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