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[SOLVED] lowpass butter worth filter design

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P.Copper

P.Copper

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Hi all

I want to design a lowpass butterworth filter with a cutoff frequency of 650Hz. How do i choose a passband and stopband so to achieve the desired cutoff frequency?

Thanks!
 

You build a lowpass filter with a corner frequency of 650Hz. The passband is DC to 650Hz and the stopband is anything above 650Hz.

What amount of stopband rolloff do you need? Since you can't make a brickwall filter, there needs to be a gradual rolloff into the stopband region. The slope of the rolloff is determined by the order of the lowpass filter. Each additional filter order increases the rolloff by 6dB/octave.
 

By the passband of DC to 650Hz, do you mean that the passband has to be from 0 to 650 Hz? if that's the case i get your point. In my design i chose the passband of 49Hz and stopband of 700Hz. but this values only gives me the cutoff frequency of about 68Hz which is way lower than what i'm designing for.

I'm not really certain what stopband rolloff i need,Do i necessarily have to know the filter order before hand?

Thanks
 

A passband is a range of frequencies, not a single frequency. What exactly is the range of frequencies you want to pass?

You need the filter order so you can get the desired rolloff into the stopband. If you don't know what you need than how can you do a design? :-? What is your application?
 

If you call it a low-pass filter, then it will start of at DC and cutoff at some frequency. IF it does not start at DC (if no DC current can flow between input and output) it will be a bandpass filter technically.
 

crutschow said:
A passband is a range of frequencies, not a single frequency. What exactly is the range of frequencies you want to pass?

You need the filter order so you can get the desired rolloff into the stopband. If you don't know what you need than how can you do a design? :-? What is your application?
Click to expand...

I want to pass frequencies ranging from 49Hz up to the 6th harmonic(round about 650Hz).
What i did was to work with the minimum passband frequency and calculate the filter order, which was insane(n=70). The application is to do signal analysis of home appliances using their harmonic content.
 

If your mains is 50Hz or 60Hz then the harmonics are from 100Hz or 120Hz and up so you do not need to cut low frequencies.
 

And how much do you need to attenuate the signals above 650Hz (for example the next harmonic) and below 49Hz? That's what determines the filter order. (Don't understand how you got n=70??). And the passband is not 49Hz, the passband is 49Hz to 650Hz. The stopband is above 650Hz.

How do you get the 6th harmonic as being 650Hz if 49Hz is the fundamental? I calculate it as being around the 13th harmonic.
 

P.Copper,


You must specify the design application for which this filter was proposed.
Perhaps we can help you to define better what is the filter requirements.

+++
 

crutschow said:
And how much do you need to attenuate the signals above 650Hz (for example the next harmonic) and below 49Hz? That's what determines the filter order. (Don't understand how you got n=70??). And the passband is not 49Hz, the passband is 49Hz to 650Hz. The stopband is above 650Hz.

How do you get the 6th harmonic as being 650Hz if 49Hz is the fundamental? I calculate it as being around the 13th harmonic.
Click to expand...

I chose my attenuation to be -3dB. I was working with a voltage sensor to sense a 230V supply, my fundamental frequency is 50Hz. I checked the FFT and the 1st harmonic(noticeable spike) was at 150Hz , the 2nd at 250Hz and the 3rd at 350Hz. I assumed that 150Hz was the first harmonic hence i got to a point that the 6th harmonic should be at 650Hz.

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andre_teprom said:
P.Copper,


You must specify the design application for which this filter was proposed.
Perhaps we can help you to define better what is the filter requirements.

+++
Click to expand...

All this filtering process is part of my signal conditioning circuit. I'm designing an energy meter that can classify home appliances based on their harmonic content. "I'm working with 230V, 50Hz supply"
Thanks.
 

P.Copper,


You must work with FFT analysis, so that can measure each component of bandwidth frequency spectrum.
There are many code avaliable in C language on the web, and I even already used in an embedded system.


+++
 

For a 50Hz fundamental frequency, the second harmonic (actually the first harmonic that occurs) is 100Hz which happens if the waveform is not symmetrical. Also other even-numbered harmonics might occur when the waveform is not symmetrical.

When the waveform is squashed (becoming a symmetrical square-wave) then the third harmonic (150Hz) and maybe other odd-numbered harmonics might occur.

Why don't you allow 50Hz to be shown at its full level? Then the levels of the harmonics can be compared in dB to its level.
 

andre_teprom said:
P.Copper,


You must work with FFT analysis, so that can measure each component of bandwidth frequency spectrum.
There are many code avaliable in C language on the web, and I even already used in an embedded system.


+++
Click to expand...

which websites do you recommend, i don't what to be all over the web.

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Audioguru said:
For a 50Hz fundamental frequency, the second harmonic (actually the first harmonic that occurs) is 100Hz which happens if the waveform is not symmetrical. Also other even-numbered harmonics might occur when the waveform is not symmetrical.

When the waveform is squashed (becoming a symmetrical square-wave) then the third harmonic (150Hz) and maybe other odd-numbered harmonics might occur.

Why don't you allow 50Hz to be shown at its full level? Then the levels of the harmonics can be compared in dB to its level.
Click to expand...

What do you mean by "Allow 50Hz to be shown at its full level". thanks
 

P.Copper said:
What do you mean by "Allow 50Hz to be shown at its full level"?
Click to expand...
If you use a 49Hz highpass filter then the 50Hz reference level will be reduced.
You do not need a 49Hz highpass filter. Instead a simple 10Hz highpass filter will block DC but pass the 50Hz fundamental and all the harmonics you want.

The impedance of the electricity line affects the harmonics levels so your test results will be different in different homes.
 

It sounds like your filter requirements are minimal so likely a 1st order RC low-pass active filter will suffice (series R with C to ground). The -3dB point of such a filter is 1 / (3.14 RC). For example if you use R = 9.09kΩ then C would be 27nf for a 650Hz -3db point.
 

I agree with the RC values. They refer to fc = 1 / (6.28 RC) however.
 

I have not used pi for many years. I use 0.16/RC instead. Then the frequency is 0.16/ (9.09k x 27nF)= 651.9Hz which is close to the actual number.
 

crutschow said:
It sounds like your filter requirements are minimal so likely a 1st order RC low-pass active filter will suffice (series R with C to ground). The -3dB point of such a filter is 1 / (3.14 RC). For example if you use R = 9.09kΩ then C would be 27nf for a 650Hz -3db point.
Click to expand...

This example filter is it just an active filter?

- - - Updated - - -

Thanks to everyone for all the replies.
 

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