You mean "reconstruction filter"Now, this is an antialiasing filter after a DAC
means you need "higher order" filterI need to add a stronger filter
do an internet search for "online sallen key calculator"How can I calculate the new filter?
A 4th order transfer function can be decomposed into two 2nd order function, the same with higher order filters. Filter design tools do already calculate the individual second order blocks (bi-quads).
That is why the Q of each second-order filter is adjusted for a 4th order filter.But mind:
[40kHz 2nd order] + [40kHz 2nd order] is not [40kHz 4th order]
--> it will result in lower cutoff frequency but 4th order.
Klaus
But a filter cutoff frequency is defined by the amplitude to drop to 70.7% = -3dB.
And if you connect two LPF in series, each defined with -3dB at 40kHz it will result in -6dB at 40kHz.
--> The -3dB cutoff frequency of the combined filter is lower than 40kHz then.
Filter design tables contain the necessary Q and normalised cut-off frequencies for the required order and characteristic. You should use one to calculate the next 2nd or 4th order stage(s).
Here is one: http://alanmacy.com/design-test/ Somewhere at the bottom.
This is what I wanted to explain with posts#5 and #8.the filter I posted is correct, in fact the 39k, 39k, 100p, 100p give a cutoff at 40kHz.
However, I simulated this filter with LTSPICE and it seems that the cutoff is at 27kHz, while at 40kHz I have exactly -6dB.
??? Of course you can modify it at will. But you should decide about the intended filter specification first:but I start also being a bit worried since I cannot modify the first stage of the filter
Interesting. Never heared of that.Cut-off frequencies are not always calculated for -3 dB (half power point) attenuation. The Okawa tool apparently uses -6dB point, which explains the differences.
There are many different types of filter circuits, with different responses to changing frequency. The frequency response of a filter is generally represented using a Bode plot, and the filter is characterized by its cutoff frequency and rate of frequency rolloff. In all cases, at the cutoff frequency, the filter attenuates the input power by half or 3 dB.
What´s the idea behind defininig a filter cutoff criterium other than -3dB?
Klaus
Hi,
With additional LPF stages you can only shift the cutoff frequency to the left (lower frequency).
I assume there is no way around this.
And this is why I am asking in this forum!Another point is that an ideal reconstruction filter should be sin(x)/x. This filter characteristic is theoretically only and can be built neither with analog nor with digital filters.
Thus one uses filters that aproximate the ideal filter characteristic.
I don´t know if the original filter is designed for this .. in either way: adding new filter stages will modify the total characteristic.
It may improve the reconstruction filter - but it also may make it worse. (especially when you expect the output waveform to be exactly as the input waveform - even regarding phase shift.)
Ok, this is the reason. The signals are generated by a DAC at 100kHz S/s, and they are synthesized, not sampled. Therefore there is no energy over Nyquist.***
Another - important to know - point is: Why do you want to modify the filter at all. I assume you are not satisfied how it works now.
If so, you should say in which regard. What´s the problem now?
Its important to tell us values.
Without values we can only guess. This leads to "trial and error". But for "trial and error" you don´t need us - you can simply experiment on your own.
Also we need values how you want it to be.
Values could be: Passband ripple, passband phase shift, passband frequency, stopband frequency, stopband attenuation...
Sorry, I do not understand this point. This is one filter with 2 poles, not 2 filters. However it is not that important, it is a matter of terms.Klaus
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Hi,
This is what I wanted to explain with posts#5 and #8.
***
It is true, that 39k with 100pF gives 40kHz,
But two of them in series give 27kHz (and not 40kHz), since cutoff frequency is defined at -3dB.
Klaus
A filter with a flat frequency response and a sharp cutoff corner is called Butterworth. Its Q is 0.707.
A filter with a droopy frequency response and a gradual cutoff corner is called Bessel, but it has a better phase response and group delay than a Butterworth. Its Q is about 0.50.
The original filter in this thread is a Bessel filter.
When two Bessel filters are cascaded then the frequency response is VERY droopy and the cutoff corner is VERY gradual.
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