I have not seen such a formula. Most filters of this nature seem to be ad hoc designs. You are correct in your observation because each stage will provide a frequency-dependent load to the previous stage. One can easily (?) create an equation for the transfer function of an "Nth" order filter. Even without doing that, you could probably create an Excel spreadsheet to calculate the response.
I'd suggest using one of the free SPICE programs, such as TINA-TI and fiddle with the design until you get something resembling what you want.
I'd suggest using one of the free SPICE programs, such as TINA-TI and fiddle with the design until you get something resembling what you want.
There are lots of pages with such information. Google gives you lots of sites to look up.
Look up
http://www.google.co.in/search?hl=en&q=sallen+key+filter+design&meta=
and
http://www.google.co.in/search?hl=en&q=active+rc+filter+design&btnG=Search&meta=
Plenty to keep you occupied. Look at the PDF files first. You will also find application notes ( AN-? ) from TI , Analog Devices ,Cirrus and other manufacturers. Check their web sites for application notes. I have some of them somewhere but right now I don't have time to search for them.
Have fun !
Edit:
Hoho ! Just noticed you said passive filters . Well change the search string to " passive RC filter design " on the google search.
But then you can also do that fairly easily mathematically ! How many poles are you talking about ? You don't mind the degrading Q as you keep increasing the order ?
Look up
http://www.google.co.in/search?hl=en&q=sallen+key+filter+design&meta=
and
http://www.google.co.in/search?hl=en&q=active+rc+filter+design&btnG=Search&meta=
Plenty to keep you occupied. Look at the PDF files first. You will also find application notes ( AN-? ) from TI , Analog Devices ,Cirrus and other manufacturers. Check their web sites for application notes. I have some of them somewhere but right now I don't have time to search for them.
Have fun !
Edit:
Hoho ! Just noticed you said passive filters . Well change the search string to " passive RC filter design " on the google search.
But then you can also do that fairly easily mathematically ! How many poles are you talking about ? You don't mind the degrading Q as you keep increasing the order ?
gaetan8888 said:
The formulas would be much closer to exact if you had buffers between the passive stages. In other words, with the stages all cascaded together, you would have to derive the equations for the whole filter at once, since each stage will affect the one before it, etc. It's not difficult to do, if you know how. But you could also just use a simulator, such as the free LTspice (aka switchercad) from linear.com, and tweak the component values until you get the plot you want , or, maybe you could find some already-derived cascaded-filter equations on the web.
Hello
I did a Google search for passive filter but I did found only for one pole type formula or only generalities for the multipole type.
I want to do a 19khz RC type 4 pole low pass passive filter to put it before a mu-follower tube stage I-V output for a TDA1541 NOS Dac.
I found out that passive filter do have less phase shift than active type.
I did try with Tina but it's not easy to go by guessing and try and errors.
Thank
Bye
Gaetan
I did a Google search for passive filter but I did found only for one pole type formula or only generalities for the multipole type.
I want to do a 19khz RC type 4 pole low pass passive filter to put it before a mu-follower tube stage I-V output for a TDA1541 NOS Dac.
I found out that passive filter do have less phase shift than active type.
I did try with Tina but it's not easy to go by guessing and try and errors.
Thank
Bye
Gaetan
gaetan8888 said:
Hi Gaetan,
You need much more information about filters.
Please go to the link below and download Chapter 5:
http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html
You would need to first choose the 'type of response' that you want the filter to have, such as Butterworth, Chebyshev (several options), Bessel, Linear Phase (several options), Gaussian (several options), etc.
Then, you need to pick the 'filter realization' type, i.e. the actual circuit topology, for the filter's physical implementation, such as: passive RC sections, passive LC sections, integrator, Active Inductor, Frequency-Dependent Negative Resistor (FDNR), Sallen-Key, Multiple Feedback, State Variable, or Biquadratic. (Other filter types can also include Dual Amplifier Band Pass, Twin-T Notch, Bainter Notch, Boctor Notch, "one minus bandpass" Notch, First-Order All-Pass, Second-Order All-Pass, et al.)
In general, any of the 'filter response types' can be implemented with any of the 'filter realization types' listed in the first group above (the ones not included in the set of types in parentheses).
You will almost-certainly want to use an active filter, made with opamps, or, at the least, you would consider passive stages with opamp buffers between them. But, if you were going to use buffers between passive stages, then you might as well just use active filter stages, instead. So I think that you'll want to use active filter stages.
According to the well-respected Walt Jung/Analog Devices "Op Amp Applications Handbook", from the link above, which has Copyright 2006 (i.e. it's probably new-enough): for a reconstruction filter for the output of a DAC, "the STANDARD in the audio industry" is a 3rd-order Bessel filter. The Bessel type of filter response is used because it has the best phase response.
But they go on to show that a 3rd-order Bessel response would only give about 9-bit accuracy for the case they analyze (i.e. Assuming 8x oversampling of 48 kSPS datastream, then assuming bandedge is 30 kHz instead of 20 kHz to minimize passband roll-off, and seeing only 55dB attenuation at 12 x fo = 364kHz).
They also show that by using a 7th-order filter, with a 'Linear Phase with .05-degree equiripple error' filter response type, instead of a Bessel type, they can get close to a 20-bit system, since the stopband attenuation would be increased to about 120 dB at 12 x fo.
[But note that I don't know anything about your particular DAC device.]
They arbitrarily chose to use the FDNR 'filter realization type', because a) it has low sensitivities to component tolerances, and b) the opamps are in the shunt arms instead of directly in the signal path.
The complete schematic, and the Audio Precision analyzer's performance plots, for their finished DAC output filter design (called 'CD Reconstruction Filter') are given near the end of Chapter Five, from the link above. (Note that without the Williams book of filter-parameter tables, you probably could not design such a filter, yourself, unless automatic-filter-design software were used. If you want to try to do that, download FilterPro, from http://www.ti.com .)
Their finished filter design uses three dual opamps, seven 1 nF capacitors, and a number of resistors. The performance plots look QUITE excellent.
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