Easy Filter Design

Thread Starter

lindula

Joined Sep 23, 2016
42
Hello, my co-worker gave me the a quick guide for filter design.

Low_pass_filter.jpg
Has anyone seen something like this in filter design? I've working the numbers to see if it is valid.

Thanks
Joe
 

crutschow

Joined Mar 14, 2008
24,045
Has anyone seen something like this in filter design?
Yes.
Those are the equations for the common multiple-feedback, 2nd-order, low-pass, active filter configuration.

The other common configuration for active filters is the Sallen-Key.

The are programs available from TI and others, to calculate all the component values of these active filters for various filter order, frequency corner, and type (Bessel, Butterworth, Chebyshev, etc).
 

LvW

Joined Jun 13, 2013
888
Yes - the given formulas are correct.
The table contains the design parameters for the second-order lowpass in MFB topology - however, for a special case only: R3=R4.
(In some cases, another design strategy may be preferred: Selection of standard capacitor values).

It should be mentioned that the given set of equations can be used not only for Butterworth responses because the parameter α ("coupling factor") is the inverse of the well-known quality factor Qp (α=1/Qp) and the frequency ωo is identical to the pole frequency (ωo=ωp). However, only for a Butterworth response the pole frequency is identical to the 3dB cutoff frequency.
These pole parameters are available (tabulated) for Butterworth and Thomson-Bessel reponses as well as a variety of Chebyshev responses and can be found in many documents.
 
Last edited:

Thread Starter

lindula

Joined Sep 23, 2016
42
Yes - the given formulas are correct.
The table contains the design parameters for the second-order lowpass in MFB topology - however, for a special case only: R3=R4.
(In some cases, another design strategy may be preferred: Selection of standard capacitor values).

It should be mentioned that the given set of equations can be used not only for Butterworth responses because the parameter α ("coupling factor") is the well-known quality factor Qp (α=Qp) and the frequency ωo is identical to the pole frequency (ωo=ωp). However, only for a Butterworth response the pole frequency is identical to the 3dB cutoff frequency.
These pole parameters are available (tabulated) for Butterworth and Thomson-Bessel reponses as well as a variety of Chebyshev responses and can be found in many documents.
Hello, thank you for responding to my post. can you add more to your comment, "for a special case onlye: R3 = R4"? What cases is this not okay?

Thank you very much,
Respectfully,
Joe
 

Thread Starter

lindula

Joined Sep 23, 2016
42
Can someone look at the calculations for the Band-pass Negative Feedback the R2 calculation seems to always be negative. Do you take the absolute value of the term?

Thanks,
Joe
 

Thread Starter

lindula

Joined Sep 23, 2016
42
I found some errors in the Positive Feedback HPF and BPF so I've modified the Word document. I also did a spreadsheet to calculate the equations. I'll try some examples to test everything out. I see that for the Postive Feedback you can have the gain of 1.

Let me know of see errors.

Respectfully,
Joe
 

Attachments

Thread Starter

lindula

Joined Sep 23, 2016
42
I downloaded the FilterLab from Microchip. Here is a screen shot of a compare for a low-pass negative feedback fc of 8200.

lowpass_neg_compare.jpg

Most of the device parameters are the same except R3 and R13.
Now onto the a high pass filter compare.
 

LvW

Joined Jun 13, 2013
888
Hello, thank you for responding to my post. can you add more to your comment, "for a special case onlye: R3 = R4"? What cases is this not okay?
Hi Joe....In principle, there is an infinite number of alternatives for finding/selecting parts values for such a circuit. However, why not simplify formulas and start with some good assumptions? For example: R3=R4......
However, as a consequence of this start you have to live with capacitor values which are "uneven" - and possibly not easy to realize? Therefore, you can start with selecting the two capacitors (standard values). This will end up with "uneven" resistor values which - perhaps - are easier to realize......
 

LvW

Joined Jun 13, 2013
888
Can someone look at the calculations for the Band-pass Negative Feedback the R2 calculation seems to always be negative. Do you take the absolute value of the term?
No, you must select all the variables and parameters so that the parts values are positiv.
 

LvW

Joined Jun 13, 2013
888
Hello, my co-worker gave me the a quick guide for filter design.

View attachment 193450
Has anyone seen something like this in filter design? I've working the numbers to see if it is valid.
Hi Joe...."something like this" can be found in many books on filter design. However, for my opinion, the given expressions in the tables are nor easy to interpret and - more than that - they are restricted to one parameter set only.
As an example, in the following I give you a set of equations for the MFB lowpass which is - for my opinion - more versatil:

With: C5=C, C2=kc*C, R1=R, R3=k3*R and R4=k4*R

we get:

Ao=k4, wp=1/[R*C*SQRT(kc*k3*k4)] and Qp=SQRT(kc*k3*k4)/[k4+k3*(1+k4)]

Note that wp and Qp are pole parameters which are given for the different lowpass approximations in tabulated form.

Now, you can use some specific selections (simplifications) - for example three equal resistors with k3=k4=1

This assumption leads to:
Ao=1, wp=1/[R*C*SQRT(kc)] and Qp=SQRT(kc)/3
 
The document that jpanhalt uploaded, is similar in approach to the many "filter cookbooks" that were very popular during the 1970s, when the first low-cost monolithic opamps gained ubiquitous popularity.

I still have the Handbook of Operational Amplifier Circuit Design, by Stout and Kaufmann, 1976.

Nowadays, most of us use one of the several online design and simulation tools, or otherwise use an Excel spreadsheet.
 
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