Low-Pass Butterworth Filter

[mod31489]

Question: A broadband low-pass unity-gain Butterworth filter operates in a system that has a cutoff frequency of 25kHz. Design this filter to have the following specifications: (a) passband gain of 20dB and (b) the gain should be down at least -40dB at 100kHz, assume µ741 OPAMPs and use 750 pF capacitors.

***I understand that the magnitude of a Butterworth filter is |H(jω)| = 1/(√(1+(ω/ωc)^2n) and that my ωc in this situation is 25kHz. But after that I'm lost, I know I'm suppose to find the transfer function and work my way backwards but I'm having trouble and was wondering if anybody could help?***

 

[audioguru]

A lousy old (43 years old) 741 opamp has trouble above only 9kHz. At 25kHz its max output swing is plus and minus 5V and its max gain is about 26dB.

If 25kHz is at -3dB and 100kHz must be at -40dB or more then the lowpass filter must have a slope of 20dB/octave which needs a 4th-order Sallen and Key active lowpass filter. I don't think old 741 opamps are suitable.

 

[mod31489]

i know a 741 is an old opamp and really not the best option, but its what i'm required to use it...so im guessing in other words that the circuit would look as the attached circuit looks, but how do i decipher what the resistors would be

 

[audioguru]

Your filters are multiple-feedback inverting circuits with a cutoff frequency of about 213kHz. They are not Butterworth.
I never made one. All my filters were Sallen and Key non-inverting Butterworth filters made with good opamps.

Weren't you taught about Butterworth filters in class or in a text book?

 

[mod31489]

no we weren't taught about butterworths in class, the professor i have is notorious for giving problems and projects that have nothing to do with what you are learning in class and this is one of the subjects he opted to skip in the syllabus but still gave us a project on

 

[audioguru]

There are plenty of tutorials about Sallen and Key Butterworth 4th-order lowpass filters on the web.

 

[simonbramble]

Have a look at this - it might help:

http://www.simonbramble.co.uk/techarticles/active_filters/active_filter_design.htm

 

[audioguru]

Here is another document that explains active lowpass filters. It shows that a pretty good opamp has trouble above 100kHz (a lousy old 741 opamp will have trouble above about 10kHz):

 

[mod31489]

Butterworth Filter Design

I Just want to check and see if I'm doing this the right way

PROBLEM DESCRIPTION
A broadband low-pass unity-gain Butterworth filter operates in a system that has a cutoff frequency of 25 kHz.
Design this filter to have the following specifications:
(a) passband gain of 20 dB
(b) the gain should be down at least -40 dB at 100 kHz
Assume 741 OPAMPs
Use 750 pF capacitors
YOU MUST USE PSPICE/ORCAD TO PLOT THE FREQUENCY RESPONSE (MAGNITUDE AND PHASE) FOR BOTH THE CIRCUIT AND THE TRANSFER FUNCTION. COMPARE THE TWO SETS OF FREQUENCY RESPONSES TO SEE IF THEY ARE THE SAME. ALSO YOU MAY USE MATLAB TO CONFIRM THE RESULTS.

I Came up with the attached circuit and was wondering if i was doing this correctly

 

[audioguru]

Why do you have two identical threads??

Your lowpass filter does not have a Butterworth response and has no voltage gain.
Its resistor values are so low that they short the output of the opamps and cause the cutoff frequency to be much too high.