Effect of R on Stop-Band Attenuation

Consider the component R of the Frequency Selective Network in a 4th order S&K LPF with Input Buffer Stage (Butterworth Filter Response)

I have noticed that as the value of R increases, the attenuation at the stop band of the Butterworth response improves (decreases). What is the explanation for this?

The rest of the parameters such as passband gain and frequency cut off can be explained through the common formulas but for the stop band attenuation, how is this rationalized?

Thanks=)

A 4th-order Sallen and Key lowpass filter uses two 2nd-order stages in series.
Each 2nd-order filter uses two resistors and the value of the resistors (and value of the two capacitors) affects the cutoff frequency. When the value of the resistors is increased then the cutoff frequency drops which improves the cutoff of high frequencies.

Each order causes a cutoff slope of 6dB/octave so a 4th-order filter has a slope of 24dB/octave.

got it=) thanks so much..

should I want to construct the S&K Butterworth Filter, are there any kinds of passive components that are not suitable for active filter design?

Use 5% film capacitors if you can. Ceramic capacitors and non-polar electrolytic capacitors might have a tolerance of 20% or worse.
You probably cannot use polarized electrolytic or tantalum capacitors.

Why do you want to chop off high frequencies? It makes music and speech sound awful.

haha...im doing it not for an application but for a test analysis =)

thanks for the great information=)

but im sorry to have to bother you again with another question...

i understand that butterworth's have no ripple in the pass and stop band but my design seems to have a ripple..attached is my circuit..may i know what causes this? thanks=)

thanks again=)

Your circuit works poorly because you used lousy old 741 opamps that are 42 years old and have trouble above only 9kHz.
It will work well up to maybe 500kHz if you use TL071, TL072 or TL074 audio opamps that work well up to 100kHz.

Your resistor values are too low. Most opamps cannot drive a load as low as 680 ohms. Look at the datasheet where they perform poorly with a 2k load and work better with a 10k load.

thank you for the wonderful advice
appreciate you so much for your help=)