Active filter design : 2nd order sharp roll-off

[nick_d]

@rutherberg I believe the fundamental problem is that what you are asking is impossible. To give an example, suppose I was a builder and I was equipped with 30 degree and 45 degree (to the horizontal) roof trusses. The client asks me for a 15 degree sloping roof. What do I do? The best that I can achieve is to put 30 degree and then a straight section and then repeat. I can construct a 15 degree roof but stepwise.

Does that make it clearer? Having said that, I believe we can get closer to what you need. Note that @grouchobyte's solution uses basically two high pass Sallen Key filters in series (look at the lower branch and ignore the upper branch), at what? 4 kHz? Let's say 4 kHz.

Introducing some terminology, what you have is a 4 pole filter. One pole is one RC network and gives you 3dB/octave (by voltage, not power). So, if you do not want it so steep at 4 kHz, remove some poles.

On the other hand, if you want it to rise steeply from say -10dB to 0dB at 4kHz using the 4 pole filter then that is fine too, you just have to use the additive ideas already discussed to make sure there is a -10dB signal already there before the 4 pole filter rolls on and adds to it.

The problem comes with your specification for <4 kHz. If you want -20dB at 100 Hz and -10 dB at 4 kHz then it cannot be done with RC networks. The closest you can do is a ONE pole high pass network, which will give you 3dB/octave or 10dB/decade (by voltage). So it will climb from -20dB at 100 Hz to -10dB at 1 kHz which is too early. It will double again twice to -4dB by 4 kHz. So the best option is basically put another straight section in from 1 kHz to 4 kHz if that is what you need.

Thing is, that gets very complicated. I understand you would LIKE to have a certain response if you can get it by changing component values or rearranging the circuit. But are you willing to put extra chips just to make this happen? May we have an idea of what this circuit will be used for? Since your requirement is an uncommon one and might be eaaily side-stepped.

cheers, Nick

[grouchobyte]

@rutherberg I believe the fundamental problem is that what you are asking is impossible. To give an example, suppose I was a builder and I was equipped with 30 degree and 45 degree (to the horizontal) roof trusses. The client asks me for a 15 degree sloping roof. What do I do? The best that I can achieve is to put 30 degree and then a straight section and then repeat. I can construct a 15 degree roof but stepwise.

Does that make it clearer? Having said that, I believe we can get closer to what you need. Note that @grouchobyte's solution uses basically two high pass Sallen Key filters in series (look at the lower branch and ignore the upper branch), at what? 4 kHz? Let's say 4 kHz.

Introducing some terminology, what you have is a 4 pole filter. One pole is one RC network and gives you 3dB/octave (by voltage, not power). So, if you do not want it so steep at 4 kHz, remove some poles.

On the other hand, if you want it to rise steeply from say -10dB to 0dB at 4kHz using the 4 pole filter then that is fine too, you just have to use the additive ideas already discussed to make sure there is a -10dB signal already there before the 4 pole filter rolls on and adds to it.

The problem comes with your specification for <4 kHz. If you want -20dB at 100 Hz and -10 dB at 4 kHz then it cannot be done with RC networks. The closest you can do is a ONE pole high pass network, which will give you 3dB/octave or 10dB/decade (by voltage). So it will climb from -20dB at 100 Hz to -10dB at 1 kHz which is too early. It will double again twice to -4dB by 4 kHz. So the best option is basically put another straight section in from 1 kHz to 4 kHz if that is what you need.

Thing is, that gets very complicated. I understand you would LIKE to have a certain response if you can get it by changing component values or rearranging the circuit. But are you willing to put extra chips just to make this happen? May we have an idea of what this circuit will be used for? Since your requirement is an uncommon one and might be eaaily side-stepped.

cheers, Nick

Nick

Well said! It seems @Rutherberg is trying to use this filter to achieve something that may be best solved some other way. I could be wrong, but many a time I find engineers boxed into a corner with their design convinced that "only if" this particular parameter or that would conform to their will, that all would be golden. I think it's time to ask @Rutherberg to tell us more about the need for this filter and why he requires the odd filter performance. Only then can we we advise him on the best way to achieve his goal. I can certainly get the performance tweaked the way he wants but I suspect there is something very wrong with tweaking it for some system requirement that may have a dependency on this filter making it difficult to manufacture, reproduce, or modify. I guess we are back to the manure conundrum

-Bob (@grouchobyte)

[schmitt trigger]

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