Chebyshev filters

[Dave Stiles]

what are the practical limitations in using chebyshev filters in place of a butterworth for "end" control(for want of a better term).
what is the realworld affect of the ripple variant if applied to our passband needs eg:subs? or other bands relevant to live sound.
i cant seem to find any info about the phase and latency characteristics with this type of filter,any leads?
i was excited to find i have this type of filtering capability,but would like to understand more about it without wadeing through volumes of complicated equasions

 

[John Roberts]

Re: Chebyshev filters

what are the practical limitations in using chebyshev filters in place of a butterworth for "end" control(for want of a better term).
what is the realworld affect of the ripple variant if applied to our passband needs eg:subs? or other bands relevant to live sound.
i cant seem to find any info about the phase and latency characteristics with this type of filter,any leads?
i was excited to find i have this type of filtering capability,but would like to understand more about it without wadeing through volumes of complicated equasions

OK, I promise no equations, but there is not a simple single answer since there are multiple variant implementations of chebyshev, based on amplitude of in band ripple that is allowed. The basic concept of all active multipole filters is to mix together under-damped (goes up before rolling off) filter sections with over-damped (only goes down) sections. By carefully selecting under and over damped sections we get the maximally flat phase, or amplitude response we desire.

Chebyshev alignment throws in another variable. In addition to mixing together under- and over- damped sections, the tuning frequency is staggered with some underdamped sections beginning to roll-off at lowerfrequency than the overall effective tuning frequency. Since these lower frequency active sections are under-damped, they rise a little, before rolling off. This is what causes the in band ripple.

The trade off in Chebyshev execution is between in band ripple and and how steeply it rolls off in transition (all active multiple filters end up with the same slope past transition. Tolerating more ripple means the active poles can be spaced further apart so phase shift starts sooner. Less ripple, means the poles are spaced closer together.

In analog design the precision required for accurate constant ripple Chebyshev is fairly difficult, in the digital domain it should be easier, but I am not sure how much to trust DSP these days.

FWIW, some ported cabinets exhibit a rise before they roll off at the bottom end, not unlike the Chebyshev alignment.

JR

 

[Dave Stiles]

Re: Chebyshev filters

OK, I promise no equations, but there is not a simple single answer since there are multiple variant implementations of chebyshev, based on amplitude of in band ripple that is allowed. The basic concept of all active multipole filters is to mix together under-damped (goes up before rolling off) filter sections with over-damped (only goes down) sections. By carefully selecting under and over damped sections we get the maximally flat phase, or amplitude response we desire.

Chebyshev alignment throws in another variable. In addition to mixing together under- and over- damped sections, the tuning frequency is staggered with some underdamped sections beginning to roll-off at lowerfrequency than the overall effective tuning frequency. Since these lower frequency active sections are under-damped, they rise a little, before rolling off. This is what causes the in band ripple.

The trade off in Chebyshev execution is between in band ripple and and how steeply it rolls off in transition (all active multiple filters end up with the same slope past transition. Tolerating more ripple means the active poles can be spaced further apart so phase shift starts sooner. Less ripple, means the poles are spaced closer together.

In analog design the precision required for accurate constant ripple Chebyshev is fairly difficult, in the digital domain it should be easier, but I am not sure how much to trust DSP these days.

FWIW, some ported cabinets exhibit a rise before they roll off at the bottom end, not unlike the Chebyshev alignment.

JR

hi john,
thanks for the explanation,and u lived up to ur promiss of no calc ;^)
i really like the look of the type 2 CH filter.it seems like the perfect end control.
the filter plugin i have has a control to ajust the ripple variant.
i guess its time for a bench test to see some real world affects of its variations.