Filter design

[AndrewT]

4th order Linkwitz Riley requires a cascade of two 2nd order Butterwoth filters of identical roll-off.
i.e. for a 100Hz LR4, use two 100Hz B2

 

[DF96]

The reason I'm chiming in is because I'm hoping someone will want to explain the concept of Q in low and high pass filters, it just seems a little nebulous to me at this point. I have seen damping and Q factors in equations, but I just don't understand what they're talking about.

Q is a parameter in the formula for the gain of a second-order filter. For a low or high pass second-order filter it is equal to the voltage gain at the corner frequency. It also tells you how sharp the knee is. For Q=0.707 (Butterworth) and below the curve is monotonic: no peak. For higher Q there is a peak, which gets higher as Q increases.

Try to avoid thinking of this Q as being the same as the Q of a bandpass filter, as they are not quite the same. For a resonant system (i.e. second order bandpass filter), Q is related to the ratio of stored energy and energy dissipated per cycle.

Another thing to bear in mind is that the result of cascading filters depends on whether they interact. RCRC gives a different result from RC-buffer-RC.

 

[garybdmd]

Thank you and here's a little illustration

Thank you so much guys this has been very helpful.

For anyone interested, here is an experiment I did. I started off with a source resistance of 10 ohms and went into a 22k ohm input. I used the same RC time constant or cutoff frequency (used 600hz) and ran them altogether, 1st order, second order and 3rd order. For the 1st order I stepped up impedance for matching by 47x's at each stage. (sqrt22k/10). For the 2nd order I stepped up the impedance by 13x's (22k/10)^.33. For the 3rd order I stepped up the impedance by 6.8x's (22k/10)^.25.
The figure shows the db loss from impedance mismatch, and also the change in frequency due to cascading.