re L-R
In his original paper Linkwitz pointed out the lobe wandering effect caused by two drivers being out of phase through the crossover region. He showed that lobe wandering does not occur for the second order Butterworth filter, but the amplitude responce adds to a 3db. peak, a q=.5, .707^2, being nessesary to flatten this peak. Riley pointed out that a filter that is in phase and sums to a flat amplitude is a Butterworth squared one, i.e. the second order L-R filter is the convolution of two first order sections, this being so all L-R filters must be even order since any number squared is always even.
Third order Butterworth filters are all pass since they have a constant quadrature phase shift between the two outputs, but the phase shift causes lobe wandering and the primary aim of the L-R filter is to remove this.
In his original paper Linkwitz pointed out the lobe wandering effect caused by two drivers being out of phase through the crossover region. He showed that lobe wandering does not occur for the second order Butterworth filter, but the amplitude responce adds to a 3db. peak, a q=.5, .707^2, being nessesary to flatten this peak. Riley pointed out that a filter that is in phase and sums to a flat amplitude is a Butterworth squared one, i.e. the second order L-R filter is the convolution of two first order sections, this being so all L-R filters must be even order since any number squared is always even.
Third order Butterworth filters are all pass since they have a constant quadrature phase shift between the two outputs, but the phase shift causes lobe wandering and the primary aim of the L-R filter is to remove this.
lobing
Linkwitz claims these effects to be audible. The total amount of wandering that occurs sems to be in the 15-20 degrees region, this would seem to be more of a problem with narrower vertical lobes, i.e. crossover frequencies at which the centre to centre distance is much greater than a wavelength.
Linkwitz claims these effects to be audible. The total amount of wandering that occurs sems to be in the 15-20 degrees region, this would seem to be more of a problem with narrower vertical lobes, i.e. crossover frequencies at which the centre to centre distance is much greater than a wavelength.
Interesting!
I am building a car audio system using some Focal TN45 tweeters and it looks like an 18 dB slope would suit my system best (along with alot of attenuation)!
Without having the benefit of a L-R design, do I have other options to flatten the frequency response so as not to yield a 3 dB gain at the cutoff?
Thanks
I am building a car audio system using some Focal TN45 tweeters and it looks like an 18 dB slope would suit my system best (along with alot of attenuation)!
Without having the benefit of a L-R design, do I have other options to flatten the frequency response so as not to yield a 3 dB gain at the cutoff?
Thanks
re crossovers
The general rule for crossover systems is that if the tweeter is crossed over at least an octave above its resonant frequency then the result is in practice good enough, since acoustic offset causes more abheration than the drivers own transfer function.
This is the critical matter, the L-R crossover assumes that the transfer functions of the drivers are sufficiently small in phase shift so that the filter function predominates.
There are exact, at least through the crossover region, solutions that have been described by Thiele and Leach, these are the quasi L-R types of crossovers, the Leach type requires that the crossover frequency of the tweeter is 1.85 times its resonant frequency and is third order Butterworth, the l.f. driver being 4th. order L-R.
The Thiele sort has a fifth order tweeter crossover and a fourth order woofer one with the crossover frequency at around 1.1 times the tweeter resonance.
In practice if the acoustic centres are not aligned the crossover region always has ripple of some sort even when the driver transfer functions are taken into account and practicle crossovers are tweaked to give the flatest overall curve.
The general rule for crossover systems is that if the tweeter is crossed over at least an octave above its resonant frequency then the result is in practice good enough, since acoustic offset causes more abheration than the drivers own transfer function.
This is the critical matter, the L-R crossover assumes that the transfer functions of the drivers are sufficiently small in phase shift so that the filter function predominates.
There are exact, at least through the crossover region, solutions that have been described by Thiele and Leach, these are the quasi L-R types of crossovers, the Leach type requires that the crossover frequency of the tweeter is 1.85 times its resonant frequency and is third order Butterworth, the l.f. driver being 4th. order L-R.
The Thiele sort has a fifth order tweeter crossover and a fourth order woofer one with the crossover frequency at around 1.1 times the tweeter resonance.
In practice if the acoustic centres are not aligned the crossover region always has ripple of some sort even when the driver transfer functions are taken into account and practicle crossovers are tweaked to give the flatest overall curve.
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