Hi there,

I read somewhere that, "The Bessel low-pass filters have a linear phase response over a wide frequency range, which results in a constant group delay in that frequency range. Bessel low-pass filters, therefore, provide an optimum square-wave transmission behavior."

I don't really understand the concept of phase response. Does a linear phase response mean that all the frequency components of the signal are shift by a linearly changing phase? Then will the whole output signal from the filter be shifted by a certain phase?

The reason I ask is that if I have a time multiplexed impulse/square wave train going into (non-linear) Bessel filter, how then can I demultiplex/deconvolve it on the output? Yes, I could use the clock source of the signal, but if there is a phase shift, the clock signal won't match the actual signal anymore, and I'll be picking up a totally different part of the signal...

Please help

Thanks

 

Yes, that's exactly what it means, but it means also that the phase changes linearly with increasing frequency. Actually, a Bessel filter is essentially a constant time delay and it is not non-linear. Therefore, it will not attenuate like most low-pass filters. If you want a linear phase LPF, use a butterworth filter as it has generalized linear phase in the passband, but you pay for that with less attenuation after the cutoff frequency compared to a Chebychev (ripples in the passband) or an Eliptical (ripples in the passband and the stopband). However, even these filters can be used on audio without messing it up due to non-linear phase vs frequency. These can be designed with arbitrarily low ripple voltage in the passband, like 1 dB, which will be unnoticed on audio signals. The answer to your second question about demuxing is way beyond the scope of this forum and needs a BSEE and probably an MSEE as well to fully understand this theory. Try to find a ready-made ckt you can copy from an IC datasheet or application note. All IC manufactureres have them and have application engineers on hand to help you, although I would not tell them that this is for a home project or you may not get help. But most IC mfgs websites are full of great info in datasheets, app notes, and white papers even so.
Good luck,
Kamran Kazem

 

Thanks for your reply kkazem,

Perhaps I could phrase the second question more simply... Will the filter introduce a time delay in the pulse train coming in? Straight after the filter, I'm putting the signal into an ADC in a micro, which will alternatively convert each component of the time multiplexed signal. So if there is a time delay, will using the clock source (way before the filter) as the "flag bit" to start each ADC conversion work?

*Correction - I'm using a Butterworth filter.

 

You're quite correct, Bessel is the response you want if integrity in the time domain is most important to you. There will always be a group delay, and you'll have to account for this. Find this delay by simulation or normalised filter tables. I'm guessing that you're using a Sallen and Key architecture (albeit with a Butterworth response); if so you'll just need to change some component values to make this a Bessel. Butterworth has a damping factor (zeta) of 0.707; Bessel is 0.8659, IIRC.

Watch out for sensitivity to component tolerances, as certain architectures magnify value deviations more than others, which will affect the response in both the time and frequency domain. S&K filters with inbuilt gain are particularly bad for this, but the unity gain variants are much tighter.