# Low Pass Bessel Filter

#### 1:1

Joined Jan 25, 2007
27
Hai dear Forum member,

I was wonder that what is low pass Bessel Filter and it application.

Thank

Regards,

Tokeda

#### hgmjr

Joined Jan 28, 2005
9,027
A low pass active filter with a Bessel response is used when the filter needs to exhibit minimum differential delay between the various frequency components of interest contained within the input signal being filtered. In essence this means that the fundamental frequency of say an applied squarewave experiences the same input-to-output delay as the other harmonics within the filter's pass-band. This results in a high degree of fidelity of the output signal relative to the input signal.

hgmjr

#### 1:1

Joined Jan 25, 2007
27
Thank hgmjr,

Do you have any example circuit?What is the different between Butterworth filter and Bessel filter?

Regards,

Tokeda

#### hgmjr

Joined Jan 28, 2005
9,027
Here is a link to some material on Thompson Phase Approximation Filters (Bessel Filters) and Butterworth Filters. The author is a professor at Georgia Tech. This is a fairly mathematically intense document.

http://users.ece.gatech.edu/~mleach/ece4435/filtrpot.pdf

One thing that is traded off when using a Bessel Filter is the gain roll-off rate on either side of the -3dB frequency. This roll-off rate is the rate at which the gain decreases as a function of frequency. It is fairly gentle in a Bessel Filter when compared to the Butterworth Filter for a given n-order filter. This is what allows the Bessel Filter to preserve the phase of the various components within the input signal.

With a Butterworth Filter, the phase of each of the different frequencies in a squarewave input signal undergo slightly longer delays as they pass through the filter. This will result in some loss of fidelity since the phase realtionship of the fundamental frequency and the harmonics contained in the input signal no longer have exactly the same phase relationship that they had in the original input signal. The Butterworth filter response exhibits a relatively constant gain as it approaches the -3dB frequency and then drops off more steeply just after the -3dB frequency than does the Bessel Filter.

Keep in mind that all filters eventually reach a frequency range at which they have the same rate of decrease in gain as a function of frequency. This rate of decrease is function of the order of the filter.

All of the above comparisons assume that the filters being compared are of the same order.

The best way to see the phenomenon that I have attempted to describe is to find a Bode plot of a Bessel filter of order n and compare it to a Butterworth Filter of order n. The differences will be readily apparent.

Filters are fairly straightforward circuits but it takes some study to gain an appreciation of their strengths and there weakness when it comes to their application.

hgmjr

hgmjr

#### Dave

Joined Nov 17, 2003
6,969
Can I suggest that whilst you are looking at Bessel and Butterworth Filters, you could also have a look at Chebyshev Filters as an additional type of linear phase filter, which provides a sharp (steep) passband-stopband transition zone at the expense of increased passband ripples.

Don't overload yourself with information, but I thought I would bring your attention to this filter type.

Dave

#### 1:1

Joined Jan 25, 2007
27
Thank hgmjr and Dave

Regards,

Tokeda