Filter Design Part 7. Compare Between Bessel Vs Butterworth Vs Chebyshev Vs Elliptic Filter Design.

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• Filter Design Part 1. ...
Many types of filters, they bear the names of the men who developed them. The common ones are 1) Butterworth, 2) Chebychev, 3) Elliptic, 4) Bessel, etc.
Each filter design types has its own strengths depending on the applications.
Filter Design (Bessel)
Characteristics
The Bessel filter has the most gentle response (slope) from the group.
It doesn't have a sharp cutoff but it offers superior phase shift (delay).
The Bessel filter requires the most stages (most components); however, it offers excellent characteristics like low sensitivity to component tolerance and superior step response (input).
Advantages
Best step response-very little overshoot or ringing
Smooth roll off.
No ripples.
Shortest time delay
Disadvantages
Very slow roll off speed.
Filter Design (Butterworth)
Characteristics
A medium Q filter. Initial attenuation steepness are not as good.
The Butterworth filter is commonly referred to as the "maximally flat" option because the passband response offers the steepest roll-off without inducing a passband ripple.
Designs which require the amplitude response to be as flat as possible.
Better phase response linearity than Chebychev but not Bessel.
Rate of change of phase shift occurs close to the cutoff frequencies, resulting in signal distortion if the input signal have spectral components near to the cutoff frequencies.
Possible solution: design a bandwidth that is 20% wider than needed (not always feasible).
Not recommended for band-reject filter as such filters usually require much steeper slopes than Butterworth filter can provide.
Filter order is equal to number of frequency sensitive components (L and C).
Advantages
Reasonable roll-off rate for high order filter. Smooth & reasonably flat response in the passband and stopband.
Easy to construct and tune. LC filter need only low Q ( Q of 15)
Reasonably smooth phase shift and constant time delay away from cutoff frequency.
Disadvantages
Sharp cutoff filter need high order and therefore lots of components.
Amplitude response is NOT actually flat in the passband, particularly near cutoff.
Not possible to modify shape of amplitude response once the filter order is chosen.
Filter Design (Chebyshev)
Characteristics
The Chebyshev filter is known for it's ripple response. This ripple response can be designed to be present in the passband (Chebyshev Type 1) or in the stopband (Chebyshev Type 2). The amplitude of the ripple is directly proportional to steepness of the rolloff. That is, if you want a steeper response, you'll see a larger ripple response.
Designer can ‘control’ the shape of the filter amplitude response unlike the Butterworth design which is completely defined by the filter order. i.e steepness factor - passband ripple tradeoff.
Even order Chebychev filters do not have 0dB loss at zero frequency, therefore can’t designed for equal Rs & RL. Therefore, (even order) not commonly used.
The phase response of the Chebyshev filter is relatively non-linear, which ultimately wreaks havoc on demodulators because it tends to distort pulses because of the non-linear delays.
Phase shift and group delay are not as smooth (i.e ripples) compared to Butterworth filter.
Group delay is larger (because of higher Q) than a Butterworth of the same order, particularly near cutoff. For this reason, the cutoff frequency is chosen higher for LPF and lower for HPF designs.
Advantage
Amplitude Response can have flatter (but not smoother ripples) response in the passband and stopband.
Steeper rolloff compared to Butterworth.
Rolloff can be traded for passband or stopabnd ripple. (ie if passband ripples is larger, rolloff increases.)
Easier to tune and less expensive to build due to lower order required.
Disadvantage
Passband amplitude response not smooth.
Greater phase shift and group delay.
Greater sensitivity to component values compare to Butterworth.
Filter Design (Elliptic)
Characteristics
The elliptic filters is characterized by ripple that exists in both the passband and stopband. The passband ripple (can be controlled) of the elliptic filter is similar to the Chebyshev filter, however the selectivity is greatly improved.
Steepest roll-off compared to Butterworth and Chebychev.
Elliptic filters are particularly sensitive to capacitance values and therefore capacitors used (series/parallel) must be as close as possible to the design value
Advantage
Fastest roll off speed of all the filters among the four. Ideal for applications that want to effectively eliminate the frequencies in the immediate neighbourhood of passband.
Disadvantage
Ripples in both pass and stop bands.
Requires more components than other filters.
Largest time delay and non-linear phase, that leads to phase distortion.
High complexity.

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