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LS404M Scheda tecnica(PDF) 6 Page - STMicroelectronics |
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LS404M Scheda tecnica(HTML) 6 Page - STMicroelectronics |
6 / 11 page LS404 6/11 APPLICATION INFORMATION: Active low-pass filter BUTTERWORTH The Butterworth is a "maximally flat" amplitude re- sponse filter (figure 10) Butterworth filters are used for filtering signals in data acquisition sys- tems to prevent aliasing errors in samples-data applications and for general purpose low-pass fil- tering. The cut-off frequency Fc, is the frequency at which the amplitude response is down 3dB. The attenu- ation rate beyond the cutoff frequency is n6 dB per octave of frequency where n is the order (number of poles) of the filter. Other characteristics : u Flattest possible amplitude response u Excellent gain accuracy at low frequency end of passband BESSEL The Bessel is a type of “linear phase” filter. Be- cause of their linear phase characteristics, these filters approximate a constant time delay over a limited frequency range. Bessel filters pass tran- sient waveforms with a minimum of distortion. They are also used to provide time delays for low pass filtering of modulated waveforms and as a “running average” type filter. The maximum phase shift is radians where n is the order (number of poles) of the filter. The cut-off frequency fc, is defined as the frequency at which the phase shift is one half of this value. For accurate delay, the cut-off frequency should be twice the maximum signal frequency. The following table can be used to obtain the -3dB frequency of the filter. Other characteristics : u Selectivity not as great as Chebyschev or Butterworth u Very little overshoot response to step inputs u Fast rise time CHEBYSCHEV Chebyschev filters have greater selectivity than ei- ther Bessel ro Butterworth at the expense of ripple in the passband (figure 11). Chebyschev filters are normally designed with peak-to-peak ripple values from 0.2dB to 2dB. Increased ripple in the passband allows increased attenuation above the cut-off frequency. The cut-off frequency is defined as the frequency at which the amplitude response passes through the specificed maximum ripple band and enters the stop band. Other characteristics : u Greater selectivity u Very non-linear phase response u High overshoot response to step inputs The table below shows the typical overshoot and setting time response of the low pass filters to a step input. Design of 2nd order active low pass filter (Sallen and Key configuration unity gain op-amp) n π – 2 ----------- 2 Pole 4 Pole 6 Pole 8 Pole -3dB Frequency 0.77fc 0.67fc 0.57fc 0.50fc Number of Poles Peak Overshoot Settling Time (% of final value) % Overshoot ±1% ±0.1% ±0.01% Butterworth 2 4 6 8 4 11 14 14 1.1Fc sec. 1.7/fc 2.4/fc 3.1/fc 1.7Fc sec. 2.8/fc 3.9S/fc 5.1/fc 1.9Fc sec. 3.8/fc 5.0S/fc 7.1/fc Bessel 2 4 6 8 0.4 0.8 0.6 0.1 0.8/fc 1.0/fc 1.3/fc 1.6/fc 1.4/fc 1.8/fc 2.1/fc 2.3/fc 1.7/fc 2.4/fc 2.7/fc 3.2/fc Chebyschev (ripple ±0.25dB) 2 4 6 8 11 18 21 23 1.1/fc 3.0/fc 5.9/fc 8.4/fc 1.6/fc 5.4/fc 10.4/fc 16.4/fc - - - - Chebyschev (ripple ±1dB) 2 4 6 8 21 28 32 34 1.6/fc 4.8/fc 8.2/fc 11.6/fc 2.7/fc 8.4/fc 16.3/fc 24.8/fc - - - |
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