Active Filters: conceptsApplications of Analog FiltersButterworth low-pass filterLow-pass filter: Sallen-Key CircuitsSlide 5Slide 6Slide 7Butterworth high-pass filterButterworth high-pass filter: Sallen-KeyBand-pass filter: Sallen-Key CircuitsSlide 11A summaryApplication: Equalizer (EQ)Active Filters: concepts•All input signals are composed of sinusoidal components of various frequencies, amplitudes and phases.•If we are interested in a certain range of frequencies, we can design filters to eliminate frequency components outside the range•Filters are usually categorized into four types: low-pass filter, high-pass filter, band-pass filter and band-reject filter. •Low-pass filter passes components with frequencies from DC up to its cutoff frequency and rejects components above the cutoff frequency. •Low-pass filter composed of OpAmp are called active filter (as opposed to lumped passive filter with resistor, capacitor and inductor)•Active filters are desired to have the following characteristics:Contain few componentsInsensitive to component variationNot-too-hard-to-meet specifications on OpAmpEasy reconfiguration to support different requirements (like cutoff freq)Require a small spread of component valuesApplications of Analog Filters• Analog filters can be found in almost every electronic circuit.• Audio systems use them for pre-amplification, equalization, and tone control. • In communication systems, filters are used for tuning in specific frequencies and eliminating others (for example, to filter out noise). • Digital signal processing systems use filters to prevent the aliasing of out-of-band noise and interference.Butterworth low-pass filter•Many low-pass filter are designed to have a Butterworth transfer function with magnitude response as follows:DC.at magnitudegain theis H frequency, cutoff 3db theis f andfilter theoforder theisn where,)/(1|)(|0b20nbffHfHGraphs from Prentice HallLow-pass filter: Sallen-Key Circuits•Active low-pass Butterworth filter can be implemented by cascading modified Sallen-Key circuits.•The Sallen-Key circuit itself is a 2nd order filter. To obtain an nth order filter, n/2 SK circuits should be cascaded•During design, capacitance can be selected first and then resistor values. •As K increase from 0 to 3, the transfer function displays more and more peaking.•It turns out that if K>3, then the circuit is not stable.•Empirical values have been found for filters of different orders)2/(1f isfrequency cutoff 3db the,)3(1)()()(b222RCsCRRCsKKsVsVfHinoExample of a 4th-order Lowpass filter by cascading two 2nd-order SK filtersComparison of gain versus frequency for the stages of the fourth-order Butterworth low-pass filter.Butterworth high-pass filter•By a change, the lowpass Butterworth transfer function can be transformed to a high-pass function.DC.at magnitudegain theis H frequency, cutoff 3db theis f andfilter theoforder theisn where,)/(1|)(|0b20nbffHfHButterworth high-pass filter: Sallen-Key•By a change, the lowpass Butterworth transfer function can be transformed to a high-pass function.•With real OpAmp, the Sallen-Key is not truly a high-pass filter, because the gain of the OpAmp eventually falls off. However, the frequencies at which the OpAmp gain is fairly high, the circuit behaves as a high-pass filter.•Since the high-pass Sallen Key circuit is equivalent the same as the low-pass one, the empirical values for K would be still valid in this case also.Band-pass filter: Sallen-Key CircuitsGraphs from Prentice Hall•If we need to design a band-pass filter in which the lower cutoff frequency is much less than the upper cutoff frequency, we can cascade a low-pass filter with a high-pass filter.•The below band-pass filter uses the first stage as a low-pass filter which passes frequency less than 10KHz and the second stage as a high-pass filter that passes only frequency above 100Hz. Thus, frequency components in-between is passed to the output.Figure 11.11 Bode plots of gain magnitude for the active filter of Example 11.2.A summaryApplication: Equalizer