* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Frequency response of feedback amplifiers
Rectiverter wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Spectrum analyzer wikipedia , lookup
Regenerative circuit wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Superheterodyne receiver wikipedia , lookup
Phase-locked loop wikipedia , lookup
Radio transmitter design wikipedia , lookup
RLC circuit wikipedia , lookup
Index of electronics articles wikipedia , lookup
Waveguide filter wikipedia , lookup
Zobel network wikipedia , lookup
Audio crossover wikipedia , lookup
Mechanical filter wikipedia , lookup
Multirate filter bank and multidimensional directional filter banks wikipedia , lookup
Equalization (audio) wikipedia , lookup
Analogue filter wikipedia , lookup
Distributed element filter wikipedia , lookup
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, highpass 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 values Applications 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 outof-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: | H ( f ) | H0 1 ( f / fb ) 2n , where n is the order of the filter and f b is the 3db cutoff frequency, H 0 is the gain magnitude at DC. Graphs from Prentice Hall Low-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 H( f ) Vo ( s) K , the 3db cutoff frequency is f b 1 /( 2RC ) 2 2 2 Vin ( s ) 1 (3 K ) RCs R C s • 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 Example of a 4th-order Lowpass filter by cascading two 2nd-order SK filters Comparison 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. | H ( f ) | H0 1 ( fb / f ) 2n , where n is the order of the filter and f b is the 3db cutoff frequency, H 0 is the gain magnitude at DC. 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 Circuits • 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. Graphs from Prentice Hall Figure 11.11 Bode plots of gain magnitude for the active filter of Example 11.2. A summary