Analog Filters Filters can be used to attenuate unwanted signals such as interference or noise or to isolate desired signals from unwanted. They use the frequency response of a measuring system to alter the dynamic characteristics of a signal. A common instrumentation filter application is the attenuation of high frequencies to avoid frequency aliasing in the sampled data. Filters can be broadly classified as: Low-pass eliminate high frequency components.High-pass eliminate low frequency components. Band-pass eliminate frequencies outside of a given range or band. Notch eliminate frequencies in a given range or band. Simple first-order systems can be used as low-pass filters because they attenuate higher frequencies more than lower frequencies. The thermocouples used in the lab would respond poorly to high frequency (> 1 Hz) temperature fluctuations.AnalogFilters.doc - December 2, 2005 - Page 1AnalogFilters.doc - December 2, 2005 - Page 2Some examples of low-pass filters are given below: (Figure from Doebelin) AnalogFilters.doc - December 2, 2005 - Page 321/21M( ) = (3.10)[1 + ()]ωωτ tan-1( ) = - (3.9)φω ωτ log logdB = 20 M( ) = 20 M(f)ω We can improve the roll-off characteristics of a low-pass filter by cascading several stages: Figure 6.31 in 2nd and 3rd Edition For the cascaded filter, the magnitude ratio and phase shift are: 121[1 ( )](6.57 , 6.60 )2k1/2ckii=1M(f)=+f/f (f)= (f)φφ∑,3 The magnitude ratio is plotted as a function of frequency for values of k = 1,2,3 and 4 below: AnalogFilters.doc - December 2, 2005 - Page 4The phase shift is increased by the cascading, but that is usually not important. AnalogFilters.doc - December 2, 2005 - Page 5Here are some examples of high pass filters, from Doebelin: AnalogFilters.doc - December 2, 2005 - Page 6Cascading can also be used to improve the performance of high-pass filters: Figure 6.32 in 2nd and 3rd Edition The filters described above are all passive, that is they involve no external power supply. Improved performance can be obtained from active filters, which use operational amplifiers. Some examples are shown below: AnalogFilters.doc - December 2, 2005 - Page 7AnalogFilters.doc - December 2, 2005 - Page 8Comparison of Common Low Pass Filter Types Figure 4 From www.maxim-ic.com Filter Basics: Anti-Aliasing AnalogFilters.doc - December 2, 2005 - Page 9Key Features of Low Pass Filter Types a. Bessel: linear phase shift, gradual roll off b. Butterworth: Steeper roll off, nonlinear phase shift c. Chebyshev: Steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratio d. Elliptic: very steep roll off, nonlinear phase shift, non-smooth pass band magnitude ratio. AnalogFilters.doc - December 2, 2005 - Page 10Example 6.6 Design a one-stage Butterworth RC Low-pass filter with a cutoff frequency of -3 dB set at 100 Hz. KNOWN fc = 100 Hz, k = 1 M(100 Hz) = - 3 dB = .707 FIND R, C and δ SOLUTION Remember τ = RC = 1/2πfc for a single pole RC filter! therefore: fc = 1/2πRC = 100 Hz RC = 1/200π = 0.00159 EXAMPLE FINAL EXAM QUESTIONS: 1. Given a 1000 ohm resistor what size capacitor would be required to build a single pole Butterworth low pass filter with a cut off frequency of 100 Hz? a. 1.59 uF b. 5 uF c. 2.5 uF d. 100 uF 2. Which low pass filter type has the steepest magnitude ratio roll off? a. Bessel b. Butterworth c. Chebyshev d. Elliptic 3. Which low pass filter type has a linear phase shift? a. Bessel b. Butterworth c. Chebyshev d. Elliptic AnalogFilters.doc - December 2, 2005 - Page
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