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PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Chapter 11Filters and Tuned AmplifiersPassive LC FiltersInductorless FiltersActive-RC FiltersSwitched CapacitorsFilter Transmission, Types and SpecificationLinear FiltersTransfer FunctionT s( )Vos( )Vis( )The Filter Transmisson found by evaluating T(s) for physical frequenciess j  T j T j ej ( )Gain FunctionG  20 log T j   dBAttenuation FunctionA  20 log T j   dBSpecification of the transmission characteristics of a low-pass filter. The magnitude response of a filter that just meets specifications is also shown.Filter SpecificationFrequency-Selection functionPassingStoppingPass-BandLow-PassHigh-PassBand-PassBand-StopBand-RejectSummary – Low-pass specs-the passband edge-the maximum allowed variation in passband, Amax-the stopband edge-the minimum required stopband attenuation, AminPassband rippleRipple bandwidthTransmission specifications for a bandpass filter. The magnitude response of a filter that just meets specifications is also shown. Note that this particular filter has a monotonically decreasing transmission in the passband on both sides of the peak frequency.Filter SpecificationExercises 11.1 and 11.2Pole-zero pattern for the low-pass filter whose transmission is shown. This filter is of the fifth order (N = 5.) The Filter Transfer Functiontransfer function zeros or transmission zerosT s( )aMs z1  s z2  s z3     s zM s p1 s p2  s p3     s pN transfer function poles or the natural polesPole-zero pattern for the bandpass filter whose transmission is shown. This filter is of the sixth order (N = 6.)The Filter Transfer FunctionThe magnitude response of a Butterworth filter.Butterworth FiltersMagnitude response for Butterworth filters of various order with  = 1. Note that as the order increases, the response approaches the ideal brickwall type transmission.Butterworth FiltersGraphical construction for determining the poles of a Butterworth filter of order N. All the poles lie in the left half of the s-plane on a circle of radius 0 = p(1/)1/N, where  is the passband deviation parameter : (a) the general case, (b) N = 2, (c) N = 3, (d) N = 4. 10 110Amax/e jButterworth FiltersSketches of the transmission characteristics of a representative even- and odd-order Chebyshev filters.Chebyshev FiltersFirst-Order Filter FunctionsFirst-Order Filter FunctionsFig. 11.14 First-order all-pass filter.First-Order Filter FunctionsSecond-Order Filter FunctionsSecond-Order Filter FunctionsSecond-Order Filter FunctionsRealization of various second-order filter functions using the LCR resonator of Fig. 11.17(b): (a) general structure, (b) LP, (c) HP, (d) BP, (e) notch at 0, (f) general notch, (g) LPN (n  0), (h) LPN as s  , (i) HPN (n < 0).The Second-order LCR ResonatorThe Antoniou inductance-simulation circuit. (b) Analysis of the circuit assuming ideal op amps. The order of the analysis steps is indicated by the circled numbers.The Second-Order Active Filter – Inductor ReplacementRealizations for the various second-order filter functions using the op amp-RC resonator of Fig. 11.21 (b). (a) LP; (b) HP; (c) BP, (d) notch at 0; The Second-Order Active Filter – Inductor Replacement(e) LPN, n  0; (f) HPN, n  0; (g) all-pass. The circuits are based on the LCR circuits in Fig. 11.18. Design equations are given in Table 11.1.The Second-Order Active Filter – Inductor ReplacementThe Second-Order Active Filter – Two-Integrator-LoopVhpViK s2s2soQ o2Two integrations of signalwith time constantosVhpVhp1QosVhpo2s2Vhp K Vi1oVhp K Vi1Qos Vhpo2s2VhpSumming PointThe Second-Order Active Filter – Two-Integrator-LoopCircuit ImplementationThe Second-Order Active Filter – Two-Integrator-LoopCircuit Design and PerformanceTa 1 2 40 b 1 2 20 j 1w0 2  103 K 3wa100 700 a Qb0.1 0.2 bTa bK j wa 2j wa 2j wa w0Qb w02The Second-Order Active Filter – Two-Integrator-LoopExercise 11.21Derivation of an alternative two-integrator-loop biquad in which all op amps are used in a single-ended fashion. The resulting circuit in (b) is known as the Tow-Thomas biquad.The Second-Order Active Filter – Two-Integrator-LoopFig. 11.26 The Tow-Thomas biquad with feedforward. The transfer function of Eq. (11.68) is realized by feeding the input signal through appropriate components to the inputs of the three op amps. This circuit can realize all special second-order functions. The design equations are given in Table 11.2.Fig. 11.37 A two-integrator-loop active-RC biquad and its switched-capacitor counterpart.Fig. 11.47 Obtaining a second-order narrow-band bandpass filter by transforming a first-order low-pass filter. (a) Pole of the first-order filter in the p-plane. (b) Applying the transformation s = p + j0 and adding a complex conjugate pole results in the poles of the second-order bandpass filter. (c) Magnitude response of the firs-order low-pass filter. (d) Magnitude response of the second-order bandpass filter.Fig. 11.48 Obtaining the poles and the frequency response of a fourth-order stagger-tuned narrow-band bandpass amplifier by transforming a second-order low-pass maximally flat


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CALVIN ENGR 332 - Chapter 11

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