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ch14 - Chapter 14 Analog Filters 14.1 14.2 14.3 14.4 14.5...

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Chapter 14 Analog Filters 14.1 General Considerations 14.2 First-Order Filters 14.3 Second-Order Filters 14.4 Active Filters 14.5 Approximation of Filter Response 1
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Outline of the Chapter 2 CH 14 Analog Filters
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Why We Need Filters In order to eliminate the unwanted interference that accompanies a signal, a filter is needed. 3 CH 14 Analog Filters
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Filter Characteristics Ideally, a filter needs to have a flat pass band and a sharp roll- off in its transition band. Realistically, it has a rippling pass/stop band and a transition band. 4 CH 14 Analog Filters
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Example: Filter I Design goal: Signal to Interference ratio of 15 dB Solution: A filter with stop band of 40 dB Given: Adjacent channel Interference is 25 dB above the signal 5 CH 14 Analog Filters
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Example: Filter II Given: Adjacent channel Interference is 40 dB above the signal Design goal: Signal to Interference ratio of 20 dB Solution: A filter with stop band of 60 dB at 60 Hz 6 CH 14 Analog Filters
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Example: Filter III A bandpass filter around 1.5 GHz is needed to reject the adjacent Cellular and PCS signals. 7 CH 14 Analog Filters
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Classification of Filters I 8 CH 14 Analog Filters
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Classification of Filters II Continuous-time Discrete-time 9 CH 14 Analog Filters
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Classification of Filters III Passive Active 10 CH 14 Analog Filters
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Summary of Filter Classifications 11 CH 14 Analog Filters
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Filter Transfer Function Filter a) has a transfer function with -20dB/dec roll-off Filter b) has a transfer function with -40dB/dec roll-off, better selectivity. A B 12 CH 14 Analog Filters
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General Transfer Function P n =n’th pole Z m =m’th zero ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 2 ( ) m m s Z s Z s Z H s s P s P s P α - - - = - - - L L 13 CH 14 Analog Filters
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Pole-Zero Diagram 14 CH 14 Analog Filters
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Position of the Poles Poles on the RHP Unstable (no good) Poles on the jω axis Oscillatory (no good) Poles on the LHP Decaying (good) 15 CH 14 Analog Filters
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Imaginary Zero Imaginary zero is used to create a null at certain frequency. 16 CH 14 Analog Filters
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Sensitivity P C dP dC S P C = Sensitivity measures the variation of a filter parameter due to variation of a filter component. P=Parameter C=Component 17 CH 14 Analog Filters
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Example: Sensitivity ( 29 1 1 / 1 0 1 1 1 0 0 1 2 1 1 0 1 1 0 - = - = - = = ϖ ϖ ϖ ϖ ϖ R S R dR d C R dR d C R 18 CH 14 Analog Filters
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First-Order Filters 1 1 ( ) s z H s s p α + = + First-order filters are represented by the transfer function shown above. Low/high pass filters can be realized by changing the relative positions of poles and zeros.
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