A - ECSE ECSE 210: Electric Circuits 2 Chapter 13 Chapter...

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ECSE 210: Electric Circuits 2 hapter hapter 3 3 Chapter Chapter 13 13 requency Response Frequency Response
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Example What is V o as a function of V I ? R V o Z C 1 s C s j V I + - C R R Z Voltage divider: V o 1 s C 1 V I 1 1 s RC V I 1 1 j RC V I R s C
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Frequency Characteristics H ( s ) V o 1 1 C 1 RC 1 k R 1 f 2 V I s s RC F C 1 V o 1 1000 1000 H ( s ) V I 1 s RC s 1000 1000 ) ( j j H f 0 0 100 628 159 50 314 1000 250 1570 500 3141 1000 6283 10000 62832 100000 628320 ) ( j H 1 85 . 0 95 . 0 707 . 05 4 . 03 . 01 6 . 0 016 . 0 0016 . 0 ) ( j H 0 32 17 45 58 72 81 89 9 . 89
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Amplitude Plot 9 1 9 1 0.7 0.8 0.9 0.7 0.8 0.9 0.4 0.5 0.6 |H(j )| 4 0.5 0.6 |H(s)| .1 0.2 0.3 0.2 0.3 0.4 0 1 2 3 4 5 6 7 8 9 10 x 10 4 0 0.1 Frequency (Hz) 0 1 2 3 4 5 6 7 8 9 10 10 4 0 0.1 requency x 10 Frequency Frequency on a linear scale
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Amplitude Plot 0.9 1 0.9 1 0.6 0.7 0.8 0.7 0.8 3 0.4 0.5 |H(j )| 0.4 0.5 0.6 |H(s)| 0.1 0.2 0.3 0.2 0.3 10 0 10 1 10 2 10 3 10 4 10 5 0 Frequency (Hz) 10 0 10 1 10 2 10 3 10 4 10 5 0 0.1 requency Frequency on a log scale Frequency
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Phase Plot -10 0 -0.2 0 Radians -30 -20 egrees) -0.6 -0.4 H(s) -60 -50 -40 Angle of H(j ) (d -1 -0.8 Angle of H -45 o -80 -70 -1.4 -1.2 requency on a log scale 10 0 10 1 10 2 10 3 10 4 10 5 -90 Frequency (Hz) 10 0 10 1 10 2 10 3 10 4 10 5 -1.6 Frequency (Hz) -90 o Frequency on a log scale
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Decibel Scale he unit used to compare powers is the The unit used to compare powers is the decibel which is defined as: A ( dB ) 10log 0 P 1 10 P 2 where P1 and P2 are the powers to be compared.
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Intensity of Various Sounds Example Decibels Softest detectable sound Soft whisper 0 20 Quiet neighborhood verage conversation 40 0 Average conversation Loud music from a radio eavy automobile traffic 60 80 00 Heavy automobile traffic Very loud thunder, rock concert 100 120 Threshold of pain Jet airplane taking off 130 140 Loudest rock band on record Spacecraft launch 9 from 150 ft. 160 180
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dB Scale for Voltages Compare two voltages V 1 and V 2 : hoose a reference resistor Choose a reference resistor R The power that V 1 would dissipate in R is: R V P 2 1 1 The power that V 2 would dissipate in R is: R V P 2 2 2 2 2 2 1 10 2 1 10 log 10 log 10 ) ( V R R V P P dB A 1 10 2 1 10 log 20 log 10 V V 2 2 V V
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dB Scale for a Transfer Function Voltage transfer function: H ( j ) V o V I   ) ( log 20 ) ( 10 j H dB A 000 000 Example: 1000 1000 ) ( j j H 2 2 1000 1000 ) ( j H f 0 0 100 628 159 50 314 1000 250 1570 500 3141 1000 6283 10000 62832 100000 628320 ) ( j H 1 85 . 0 95 . 0 707 . 05 4 . 03 . 01 6 . 0 016 . 0 0016 . 0 dB 0 4 . 1 4 . 0 3 3 . 5 5 . 10 9 . 15 9 . 35 9 . 55
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dB Scale for a Transfer Function 0 2 2 1000 1000 ) ( j H -10 Decibels inear scale) -30 -20 )| (dB) (linear scale) -40 |H(j -20dB/dec. -60 -50 10 0 10 1 10 2 10 3 10 4 10 5 Frequency (Hz) Frequency (log scale)
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