lecture 18 - 1 1 Summary of Lecture #18 10/04/2010...

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Unformatted text preview: 1 1 Summary of Lecture #18 10/04/2010 Amplitude and phase responses, examples Decibel (dB) What are electric filters for? LP, HP, BP and BR filters Normalized circuits or prototype circuits 1 and 1 rad/s Magnitude scaling How and its effect Examples Frequency scaling How and its effect Examples 2 Ex. 4. Sketch the magnitude and phase responses. 2 1 | ) j ( H | + = 2 ) 1 s ( s ) s ( H + = 2 1 2 2 ) tan 1 ( 90 ) 1 j ( j ) j ( H + = + = - j xx - = - 1 tan 2 90 ) j ( H r s 1/s Is the system stable? 3 |H(j )| Angle H(j ) |H(j )| 2 1 | ) j ( H | + = - = - 1 tan 2 90 ) j ( H 4 1 s 2 s s ) s ( H 2 + + = Use MATLAB to plot frequency response freqs, abs, angle 5 Ex. 5. Plot magnitude and phase responses. 2 / 1 4 2 2 ] 5 . 1 25 . 1 [ 25 . 1 | ) j ( H | + - = ) j 5 . s )( j 5 . s ( 25 . 1 25 . 1 s s 25 . 1 ) s ( H 2- + + + = + + = )) 25 . 1 /( ( tan ) j ( H 2 1 - - = -- 1/2 j1- j1 j 6 |H(j )| |H(j )| Angle H(j ) 2 / 1 4 2 2 ] 5 . 1 25 . 1 [ 25 . 1 | ) j ( H | + - = )) 25 . 1 /( ( tan ) j ( H 2 1 - - = - 2 7 1 2 3 4 5 6 7 8 9 10 0.5 |H(j )| 10-2 10-1 10 10 1 10 2 0.5 |H(j )| 10-2 10-1 10 10 1 10 2 10-2 10-1 |H(j )| 1 2 s H (s) s 2s 1 = + + 2 2 4 3 2 s H (s) s 4s 6s 4s 1 = + + + + plot semilogx loglog 8 Decibels Transfer function Phase or angle response, H(j ) vs. plot Amplitude response, |H(j )| vs . plot Voltage or current gain or loss in decibels (dB) Note: log 10 (1/ 2) = - 0.150515 , 20 log 10 (1/ 2) = - 3.0103 . 1/ 2 is exactly- 3.0103 dB and approx.- 3 dB. 1/10 is - 20.00 dB and 1/100 is - 40.00 dB....
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lecture 18 - 1 1 Summary of Lecture #18 10/04/2010...

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