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lecture 18

# lecture 18 - 1 1 Summary of Lecture#18 • Amplitude and...

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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 Ω 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 | ϖ + ϖ = ϖ 2 ) 1 s ( s ) s ( H + = 2 1 2 2 ) tan 1 ( 90 ) 1 j ( j ) j ( H ϖ ∠ ϖ + ° ∠ ϖ = + ϖ ϖ = ϖ- σ j ϖ xx ϖ- = ϖ ∠- 1 tan 2 90 ) j ( H r s 1/s Is the system stable? 3 |H(j ϖ )| Angle H(j ϖ ) |H(j ϖ )| ϖ 2 1 | ) j ( H | ϖ + ϖ = ϖ ϖ- ° = ϖ ∠- 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 | ϖ + ϖ- = ϖ ) j 5 . s )( j 5 . s ( 25 . 1 25 . 1 s s 25 . 1 ) s ( H 2- + + + = + + = )) 25 . 1 /( ( tan ) j ( H 2 1 ϖ- ϖ- = ϖ ∠-- 1/2 j1- j1 σ j ϖ 6 |H(j ϖ )| |H(j ϖ )| Angle H(j ϖ ) ϖ 2 / 1 4 2 2 ] 5 . 1 25 . 1 [ 25 . 1 | ) j ( H | ϖ + ϖ- = ϖ )) 25 . 1 /( ( tan ) j ( H 2 1 ϖ- ϖ- = ϖ ∠- 2 7 1 2 3 4 5 6 7 8 9 10 0.5 ϖ |H(j ϖ )| 10-2 10-1 10 10 1 10 2 0.5 ϖ |H(j ϖ )| 10-2 10-1 10 10 1 10 2 10-2 10-1 ϖ |H(j ϖ )| 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 ϖ ) vs. ϖ plot Amplitude response, |H(j ϖ )| vs . ϖ 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 • Amplitude and...

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