Lesson+21

# Lesson+21 - Marketing vs Engineering May you live in...

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Marketing vs. Engineering May you live in interesting times. (Chinese curse) 1 Lesson 21

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Challenge 20 Bode Plots (15.1) Active Filters (15:1-3) Chapter 15:1-2 Challenge 21 Lesson 21 2 Lesson 21
Design a 2 nd order bandpass filter : such that: H(j0)=0; H(j )=0; Poles at s = -a j10 Zero=0. 0 What is the approximate frequency that maximizes the filter’s gain if a=1? ) ( ) )( ( ) ( 2 2 100 2 10 10 a as s s j a s j a s s s H Since 0 2 =101, 0 =10.05~10 r/s 0 2 3 Lesson 21

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For a=1 , filter’s gain peaks at 0 ~10.05 r/s. >> w=0:0.1:100; >> b=[1 0]; a=[1 2 101]; >> freqs(b,a,w); ) ( ) )( ( ) ( 2 2 100 2 10 10 a as s s j a s j a s s s H What if |a|>>1? What if |a|<<1? 4 Lesson 21 ~10
5 Lesson 21 ~14.1 ~10 a=10 0 2 =200 0 =14.1 a=0.1 0 2 =100.01 0 ~10

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6 Lesson 21 Since the dawn of the time of engineers, when posed with a technical problem, immediately began to sketch a solution in the dirt. Engineering is, in part, a visual experience. In the absence of a digital computer, how would an engineer create the graphs shown below. Lesson 21
A common means of displaying the frequency response of a filter is as a log-log ( Bode ) plot graph. What is a @#@\$%%@ Bode representation? 7 Lesson 21

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A Rapid Graphical Frequency Response Technique 1. Bode Plot (Old School) for manual plotting, or 2. Bode Plot for computer generated responses For manual use: Simple (additive) construction rules Approximation (only) Bode plot (text) – 560-563, 741-757 (Appendix E) 8 Lesson 21
An amplitude “x” can be formally expressed in decibels (dB) as dB = 20 log10(x). dB = 20 log 10 (x) 10 -1 20 log 10 (10 -1 ) = -20dB 0.707 20 log 10 (0.707) = -3dB (half power point) 10 0 20 log 10 (10 0 ) = 0dB 10 1 20 log 10 (10 1 ) = 20dB Bel is a measure of power ratios. Invented by engineers of Bell Labs it was originally called the transmission unit or TU , but was renamed in the 1920’s in honor of the lab’s founder Alexander Graham Bell. The bel was found to be too large for everyday use, so the decibel (dB) ( 0.1 B ), became the standard. 9 Lesson 21 Alexander Graham Bell

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Assume that a circuit or system has been reduced to the mathematical form shown below (the form is important). In the frequency domain: 0 1 1 1 0 1 1 1 a s a s a s b s b s b s b s G n n n m m m m ... ... ) ( others j j j j K j G s G j s 1 2 1 1 1 2 1 1 ) ( ) ( others s s s s K s G 1 2 1 1 1 2 1 1 β β δ α ) ( 10 Lesson 21
Interpretation: In its simplest form, the system is shown to be decomposed into four (4) basic cases.

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