EECE 301 Discussion 11 Bode Plot Method and Example

EECE 301 Discussion 11 Bode Plot Method and Example - 1/13...

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Unformatted text preview: 1/13 EECE 301 Signals & Systems Prof. Mark Fowler Discussion #11 • Bode Plot Method and Example 2/13 10 10 2 10 3 10 4 10 5 10 6 –10 –20 –30 –40 –50 10 20 30 40 a ω (rad/sec) | H ( ω )| (dB) a s a s H + = ) ( a a s s H + = ) ( e have seen two cases: Real Pole & Real Zero Real pole So we still need a way to handle two other cases. -zero/pole at s = 0 -zero/pole complex conjugate pairs – 2 nd order term Real zero This allows us to handle all real poles/zeros in the left-hand plane . 3/13 ero/Pole at s = 0 s s H = ) ( s s H 1 ) ( = Zero at s = 0 Pole at s = 0 Replace s → j ω and take magnitude: ) ( log . ) ( log 20 10 10 ω ω vs ± Line of slope ± 20 that goes through 0dB at ω = 1 4/13 omplex Conjugate Pair (0 ≤ ζ ≤ 1) 2 2 2 n n n s s ω ζω ω + + n n n s s ω ω ζω 2 2 2 + + Complex pair of poles Complex pair of zeros breakpoint n ω for 0 ≤ ζ ≤ 1 ζ = 1 gives repeated real roots. on j ω axis ) ( log . 1 2 log 20 10 2 10 ω ω ω ζ ω ω vs j j n n ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⇒ n n for dB for dB ω ω ω ω >> ± ≈ << ≈ decade per 40 (constant) General Form : 5/13...
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EECE 301 Discussion 11 Bode Plot Method and Example - 1/13...

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