5173 fall 2009 HW06 solutions

5173 fall 2009 HW06 solutions - F EEL5173 HW # 6, Page 6-2...

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EEL5173 Signal and System Analysis HW # 6, Page 6-1 Fall 2009 1. P o = 0. For k > 0, Case A : When -1 < -5 k , P o = 0, N c = 0, Z o = P o + N c = 0, stable, i.e. when 0 < k < 1/5 = 0.2 Case B : When -5 k < -1 < - k , P o = 0, N c = 1, Z o = P o + N c = 1, unstable, Case C : When -k < -1, P o = 0, N c = 2, Z o = P o + N c = 2, unstable, For k < 0, Case D : When -1 > 2 k , P o = 0, N c = 1-1 = 0, Z o = P o + N c = 0, stable, i.e. when k < -1/2 = -0.5 Case E : When 2k > -1 > 4 k , P o = 0, N c = 2, Z o = P o + N c = 2, unstable, Case F : When 4k > -1, P o = 0, N c = 0, Z o = P o + N c = 0, stable, i.e. when 0 > k > -1/4 = -0.25 0 ω=0 ω→ ∞ 4k -k 2k E C B D A -5k GH-plane
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Unformatted text preview: F EEL5173 HW # 6, Page 6-2 2. ) 25 8 ( ) ( ) ( ) ( 2 2 + + = s s s s N k s H s G , P o = 0. The pole at s = 0 is of multiplicity of 2. 2 = = m GH For k &gt; 0, Case A : P o = 0, N c = 1, Z o = P o + N c = 1, unstable, i.e. when 0 &lt; k &lt; 1/5 = 0.2 For k &lt; 0, Case B : When -1 &gt; 2.5 k , P o = 0, N c = 1-1 = 0, Z o = P o + N c = 0, stable, i.e. when k &lt; -1/2.5 = -0.4 Case C : When 2.5 k &gt; -1, P o = 0, N c = 2, Z o = P o + N c = 2, unstable, C B 0+ 0 2.5k GH-plane A...
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5173 fall 2009 HW06 solutions - F EEL5173 HW # 6, Page 6-2...

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