two_port_stability

two_port_stability - class notes, M. Rodwell, copyrighted...

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class notes, M. Rodwell, copyrighted 2009 ECE145a / 218a Bilateral Tuned Amplifier Design: Stability ark Rodwell Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax
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class notes, M. Rodwell, copyrighted 2009 Stability input. zero h output wit zero - non : y Instabilit : versions equivalent many : theory Stability p p oles op osed f art al Find margin. phase find : methods Nyquist Bode theory system control Classical : eory Network th ? plane - s of half right in lie any Do poles. loop - closed of part real . ) ( / ) ( in poles Find analysis. nodal by circuit Analyze gen out s V s V ? part real negative a have ) ( Does viewpoint Impedance ? plane - s of half right in lie any Do j Z ω ? 1 an greater th of magnitude the Is viewpoint (S) lection Ref in in Γ
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class notes, M. Rodwell, copyrighted 2009 Stability: LaPlace Transform / Eigenvalue Method ) ( etc ) ( or ) ( or ) ( function. transfer limit signal - small in etc.) (circuits, system Physical = s H s V s b s V in en out )... )( ( ) ( )... )( ( ) ( ... 1 ... 1 ) ( ) ( ) ( ) ( 3 2 1 3 2 1 2 2 2 1 2 2 1 1 = + + + + + + = s s s s s s s s s s s s c s a s a s b s b c s H s s a s V p p p z z z in gen ... ) exp( ) exp( ) exp( ) ( : response Impulse 3 3 2 2 1 1 + + + = t s k t s k t s k t h p p p : complex ) (generally are Poles ) positive ( plane - s of half right in lie poles any If + = j s pi pi pi pi σ ω system. unstable limit. ut grow witho will ) exp( then t s k pi i
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class notes, M. Rodwell, copyrighted 2009 Unstable system if any pole has positive real part ecays p( negative ; + = j s pi pi pi pi σ ω rows p( positive ; + = j s pi pi pi pi system. stable decays. ) exp( t s pi system. unstable grows. ) exp( t s pi
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class notes, M. Rodwell, copyrighted 2009 Stability from Network Viewpoint : Impedances st Ie t I = ) ( st Ve t V = ) ( sC Z / 1 = sL Z = R Z = conditions initial zero assumes This
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class notes, M. Rodwell, copyrighted 2009
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two_port_stability - class notes, M. Rodwell, copyrighted...

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