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lecture 24 - Summary of Lecture#24 Circuits with real or...

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1 1 Summary of Lecture #24 10/20/2010 Circuits with real or practical inductors and capacitors Analog filters Filter types by frequency characteristic: LP, HP, BP and BR filters Filter types by key components Filter order and roll off rate Realization of LP filters, examples Transformation from LP to HP, BP and BR Frequency and magnitude scaling + - + - V in (s) V out (s) s-domain circuit + - + - v in (t) v out (t) time-domain circuit Test #2 10/26/2010 2 Parallel RLC circuits Series RLC circuits LC 1 s RC 1 s s ) C / 1 ( ) s ( Y 1 ) s ( Z 2 + + = = LC 1 s L R s s ) L / 1 ( ) s ( Z 1 ) s ( Y 2 + + = = o r m 1/ LC ϖ = ϖ = ϖ = o r m 1/ LC ϖ = ϖ = ϖ = All expressions are exact ! 3 Primary circuit element: inductance, L Parasitic circuit elements: Wire resistance, R s Capacitance between conductors, C p Leakage resistance, R p Quality factor of inductor at a certain frequency, Q L Circuit models of real inductors Values typically given: Nominal inductance, L Coil Q at certain frequency, Q L s L R L Q ϖ = L s Q L R ϖ = 4 Real inductors 5 Circuit models of real capacitors Primary circuit element: Capacitance C Parasitic circuit elements: Wire resistance R s Wire inductance L s Leakage resistance R p Quality factor of capacitor at a certain frequency Q c = ϖ CR p Dissipation factor : d c =1/Q C Values typically given: Nominal capacitance: C Dissipation factor at a certain frequency: d C p c c CR 1 Q 1 d ϖ = = L Q R C p ϖ = 6 Quality factor Dissipation factor Power factor Loss tangent Real capacitors Q c d c = 1/ Q c = tan δ
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2 7 Series and parallel circuit models s L 2 L s 2 L s p s 2 L s p s s L L Q ~ Q R ~ ) Q 1 ( R R L ~ ) Q 1 1 ( L L R / L Q ϖ + = + = ϖ = ) C Q ( / 1 ~ Q / R ~ ) Q 1 /( R R C ~ ) Q 1 1 ( C C Q / 1 d , R C Q p C 2 C p 2 C p s p 2 C p s C C p p C ϖ + = + = = ϖ = Table 16.2 8 Table 16.2 9 Circuits with real inductors and capacitors Parallel RLC circuit Series RLC circuit Real L and C Real L and C 10 Ex. 3 A filter with real circuit elements L: Nominal value 20 mH, Q L = 40 near
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