lecture 23

# lecture 23 - Summary of Lecture#23 Bandpass filters Peak...

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1 Summary of Lecture #23 10/18/2010 Bandpass filters Peak frequency: ϖ m Half power frequencies: ϖ 1 and ϖ 2 Half power bandwidth: B ϖ = ϖ 2 - ϖ 1 Pass band: [ ϖ 1 , ϖ 2 ] Quality factor Q: Q = ϖ m / B ϖ Pole-zero plots of circuits with one L and one C No finite zero and two complex poles Single zero at the origin and two complex poles Single zero off the origin and two complex poles Two finite zeros and two complex poles Circuits with real or practical inductors and capacitors Test #2 10/26/2010 2 Undamped natural freq., tank freq., LC freq. : ϖ o Reac. (or susc.) of L = reac. (or susc.) of C Resonant frequency: ϖ r i in (t) and v in (t) are in time phase. ϖ r , if exists, is proportional to ϖ o . Im [Z in (j ϖ )] = 0 or Im[Y in (j ϖ )] = 0 at ϖ r Peak freq uency , ϖ m , (Fig. 16.1) Pole frequency . ϖ p , (Fig. 16.2) Damped oscillation freq . ϖ d , (Fig. 16.2) L C iin(t) vin(t) + - LC 1 o = ϖ 3 Bandpass characteristic of parallel RLC circuits x x o 2 o r 1/ 2 2 2 1 1 Y(s) Cs R Ls 1 (1/ C)s Z(s) s 1 Y(s) s RC LC 1 Z(j ) 1 1 j( C ) R L Im[ Z(j ) ] 0 if 1/ LC 1 1 | Z(j ) | ( C ) R L - = + + = = + + ϖ = + ϖ - ϖ ϖ = ϖ = ϖ = ϖ = + ϖ - ϖ . LC / 1 at peak its reaches | ) j ( Z | o r m ϖ = ϖ = = ϖ ϖ Z(j0) = 0 4 Bandpass characteristic of parallel RLC circuits m r o 2 1 o 2 2 1 m 1 LC B 1 1 1 2RC LC 2RC 2 1 B RC C Q R B L ϖ ϖ ϖ ϖ = ϖ = ϖ = ϖ = + ≈ ϖ = ϖ - ϖ = ϖ = = x x o if LC << 4R 2 C 2 5 Peak frequency : ϖ m Half power frequency: ϖ 1 and ϖ 2 Half power bandwidth : B ϖ = ϖ 2 - ϖ 1 Pass band: [ ϖ 1 , ϖ 2 ] Quality factor Q: High Q: Q > 8 or 10 Low Q: Q < 1 For high Q circuits, 2 B ~ 0 1 2 ϖ ± ϖ ϖ ϖ ϖ ϖ ϖ ϖ = B / ~ B

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lecture 23 - Summary of Lecture#23 Bandpass filters Peak...

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