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L12_transfer_function

# L12_transfer_function - ESC102 Introduction to Electronics...

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Frequency Response ESC102 : Introduction to Electronics A.R. Harish Dept. of EE, IIT Kanpur Aug 17, 2010

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Series Resonant Circuit v S C i(t) L R Resonance is a condition in which capacitive and inductive reactance cancel each other to give rise to a purely resistive circuit 1 eq Z R j L j C ϖ ϖ = + - Resonant frequency: 1 1 0 O O O j L j C LC ϖ ϖ ϖ - = = 1 2 O f LC π = eq Z R = Current and voltage are in phase (power factor is unity) and current is maximum ! 2 L12_transfer_function
v S C i(t) L R 2 2 ( ) 1 ( ) m V I R L C ϖ ϖ ϖ = + - ϖ 1 and ϖ 2 are called half-power frequencies since P I 2 3 L11_transfer_function

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2 2 ( ) 1 ( ) m V I R L C ϖ ϖ ϖ = + - 1 2 2 1 1 ( ) 1 2 ( ) m m V V I R R L C ϖ ϖ ϖ = = + - 2 2 2 2 2 ( ) 1 2 ( ) m m V V I R R L C ϖ ϖ ϖ = = + - 4 L11_transfer_function
1 2 O ϖ ϖ ϖ = 2 1 R B L ϖ ϖ = - = Quality (Q) factor: Sharpness of resonance Peak Stored Energy 2 Energy dissipated in one period at resonance Q π = 2 2 1 2 2 1 2 m O m O L I L Q R I R T ϖ π × = × = × 1 1 O O Q CR LC ϖ ϖ = = 5 L12_transfer_function

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2 1 R B L ϖ ϖ = - = O L Q R ϖ = O O Q B ϖ ϖ ϖ = = Hence Q represents sharpness of resonance For high Q circuits:
-40dB/decade v S C v O (t) L R O L Q R ϖ = Stopband Attenuation Passband Insertion loss

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R-L-C filters v S C v O (t) L R j L ϖ j C ϖ - v S v O (t) R C L j L ϖ j C ϖ - 8 L12_transfer_function
v O (t) L R C v S j L ϖ j C ϖ - v S R v O (t) L C j L ϖ j C ϖ - 9 L12_transfer_function

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L12_transfer_function - ESC102 Introduction to Electronics...

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