L11_transfer_function

L11_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 16, 2010 1 L11_transfer_function
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L11_transfer_function 2 v s ( t )=100cos( ϖ t )
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The magnitude of transfer function is often specified in decibels 2 10 1 10log ( ) dB P G P = 2 10 1 20log ( ) dB V G V = 2 10 1 20log ( ) dB I G I = Because power is proportional to V 2 or I 2 , voltage gain and current gain in decibels is specified as 3 L10b_transfer_function
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|H| 20Log 10 (|H|) 1000 60 100 40 10 20 2 6 2 3 1 0 1/ 2 -3 0.5 -6 0.1 -20 0.01 -40 Decibel Scale 4 L10b_transfer_function
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dB Scale 1 0.1 0.01 0.001 A plot of the decibel magnitude of transfer function versus frequency using a logarithmic scale for frequency is called a Bode plot ϖ (rad/s) 5
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How to determine the transfer function? R V S 0 V O 1/j ϖ C 1 ( ) tan ( ) CR φ ϖ ϖ - = - ) ( ) ( ) ( 0 ϖ ϖ ϖ j V j V j H S = RC j j H ϖ ϖ + = 1 1 ) ( ( 29 2 1 1 ) ( RC j H ϖ ϖ + = 6
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2 3 10 1 log 20 + - = dB dB H ϖ ϖ ( 29 2 10 1 log 20 RC H dB ϖ + - = RC dB 1 3 = ϖ dB 3 ϖ ϖ - dB dB H 3 10 log 20 ϖ ϖ dB 3 ϖ ϖ << ( 29 0 1 log 20 10 = - dB H
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dB 3 ϖ ϖ - dB dB H 3 10 log 20 ϖ ϖ ϖ H dB ϖ 3dB 0 10 ϖ 3dB -20 100 -40 ϖ H dB ϖ 3dB 0 2 ϖ 3dB -6 4 ϖ 3dB -12 -20 dB per decade -6 dB per octave 301 . 0 2 log 10 = 1 10 log 10 = 8 L11_transfer_function
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10 1 10 2 10 3 10 4 10 5 -40 -30 -20 -10 0 10 ϖ (rad/s) H dB RC dB 1 3 = ϖ
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