Lecture 34+35 - Lectures 34+35 More poles, zeros,...

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Spring 2011 ECE 2100, Cornell Univ. Prof. Molnar 1 Lectures 34+35 More poles, zeros, equalizers
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Spring 2011 ECE 2100, Cornell Univ. Prof. Molnar 2 Example: equalizers • Assume stuck with RC: – Time constant = RC – Loses gain at ω = 1/RC • Transfer function? – 1 pole at s =-1/RC: • Idea: build a circuit to cancel the pole: – Eliminate time constant – Increase bandwidth Z F = R F Z 1 =(1/sC 1 )||R 1 V 1 V in - + R 1 C 1 Vout R C Vin s RC RC s Vin s Vout + = 1 1 ) ( ) (
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Spring 2011 ECE 2100, Cornell Univ. Prof. Molnar 3 Concept: equalizers + - = + - = 1 1 1 1 1 1 1 1 C R s C R C sR R R Vin Veq F F What is the transfer function? Veq = -Vin(Z F /Z 1 ) – Z F = R F – Z 1 = R 1 ||1/sC 1 =R 1 /(1+sR 1 C 1 ) Zero at -1/(R 1 C 1 ) – Choose R 1 C 1 to cancel pole Z F = R F Z 1 =(1/sC 1 )||R 1 V 1 V in - + R 1 C 1 Z F = R F Z 1 =(1/sC 1 )||R 1 V 1 V in - + R 1 C 1 Vout R C V eq ( 29 1 1 1 1 1 1 1 1 R R RC C R RC s RC C R s C R Veq Vout Vin Veq F F F - = - = + + - = V eq
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Spring 2011 ECE 2100, Cornell Univ. Prof. Molnar 4 Poles in resonant systems Over damped ( α > ω o ) b two distinct, real poles Critically damped (
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Lecture 34+35 - Lectures 34+35 More poles, zeros,...

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