PEMP VSD 2538

Session 8

Passive Filter Theory Session Speaker: Varun D.

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Session Objectives • To study the – Butterworth Filter – Chebyshev Filter

– Prototype Low Pass Filter Design – Transformation from Low Pass Filter To:

• High Pass, Band Pass and Band Stop • Frequency Transformation • Impedance Transformation – Richards Transformation – Kuroda’s Identities

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Session Topics • Butterworth Type Filters • Attenuation Profile-Butterworth

• Chebyshev Type Filters • Attenuation Profile- Chebyshev

• Kuroda’s Identities

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Low-Pass Filter Realizations

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Definitions int ernal.generator.resis tan ce. for.case  a  g0    int ernal . generator . conduc tan ce . for . case  b   induc tan ce. for.series.inductor    g m  capaci tan ce. for.series.capacitor (m  1,2,...N )    Load .resis tan ce.if .the.last.element.is.a.shunt.capacitor  g N 1    Load . conduc tan ce . if . the . last . element . is . a . series . inductor  

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Butterworth Type Filters These are also known as ‘maximally flat’ filters because no ripples are allowed in the attenuation profile. The insertion loss is given by

IL  10 log1  a 2 2 N 

Where,    / c In the above  denotes the cutoff frequency. The constant ‘a’ is set equal to 1, for then IL=10log2=3dB for  =1. c

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Attenuation Profile-Butterworth

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Low-Pass Butterworth Filter Coefficients

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Low-Pass Butterworth Filter Attenuation

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

Chebyshev-Type Filters The design of an equi-ripple filter type is based on an insertion loss whose functional behavior by Chebyshev polynomials TN() in the following form

© M. S. Ramaiah School of Advanced Studies, Bangalore

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PEMP VSD 2538

To appreciate the behavior of the chebyshev polynomials in the normalized frequency range -1