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ELEC Lecture 131 ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 13

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ELEC Lecture 132 Band-Pass Filter Design Example Attenuation response of a third-order 3-dB ripple bandpass Chebyshev filter centered at 2.4 GHz. The lower cut-off frequency is f L = 2.16 GHz and the upper cut- off frequency is f U = 2.64 GHz.

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ELEC Lecture 133 RF/ W Stripline Filters Filter components become impractical at frequencies higher than 500 MHz Can apply the normalized low pass filter tables for lumped parameter filters to stripline filter design Richards Transformation and Kuroda’s Identities are used to convert lumped parameter filter designs to distributed filters

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ELEC Lecture 134 Richards Transformation: Lumped to Distributed Circuit Design Open- and short-circuit transmission line segments emulate inductive and capacitive behavior of discrete components Based on: Set Electrical Length l = /8 so

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ELEC Lecture 135 Richards Transformation: Lumped to Distributed Circuit Design Richards Transform is: and For l = /8, S = j1 for f = f o = f c

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ELEC Lecture 136 Richards Transformation: Lumped to Distributed Circuit Design

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ELEC Lecture 137 Unit Elements : UE Separation of transmission line elements achieved by using Unit Elements (UEs) UE electrical length: = /4 UE Characteristic Impedance Z UE

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ELEC Lecture 138 The Four Kuroda’s Identities

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ELEC Lecture 139 Kuroda’s Equivalent Circuit

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ELEC Lecture 1310 Realizations of Distributed Filters Kuroda’s Identities use redundant transmission line sections to achieve practical microwave filter implementations Physically separates line stubs Transforms series stubs to shunt stubs or vice versa Change practical characteristic impedances into realizable ones

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ELEC Lecture 1311 Filter Realization Procedure Select normalized filter parameters to meet specifications Replace L’s and C’s by o /8 transmission lines Convert series stubs to shunt stubs using Kuroda’s Identities Denormalize and select equivalent microstriplines

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ELEC Lecture 1312 Filter Realization Example 5 th order 0.5 dB ripple Chebyshev LPF g 1 = g 5 = , g 2 = g 4 = , g 3 = , g 6 =1.0

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ELEC Lecture 1313 Filter Realization Example Y 1 = Y 5 = , Z 2 = Z 4 = , Y 3 = ; and Z 1 = Z 5 = 1/1.7058, Z 3 = 1/2.5408

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ELEC Lecture 1314 Filter Realization Example Utilizing Unit Elements to convert series stubs to shunt stubs

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ELEC Lecture 1315 Filter Realization Example Apply Kuroda’s Identities to eliminate first shunt stub to series stub

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ELEC Lecture 1316 Filter Realization Example Deploy second set of UE’s in preparation for converting all series stubs to shunt stubs

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ELEC Lecture 1317 Filter Realization Example Apply Kuroda’s Identities to eliminate all series stubs to shunt stubs Z 1 = 1/Y 1 =NZ 2 = (1+Z 2 /Z 1 )Z 2 =1+(1/0.6304); Z 2 = 1 and Z 1 =

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ELEC Lecture 1318 Filter Realization Example Final Implementation

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ELEC Lecture 1319 Filter Realization Example Frequency Response of the Low Pass Filter

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