Design procedure for high-stability four-crystal single-sideband lattice filters with equiripple or maximally flat passbands and double attenuation poles at finite frequencies

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Design procedure for high-stability four-crystal single-sideband lattice filters with equiripple or maximally flat passbands and double attenuation poles at finite frequencies

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A lowpass second-order Cheby̅shev or Butterworth filter is converted into a fourth-order filter with an equiripple or maximally flat passband and a double attenuation pole at a finite frequency using the Zdunek- Möbius transformation. The double pole enables the filter to be realised as a single lattice with an identical crystal in each arm resonating at the pole frequency. Transferring these crystals to outside the lattice results in filters with a very stable transition band, since the pole frequency now depends only on crystal frequencies, whose variation is several orders of magnitude less than the variation of lumped inductors and capacitors which influence the pole frequency in a conventional crystal filter. The transformation by Zdunek for doubling the circuit order is not applied in the usual manner to obtain a higher-order characteristic of a similar type. Instead, it is used here to obtain a characteristic which is unconventional as a result of the double attenuation pole. This application is not restricted to crystal filters. The symmetrical to asymmetrical transformation is applicable to other type of bandpass crystal filter.

Inspec keywords: lumped parameter networks; band-pass filters; poles and zeros; low-pass filters; crystal filters; linear network synthesis; passive filters

Other keywords: lumped capacitors; lumped inductors; Butterworth filter; pole frequency; double attenuation poles; Chebyshev filter; symmetrical to asymmetrical transformation; maximally flat passbands; equiripple; Zdunek-Mobius transformation; stable transition band; low pass second order filters; fourth-order filter; four-crystal single-sideband lattice filters

Subjects: Lumped linear networks; Passive filters and other passive networks; Piezoelectric and ferroelectric devices

References

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      • J. Zdunek . Generation of filter functions from a given model. Proc. IEE , 2 , 282 - 294
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      • J.K. Stevenson , M. Redwood . The motional reactance of a piezoelectric resonator—a more accurate and simpler representation for use in filter design. IEEE Trans. , 568 - 572
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      • Musson, J.T.B., Struszynski, W.: `Practical design of crystal filters for equal ripples in the pass band and equal returns in the stop band (Cauer-Darlington type)', Report RD/P.1632, November 1962.
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