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Crystal band‐stop filters with improved spurious resonance behaviour
Author(s) -
Matthes Helmut
Publication year - 1976
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490040103
Subject(s) - stopband , bandwidth (computing) , electronic circuit , physics , attenuation , band pass filter , insertion loss , equivalent circuit , inductance , topology (electrical circuits) , materials science , optoelectronics , optics , electrical engineering , computer science , engineering , voltage , telecommunications , quantum mechanics
It is a well known fact that piezoelectric band‐stop filters manifest not only the desired stopband at the fundamental resonant frequency of the crystal, but also additional stopbands at its spurious resonant frequencies. The greater the degree to which such parasitic attenuation peaks are to be suppressed, the more complex is the required circuitry. The most common crystal band‐stop filter circuits can be considered as all‐pass sections in which a capacitance is ‘disturbed’ over a narrow bandwidth by a resonant circuit. If this ‘disturbance’, possibly after conversion by means of known one‐port equivalents, consists of a high impedance series resonant circuit with the inductance L s in parallel to the entire lattice arm R/jx 1 , the 3 dB bandwidth of the stopband becomes Δω 0 = R/L s (1+ x 1 2 ) in the loss‐free case. Sometimes the dual representation of the ‘disturbance’ is more appropriate. With a finite crystal Q ‐factor of Q q , the insertion loss of a desired or parasitic stopband assumes the finite maximum value ǎ ∼ In (1+ Q q Δω0/ω ∞ ). The width and height of the possible attenuation peaks are given in formulas, normalized curves and worked examples for seven band‐stop filter circuits of increasing complexity, each with a single crystal.