US3858127A

US3858127A - Stable and compact low frequency filter

Info

Publication number: US3858127A
Application number: US00423349A
Authority: US
Inventors: R Johnson
Original assignee: Rockwell International Corp
Current assignee: Boeing North American Inc
Priority date: 1973-12-10
Filing date: 1973-12-10
Publication date: 1974-12-31
Anticipated expiration: 1991-12-31

Abstract

Stable low frequency mechanical filters are provided by tworesonator filter sections with each resonator having transducer means associated therewith. Two attenuation poles are provided with each section by adding a bridging capacitor to the section; multiple attenuation-poles may be provided with highly attenuated unwanted spurious responses by cascading the sections.

Description

United States Patent 1191 [111 3,858,127 Johnson Dec. 31, 1974 STABLE AND COMPACT LOW 3,142,027 7/1964 Albsmeier et al 333/72 FREQUENCY FILTER 3,792,382 2/1974 Guenther 333/72 Inventor: Robert A. Johnson, Tustin, Calif.

Rockwell International Corporation, Dallas, Tex.

Filed: Dec. 10, 1973 App]. No.: 423,349

Assignee:

US. Cl 333/72, 310/82, 310/83,

333/71 Int. Cl. H03h 9/02, H03h 9/26 Field of Search 333/71, 72; 310/82, 8.3

References Cited UNITED STATES PATENTS l/1962 Honda et a1. 333/71 X Primary Examiner-James W. Lawrence Assistant Examiner-Marvin Nussbaum Attorney, Agent, or Firm-Howard R. Greenberg [5 7] ABSTRACT Stable low frequency mechanical filters are provided by two-resonator filter sections with each resonator having transducer means associated therewith. Two attenuation poles are provided with each section by adding a bridging capacitor to the section; multiple attenuation-poles may be provided with highly attenuated unwanted spurious responses by cascading the sections.

2 Claims, 11 Drawing Figures maminnimw 3.858.127

" SHEET 10F 3v Flea STABLE AND COMPACT LOW FREQUENCY FILTER This invention relates generally to mechanical filters and more particularly cascaded mechanical filters and modifications thereof to produce stable and compact low frequency (e.g., 2 kHz 50 kHz) bandpass filters.

The choice of electrical filters for low frequency applications includes inductor-capacitor (L-C), active, crystal, and mechanical filters. Each of these filters offers certain advantages and disadvantages, as discussed in our article entitled Build Stable, Compact, Narrowband Circuits, Electronic Design, pages 60-64, Feb. 1, 1973. As set forth therein, the mechanical filter offers several advantages including simplicity, size and cost. A major disadvantage is the presence of spurious frequency responses.

When the selectivity of more than two resonators is needed, some difficulties arise with multi-resonator designs with regard to spurious responses near the passband when the filter bandwidth exceeds certain limits; the limits being a function of center frequency and the number of resonators as well as physical considerations such as the spacing between resonators, coupling wire diameter, support means, and the like.

Another limitation is that of realizing attenuation poles with the multi-element structure. The conventional methods used with disc-wire and bar-wire mechanical filters involving acoustic wire bridging are not always practical at lower frequencies where the long wavelength of the wire necessitates diagonal bridging to opposite phase surfaces to realize pairs of finite attenuation poles. In addition, it is only possible to realize a single-pair of attenuation poles, in a four-resonator filter, using acoustic (wire) bridging.

An object of this invention is a stable and compact low frequency mechanical filter having highly attenuated spurious frequency responses.

Another object of the invention is a low frequency mechanical filter having attenuation poles.

Still another object of the invention is a low frequency mechanical filter having a wide bandwidth.

' Another object of the invention is a low frequency mechanical filter with reduced sensitivity due to aging and temperature effects.

Features of the invention include a two-resonator section comprising wire coupled, flexure mode bars with each bar having a piezoelectric ceramic transducer mounted thereon. By selectively cascading the sections, using tuning inductors and bridging capacitors, and either symmetrical or non-symmetrical sections, various stable and compact low frequency designs with reduced spurious responses and with attenuation poles are available.

The spurious response improvements result from a reduction in the number of resonators in each filter section and an additive value of attenuation effects at spurious mode frequencies. Thus, not only does each individual section have a reduction in the amplitude of any spurious response, but the addition or cascading of the sections also reduces the unwanted response amplitudes. This is in contrast to the multi-resonator filter where spurious modes are coupled from the input to the output through resonances of the entire filter structure; the more complex the structure the greater the effect of the unwanted modes.

These and other objects and features of the invention will be more fully understood from the following detailed description and appended claims when taken with the drawing, in which:

FIG. 1 is a perspective view of a two-pole, tworesonator filter section in accordance with the present invention;

FIG. 2 is an equivalent electrical schematic of the filter section of FIG. 1;

FIG. 3 is a block diagram representation of the filter in FIGS. 1 and 2;

FIG. 4 is a block diagram representation of two cascaded filter sections in accordance with the present invention;

FIGS. 5(a) through 5(d) are electrical schematics illustrating the synthesis method of obtaining the fourresonator network of FIG. 4;

FIG. 6 is a set of curves illustrating frequency responses of filter sections in accordance with the present invention with and without the use of bridging capacitors.

FIG. 7 is a representation of two-resonator sections cascaded with a variable capacitor between sections; and

FIG. 8 is a representation of two cascaded tworesonator sections utilizing variable inductors to reduce the size of ceramic transducers.

Referring now to the drawings, FIG. 1 is a perspective view of a two-pole, two-resonator mechanical filter section in accordance with the present invention including two metal

alloy resonator bars

10 and 12 each having a piezoelectric

ceramic transducer

14, 16 and coupled by

coupling wires

18, 20 which also act as support wires for the structure by virtue of the fact that they are joined at the nodal points of the bar resonator and therefore transmit a minimal amount of energy into the support. An electrical signal is applied to the input terminal and ground terminal from the generator 22 through source resistor 24. The signal from generator 22 causes transducer 14 to expand and contract, thereby causing the metal alloy bar to bend. This flexural vibration is transmitted to the second bar by means of the

coupling wires

18, 20 and 4,

coupling wires

18 and 20 vibrating in torsion and coupling wire 4 vibrating in flexure. It will be appreciated that there may be additional wires on the bar that vibrate in combinations of flexure and torsion. Energy is delivered to the load 26 or another cascaded section through output transducer l6. Capacitive bridging which results in attenuation poles is shown by the dashed lines 28.

An alternate representation of FIG. 1 is shown in FIGS. 2 and 3. FIG. 2 is an electrical equivalent circuit of FIG. 1 where C is the static capacity of the input transducer, the tuned circuits L C R and L C and R represent the composite transducer, alloy bar combination, the inductor L represents the coupling wires, and C is the bridging capacitor when attenuation poles are desired.

FIG. 3 is a block diagram representation of FIGS. 1 and 2 with bridging capacitor C shown dotted. In each of the above figures, the network 32 to the right can be a load resistor as in the single section case, or a shunt coupling capacitor followed by another tworesonator section in the cascade case. The four-pole case is shown in FIG. 4 with two

sections

30 and 32 and bridging capacitors C and C Consider now the circuit derivation for the aforedescribed circuits. The synthesis method of obtaining the four-resonator network of FIG. 4 is shown in FIG. 5. FIG. 5(a) is a simple narrow bandwidth bandpass filter well known in the prior art for filters. The networks K and K represent impedance inverters having the narrow bandwidth equivalent circuit shown in FIGS. 5(0) and 5(d). By removing shunt capacitance from each of the resonators and making parallel-to-series RC transformations at the input and output as shown in FIG. 5(b), combining the -L inductors with the resonators, and making a series of pi to tee and tee to pi transformations in the center sections, the networks of FIGS. 2-4 are derived (excluding any bridging capacitors). The element values can be found through a set of design equations or through network optimization techniques using a digital computer. The optimization methods are very useful in the design of filters with rounded response shapes such as TBT or Bessel filters, with filters having multiple requirements such as amplitude and delay and in the case of capacitive bridging.

In addition, the optimization program can be used to obtain a realization that is composed of two symmetrical, identical resonator sections. This type of realization is ideal for manufacturing in that there is a great deal of flexibility in matching the sections because the sections can be rotated 180.

FIG. 6 illustrates typical frequency response curves of filters in accordance with the invention with and without bridging capacitors. Curve 60 represents the response of a filter having no bridging capacitor and has no attenuation poles at finite frequencies. Curve 62, representing a filter having a bridging capacitor, has attenuation poles at 63, 64, 65 and 66.

Having an electrical equivalent circuit as illustrated above, consider now the mechanical (acoustic) realizability of the network. The factor of most concern is the ability to terminate the filter and couple between sections with transducers that are not so large as to cause excessive frequency shift clue to aging and/or temperature variations. This is only a consideration in the case of the wider bandwidth filters where the size of the transducers may be so large that aging and temperature characteristics outweigh characteristics of the metal alloy bar, which is very stable. It is also this particular case where the need for cascade sections is required to reduce spurious responses.

Consider now the requirements for terminating the filter and for properly capacitively coupling the filter. The basic equation is:

where BW is the maximum bandwidth filter than can be built with composite end resonators (transducer/- bar) having a driving point impedance, pole-zero spacing of Af, and a frequency response shape requiring a normalized terminating q equal to q See for example, Reference Data for Radio Engineers, 4th Edition, pages 216-219. When BW is the design goal, then Af is adjusted by the use of various transducer materials or a variation of the dimensions of the transducer relative to the metal alloy bar.

The basic equation for the realizable filter bandwidth as relating to the center (capacitive coupling) section where k is the normalized coupling coefficient between the third and fourth resonators (see Reference Data for Radio Engineers, supra). For a maximally flat amplitude response (Butterworth) q. 0.766 and k 0.542. Therefore,

Where Af is the pole-zero spacing needed by the inside resonators to realize BW,,,,,,, and Af, is the pole-zero spacing required of the end resonators in order to terminate the filter of bandwidth BW As passband ripple is increased, the Af, requirements on the outside resonators are decreased, whereas the more rounded filters have even greater pole-zero requirements on the ends. Thus, from the above considerations, the center resonators can utilize smaller transducers for ripple values less than approximately 1 dB and therefore improve the overall stability of the filter. It should be appreciated that the stability of a bandpass mechanical filter is most affected by the stability of the inside resonators. A four:one ratio of passband ripple variation due to changes in the center resonator frequencies relative to the variation due to changes in the end resonator frequencies is typical. Therefore, by using smaller transducers on the inside bars the overall stability of the filter is improved. In the limiting case, (i.e., using the smallest possible'transducer, the center coupling capacitor is not needed and the tuning frequencies of the bar will generally be different and maximum stability will be achieved. However, by providing some shunt capacity between cascaded units a simple bandwidth adjustment is provided.

FIG. 7 shows a cascade of two-resonator sections with a variable capacitor 74 between the sections. It should be noted that smaller piezoelectric

ceramic transducers

72 and 73 are needed on the inside resonators than on the outside resonators and 71). Through the use of a minimum amount of transducer material the stability of the ceramic/metal composite resonator is improved as is the over-all stability of the filter.

The stability of the cascaded filter in accordance with the present invention can be further improved by partially tuning the input and output transducers, thus reducing the size of the input and output transducers to that of the center transducers. The basic equation for implementing this is:

By adding a series of shunt inductor L the effective or apparent C is increased as is Af for a fixed size transducer. Thus, a series or transformed shunt inductive reactance reduces the reactance of the L C series combination, thus increasing the pole-zero spacing of the unit. Conversely, the addition of an inductor can result in a fixed value of Af with a smaller transducer. A very practical design from the point of manufacturing is when the inside and outside transducers are identical and the filter is optimized with a digital computer so as to result in equal resonator frequencies.

The advantage of the equal size transducer/bar resonators is that all of the filters resonators will have equal frequency shifts due to temperature variations which reduces distortion of the amplitude and delay frequency response of the entire filter. In addition, use of the inductor to reduce the size of the ceramic transducer results in a smaller average frequency shift of the filter response. FIG. 8 shows a cascade of tworesonator sections that are capacitively coupled by the variable capacitor 80 and make use of

inductors

83 and 84 to reduce the size of the

ceramic transducers

81 and 82. The

inductors

83 and 84 can be placed across (in shunt) with the source and load resistors 85 and 86. This requires a simple series-to-parallel transformation of R and L In addition to the improved stability realized by the use of input and output inductors, there is the advantage of being able to realize a wider bandwidth filter for a fixed transducer size and material, i.e., for a fixed degree of frequency stability with changes of temperature or time or a maximum coupling (maximum Af) transducer/bar composite resonator.

Low frequency, flexure mode, two-resonator filter sections in accordance with the present invention provide stable, economical, bandpass filters. Attenuation poles are provided by using capacitive bridging as described above. Further, the use of a shunt capacitor to provide coupling between sections allows bandwidth adjustment. Additionally, a reduction in sensitivity due to temperature and aging variables is achieved by using smaller transducers on the center resonators, and further reduction of sensitivity and the realization of wide bandwidth filters is provided by use of inductors on the input and output of the filters.

While the invention has been described with reference to specific embodiments, the description is illustrative and is not to be construed as limiting the scope of the invention. Various modifications and changes may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined by the appended claims.

I claim:

1. A low frequency mechanical filter comprising a plurality of cascaded two-resonator sections; each section including first and second flexure mode resonator bars, a piezoelectric transducer mounted on each bar, a bridging capacitor whereby attenuation poles above and below the filter passband are realized, and coupling wires attached to and acoustically coupling said first and second bars; and coupling means coupling said sections in cascade.

2. A low frequency mechanical filter comprising a plurality of cascaded two-resonator sections; each section including first and second flexure mode resonator bars, a piezoelectric transducer mounted on each bar, and coupling wires attached to and acoustically coupling said first and second bars; and coupling means coupling said sections in cascade with all inside transducers being smaller than the two outside transducers

Claims

2. A low frequency mechanical filter comprising a plurality of cascaded two-resonator sections; each section including first and second flexure mode resonator bars, a piezoelectric transducer mounted on each bar, and coupling wires attached to and acoustically coupling said first and second bars; and coupling means coupling said sections in cascade with all inside transducers being smaller than the two outside transducers to improve stability.