US2774042A - Electromechanical wave filter - Google Patents

Description

' DecQll, 1956 w, P, MASON Er AL 2,774,942

ELECTROMECHANICAL WAVE FILTER Filed April 29, 1953 VENTOR'S F? MASON N H. J. MC S/(lM/N ATTORNEY United States Patent ELECTROMECHANICAL WAVE FILTER Warren P. Mason, West Orange, and Herbert J. McSkimin,

Basking Ridge, N. J., assignors to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application April 29, 1953, Serial No. 351,842

7 Claims. (Cl. 333-71) This invention relates to mechanical wave filters and more particularly to those filters which are torsionally excited.

The principal object of this invention is to improve the frequency filtering characteristics of a mechanical wave filter.

One common form of mechanical wave filter consists of a relatively long, small-diameter rod of acoustic material and one or more members of greater diameter centrally connected thereto and adapted to be set into flexural vibration when longitudinal vibrations are impressed upon one end of the rod. Peaks of attenuation occur at the antiresonant frequencies of the transverse members and these peaks are usually located close to the frequency pass band limits to obtain sharp cut-ofr characteristics. In such a filter, however, when certainsignals are applied, spurious resonances resulting from mechanical coupling to other than the longitudinal mode of vibration appear and, as a consequence, the output signals are undesirably distorted in these instances. Previous to this invention, various ways, including operating the filter at low signal levels or making the frequency cut-ofi characteristics less sharp, have been tried for the purpose of eliminating this difiiculty butso far as is known none has proved as satisfactory as might be wished. The present invention is directed to a simple and inexpensive solution of this problem by means which also permit very sharp frequency cut-ofis and substantial signal levels.

In accordance with the present invention in one embodiment thereof a small-diameter rod of acoustic mate rial of length I has connected to its midpoint a larger diameter thin disk or plate of a similar material which vibrates in a torsional mode when an angular rotational torque is applied to one end of the rod. By properly dimensioning this centrally located disk, as, for example, in accordance with the formulas set forth herein, a peak of attenuation can be placed either above or below the frequency pass band at a chosen frequency, thereby facilitating almost any desired degree of sharpness in the cut-off characteristics.

The nature of this invention will be more fully understood from the following detailed description given in connection with the accompanying drawings, in which:

Fig. 1 is a perspective view of a mechanical wave filter in accordance with the invention employing a centrally positioned disk;

Fig. 2 is a diagram of the electrical equivalent of the mechanical filter shown in Fig. 1; and

Fig. 3 is a perspective view of a cascaded mechanical wave filter in accordance with the invention.

Referring now particularly to the drawings, Fig. 1 shows, for the purposes of illustration, as an embodiment of the invention mechanical filter which consists of a small-diameter rod 11 of a suitable acoustic material to which is connected disk or plate 12 of a similar or like material. This disk is fastened to rod 11 substantially midway between the ends thereof and is preferably, though not necessarily, formed as an integral part. Since disk 12 is the principal resonating element of the filter, its mechanical Q should be as high as possible in order to minimize loss and also to minimize loss distortion in the pass band and consequently to improve the cut-off characteristics of the filter. Accordingly it should be chosen from a low loss material such as a nickel-iron alloy although in many, if not all, applications certain ceramics or crystals are well suited.

The dimensions of rod 11 and disk 12 will most conveniently be set forth in connection with the formulas characterizing the electrical behavior of the equivalent circuit shown in Fig. 2. It should be noted here, however, that the dimensions of filter 10 for a given frequency of operation in the torsional mode are entirely difierent from those of a filter having the same operating frequency but excited in a longitudinal mode. One noticeable difference is that the length of filter 10 is approximately only one-half that of a comparable longitudinal mode filter.

Fig. 2 shows the electrical analogue of the mechanical filter shown in Fig. 1. This electrical equivalent circuit consists of two identical wave transmission lines 21 and 22, each having a length l/2 which is approximately a quarter wavelength long at the frequency of operation, whose adjacent ends are joined together by a serially connected parallel tuned circuit 23. The image propagation constant 0 and image impedance Z1 for the filter are given by the following S111 v Z0 OS 27) Z Lsin lsin I) Z9 21) where v is the velocity of propagation along the line, I is the total length of both sections of line, Z0 is the characteristic impedance of each line, to is angular frequency, Zs is the impedance of the resonant circuit 23 given by [L is the shear modulus in the acoustic material and p is the density. p p

The series impedance ZS for disk 12 near its antiresonant frequency vibrating in a torsional mode is jail z.-

where f is frequency r .4636r1v f.

r is the inner radius of disk 12 and r2 is the outer radius, I1=1.559 (r2 -r1 )h, and h is the thickness of disk 12, these distances in centimeters.

For the case where fr, the anti-resonant frequency of disk 12, lies below the frequency pass band, it can be shown from the above equations that the image impedance at mid-band is :1 l jiflm t t 8 luff-PG (twa n) r where fu is the upper cut-off frequency corresponding to cosh 0=--1 in Equation 1, fl. is the lower cut-off frequency corresponding to cosh 0=+1 in Equation 1,

Similarly it can be'sho'wn that where fr lies above the upper cut-off frequency shown in Fig. 3. may be used. As shown, two filters,

one having a peak above and the other below the band, may be connected in series. As discussed above, the dimensions of each section of the filter may be determined from Equations 5 and 6. By thus cascading filter sections of the type shown in Fig. 1, increasingly sharp cutoff characteristics may be obtained. Although filter 10 will have transmission bands in addition to the principal one considered here, these may, if objectionable, be eliminated by attenuation provided by the torsional input and output transducers used in conjunction with the filter.

It should be understood that the invention described herein is not limited to wholly mechanical systems but will be very useful in electromechanical filters such as telephone channel frequency-separating filters and superheterodyne radio receiver intermediate-frequency filters. These electromechanical devices of course require transducers, such as described in 'Electro-Mechanical Transducers and Wave Filters by W. P. Mason, Van Nostrand Company, 1948, to convert the electrical signals into the vibrations applied to the mechanical filters.

Changes and modifications in the illustrative embodiment described herein will occur to those skilled in the art and may be made without departing from the spirit or scope of the invention.

What is claimed is: r

1. A mechanical wave filter for transmitting a band of frequencies, said filter having a lower cut-off frequency in, and an upper cut-off frequency f0, comprising a small-diameter cylindrical rod of acoustic material of radius r1 having a length I that is approximately a half wavelength long in the torsional mode of vibration at a frequency within said band, and an annular disk of acoustic material of distributed mass having an inner radius r1, an outer radius rz, and a thickness h that is less than one-half wavelength in the torsional mode of vibration at a frequency within 'said band connectedto said rod and dimensioned to resonate in a single torsional mode at a frequency ifr when said *rod is torsionally excited by mechanical vibrations applied to an end thereof, whereby a peak of attenuation is provided at a frequency fr at a desired point outside the pass band of said filter. I

2.'The combination of elements as in claim I in which said disk is an integral part of said rod.

3. The combination of elements in claim 1 in which.

said disk is positioned symmetrically-on said rod midway between the ends thereof. v 4. A cascaded mechanical wave filter comprising a plurality of mechanical filters connectedin-series; each filter'like the filter in claim 1, at least one of said filters having its annular disk resonant at a frequency differing from the resonant frequencies of the corresponding disks of the other filters to give a peak of attenuation outside the pass band jwhereby there is a peak of attenuation i above and a peak below the band cut-off frequencies.

5; 'A mechanical wave filter comprising awave filterlike the filter in claim -1, means for'impressing torsional vibrations on one end of said rod, and means for receiving torsional vibrations at the other end of said rod.

6. A mechanical wave filter for transmitting a preassigned band of frequencies comprising means includ-C ing a rodof acoustic material having -'a length approximately equal to a half w'aveleng'thin thetorsional mode of vibration at a frequency within said =pr e'assignedfband for transmitting a band of frequencies including said preassigned band, and-means for .producing 'apeakyof I attenuation at a frequency close to one -limit-=-of fsaid preassigned ,band, said last-mentioned means including a transverse thincon'tinu'ou's annular member made of acoustic material of distributed mass cent-rally mounted near the center of said rodan'ddimensioned to resonate in a torsional mode at the frequency of said peak of attenuation when said rod is torsionally excited bymechanical vibrations applied to an end thereof. U

7. A mechanical wave filtera's in claim 1 coupled to a torsional electromechanical transducer, in which the image impedance la in the torsional mode of vibration of said mechanical wave filter is matched to the output mechanical impedance of said torsional mechanical transducer. v i

References Cited in the tile of this patent UNITED STATESJ'PATENTS i

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