US2199921A

US2199921A - Wave filter

Info

Publication number: US2199921A
Application number: US232067A
Authority: US
Inventors: Warren P Mason
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1938-07-28
Filing date: 1938-09-20
Publication date: 1940-05-07
Anticipated expiration: 1957-05-07
Also published as: BE435676A; DE742179C; US2248776A; CH215766A; FR858308A; GB531662A; NL66164C

Abstract

531,662. Impedance networks. STANDARD TELEPHONES & CABLES, Ltd. July 28, 1939, Nos. 21991, 21992 and 21993. Convention dates, July 28, 1938, Sept. 20, 1938, and Sept. 28, 1938. [Class 40 (iii)] In an unbalanced wave filter of the bridged-T type (which may degenerate into one of pi type), the series arms of the T comprise a single crystal having a split electrode on one or each side. Attenuation peaks may be located at any distance from the pass range, the number of such peaks may be increased by the addition of further crystals, and inherently high or low image impedances may be attained by the use of shunt or series terminal inductances. In the arrangement shown in Fig. 1, the series arms comprise the impedances between the part electrodes 5, 7 and 6, 8 respectively, together with shunt condensers C 1 . The bridging arm Z 1 and shunt arm Z 2 may have various forms, and the lower terminals 2, 4 may be earthed. The Specification gives the lattice network, Fig. 3 (not shown) equivalent to that shown in Fig. 1, and deduces the transmission characteristics of the filter. In a band-pass filter, Figs. 4 to 7 (not shown), the bridging arm Z 1 may be a capacitance while Z 2 is replaced by a direct connection ; the band-width can be increased by reducing the capacitance C 1 shunting the crystal, while the frequency of an attenuation peak below the pass band can be adjusted by varying the capacitance which forms the bridging arm Z 1 . The attenuation peak is located above the pass band if the poling of the part-electrodes 6, 8 is reversed, so that the electrodes shall be cross-connected, Figs. 8 to 11 (not shown). Attenuation peaks on both sides of the band can be obtained by connecting filters of the two types in cascade, Fig. 12 (not shown), their impedances being matched and their transmission bands identical. For a pass band of maximum width, the capacitances C 1 are omitted, so that the network consists of the crystal X with a bridging condenser at Z,. For a low-pass filter, Figs. 13 to 18 (not shown), the bridging arm Z 1 may be a parallel-tuned circuit while the shunt arm Z, is replaced by a direct connection. In a band-stop filter, with two attenuation peaks in the stop band, Figs. 19 to 22 (not shown), the bridging arm Z, is a parallel-resonant arm while the shunt arm Z 2 is an inductance. Fig. 23 shows a high-pass filter, in which the bridging arm Z, comprises a series resonant arm L 4 , C 9 which may be shunted by a capacitance C 10 , while the shunt arm Z 2 comprises an inductance ; and the former arm may be replaced by a crystal X, equivalent to it, Fig. 27. In another high-pass filter, Fig. 20, and Figs. 29 to 31 (not shown), the electrodes of the crystal X are reversely poled, the bridging arm Z, is a capacitance, and the shunt arm Z, is a series resonant circuit. In a band-pass filter with two attenuation peaks, Fig. 31 (and Figs. 32 to 35, not shown) the crystal X is crossconnected and is paralleled by a tee comprising a pair of inductances 4a which give the network a high-image impedance, in series with an adjustable resistance R 3 . The inductances La have a series-opposing mutual inductance. The bridging arm Z, is a capacitance which can be adjusted to vary the location of the peaks of attenuation ; and this adjustment can also be effected by adjusting the coupling of the inductances La. In the absence of such coupling one of the peaks is at zero frequency. The input and output terminals are shunted by capacitances C, which can be varied to vary the band-width. Instead of being cross-connected, the electrodes in Fig. 31 may be symmetrically connected as in Fig. 23 ; the circuit of Fig. 31 thus modified, Figs. 36, 37 (not shown) forms a band-pass filter with two attenuator peaks below the pass band ; the coupling between the inductances La may in this case be series-aiding or absent. The resistance R 5 may be replaced by a direct connection, while the capacity in the bridging arm Z, is shunted by an adjustable resistance, Figs. 30 to 41 (not shown) ; and such a shunt resistance may be used in the filters described above to compensate for dissipation in the inductances. A low image impedance is obtained by arranging inductances Lb, Fig. 42 (and Figs. 43 to 46, not shown), in series with the input and output terminals ; they may have a series-opposing mutual inductance, by decreasing which the frequency at which an attenuation peak occurs above the pass band may be raised; this peak is removed to infinite frequency when the mutual inductance falls to zero. If the crystal in Fig. 42 be cross-connected, Figs. 47, 48 (not shown), both attenuation peaks will lie above the pass band. Two crystals, X, X, Fig. 49 (and Figs. 50 to 52, not shown) may have their pairs of electrodes connected in parallel, one of the crystals having its electrodes cross connected as shown. Such a filter gives in general three attenuation peaks. To produce a high image impedance, the inductances La are connected in shunt instead of series with the input and output terminals, Figs. 53 to 56 (not shown).

Description

May 7, 1940.

'w. P. MASON WAVE FILTER Filed Sept. 28. 1958 PEACTANCE ATTENUA TION Q FIG? 7 REAC TANCE I I FREQUENCY o f1 f2 fsf f1 6 FREQUENCY E k .x-

0 n la fia fie 17 FREQUENCY INVENTOR' By WP MASON 1& ZW

A T TORNE V Patented May 7, 1940 UNITED STATES PATENT OFFICE WAVE FILTER Warren P. Mason, West Orange, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application September 28, 1938, Serial No. 232,067

22 Claims.

This invention relates to frequency-selective wave transmission networks which employ piezoelectric crystals as impedance elements and more particularly to wave filters of the unbalanced type which use a plurality of such crystals.

An object of the invention is to improve the attenuation characteristics of unbalanced bandpass wave filters which employ piezoelectric crystals as impedance elements. Another object is to reduce the cost of filters of this type which have sustained high attenuation on each side of the transmission band.

The wave filter of the present invention is of the unbalanced, band-pass type one side of which may be grounded or otherwise fixed in potential. The filter comprises as impedance elements two or more piezoelectric crystals which have divided electrodes on one or both sides. One of the crystals has a single electrode on one side which is connected to the grounded side of the filter, and two electrodes on the other side which are connected, respectively, to the input terminal and the output terminal on the high side of the filter. Another of the crystals has two pairs of oppositely disposed electrodes. An electrode on one side and a diagonally opposite electrode on the other side of the crystal are connected together and to the grounded side of the filter. The remaining two electrodes are connected, respectively, to the input terminal and the output terminal on the high side of the filter. If these two crystals have different frequencies of resonance the filter may be designed to transmit a band lying between two preassigned frequencies while attenuating all other frequencies. The filter will have two peaks of attenuation which may be located one on the lower side of the band and the other on the upper side, both below the band or both above the hand.

These two peaks of attenuation will be located at some distance from the transmission band but may be brought in closer to the band limits by the addition .of a bridging impedance branch comprising a capacitance connected between the crystal electrodes associated with the high side of the filter. The larger the value of this capacitance the closer the peaks will be to the cutoff frequencies. The width of the transmission band will ordinarily be small on a percentage basis and can be made still narrower by the addition of capacitances connected in shunt at the ends of the crystals. The larger the values of these capacitances are made the narrower will be the band.

ter showing the placing of. the electrodes;

In order to widen the transmission band and improve the attenuation characteristic inductances may be added at the ends of the filter. If a filter having an inherently low image impedance is required these inductances are connected in series at the ends of the filter. If a high image impedance is desired the inductances are connected in shunt at the ends of the filter. The addition of the inductances materially widens the band and permits the location of an attenuation peak at infinite frequency or at zero frequency. These peaks at zero or infinite frequency may be moved in toward the band limits to any desired extent by adding an inductive coupling between the inductances. For the series-connected case the inductances are connected in the series-opposing relationship if the four-electrode crystal has the lower resonance frequency, and in the series-aiding relationship if the three-electrode crystal has the lower resonance frequency. For the shunt-connected case the inductances are connected series aiding if the four-electrode crystal has the lower resonance, and series opposing if the three-electrode crystal has the lower resonance.

Additional peaks of attenuation may be provided by employing more crystals in the filter circuit. The added crystals are connected in parallel with the two crystals, and in general each additional crystal permits the provision of one more arbitrarily placed attenuation peak. There is thusprovided a crystal filter of the unbalanced type Which has any desirednumber of attenuation peaks placed on either side'of the transmission band and located at any arbitrarily chosen frequencies including zero and infinity. Due to the additional peaks the attenuation outside of the band may be sustained above any required minimum value over any desired frequency range. Considering the high discrimina- 40 tion obtainable the filter requires a minimum number of component elements and'is therefore less expensive to build than the unbalanced crystal filters heretofore known.

The nature of the invention will be more fully understood from the following detailed descrip tion and by reference to the accompanying drawing of which:

Fig. 1 is a schematic circuit showing the embodiment of the wave filter of the invention in which the inductors are connected in series at the ends of the network;

Fig. '2 is a perspective view partially broken away of the piezoelectric crystalused in the fil- Fig. 3 shows the equivalent lattice network for the filter of Fig. 1;

Fig. 4 represents the reactance-frequency characteristics of the line and diagonal impedance branches of the lattice network of Fig. 3;

Fig. 5 shows a typical attenuation characteristic obtainable with the filter of Fig. 1;

Fig. 6 is a schematic circuit representing another embodiment of the invention in which the inductors are connected in shunt at the ends of the filter;

Fig. '7 shows the equivalent lattice network for the filter of Fig. 6;

Fig. 8 represents the 'reactance-frequency characteristics of the line and diagonal impedance branches of the lattice network of Fig. 7; and

Fig. 9 shows a typical attenuation characteristic for the filter of Fig. 6.

Fig. 1 is a schematic circuit of one form or the wave filter of the invention in which the inductances are connected in series at the ends of the network. The filter is a symmetrical fourterminal network having a pair of input terminals I, 2 and a pair of output terminals 3, 4 to which terminal loads of suitable impedance may be connected. The network is unbalanced in structure so that the path connecting terminals 2 and 4 may be grounded or otherwise fixed in potential. The path connecting terminals I and 3 may be termed the high side of the filter.

The filter circuit includes two piezoelectric crystals 5, 8, a pair of equal inductors L1, L1 designated by their inductance and three capacitors C1, C2 and C2 designated by their capacitances. The two inductors are connected in series between the input terminal I and the output terminal 3 on the high side of the filter and are inductively coupled by a mutual inductance equal to K1111 where K1 represents the coefficient of coupling. The crystal 5 is provided with two electrodes 7, 8 on one of its major faces and two oppositely disposed electrodes 9, ill on the opposite face. The two diagonally opposite electrodes 8 and 9 are connected together and to the grounded side of the filter. The other two diagonally opposite electrodes 1 and II) are connected, respectively, to the inner terminals of the inductors L1, L1. The second crystal 6 has a single electrode l3 on one face connected to the grounded side of the filter and a pair of electrodes ll, l2 on the opposite face connected, respectively, to the inner terminals of the inductors. The capacitance C1 is connected between the inner terminals of the inductors, and the capacitors C2, C2 are shunted, respectively, between these terminals and the grounded side of the circuit.

The crystal elements 5 and 6 are preferably in the form of a relatively narrow rectangular plate cut perpendicular to the electrical axis of the mother crystal and with its length either in the direction of the mechanical axis or making a selected acute angle therewith. Such a crystal will vibrate longitudinally when an alternating potential is applied to electrodes placed on the larger surfaces. Other well-known types of crystal cut may be used and, under certain conditions, they may be preferred. The crystals shown in Fig. 1 are of the rectangular type described above but for convenience are shown in end elevation.

The placing of the electrodes on the crystals is shown more clearly in Fig. 2 which is a perspective view of the crystal 5 with a corner broken away. The crystal 6 is the same as crystal 5 except that the former has on one side a single electrode it instead of two electrodes. The electrodes may be of silver, aluminum or other suitable metal, plated directly onto the crystal, and may be applied by plating the two major surfaces all over and afterwards removing a narrow longitudinal strip of the plating along the center of the face when it is necessary to provide two electrodes on one face. It is generally desirable also to remove narrow strips of plating around the edges of the crystal. When the crystal-vibrates in the longitudinal mode it is preferably supported between one or more pairs of oppositely disposed points or knife-edge clamps which contact the crystal in the nodal region near the center and along the optical axis. Connections to the electrodes may be made through these clamps or by attaching leads directly to the electrodes with soft solder.

Since the network of Fig. 1 is symmetrical with respect to its input terminals l, 2 and its output terminals 3, 4 its properties may be investigated rnost conveniently from a consideration of the symmetrical lattice network to which it is equivalent. Each line branch of the equivalent lattice is equal to half of the impedance measured between the high-side terminals I and 3 of Fig. l, and each diagonal branch is equal to twice the impedance measured between terminals 5 and 3 strapped together and the grounded side, that is, terminal 2 or l. It is apparent that the mechanical vibration of the four-electrode crystal 5 will occur only in the first and the mechanical vibra-- tion of the three-electrode crystal 6 will occur only in the second measurement. Therefore, the impedance representing crystal 5 will appear only in the line branch of the lattice and the impedance of the crystal 6 will appear only in the diagonal branch. However, the electrode capacitance of both crystals will appear in each branch.

The equivalent lattice for the filter of Fig. l is shown in Fig. 3 in which the impedance of the crystal 5 is represented by its equivalent electrical circuit comprising a capacitance C01 shunted by a branch consisting of an inductance L01 in series with a second capacitance C01, and the impedance of the crystal 6 is'represented by a similar circuit made up of the inductance Lea and the two capacitances C02 and C02. The capacitance C01 represents the simple electrostatic capacitance between a pair of oppositely disposed electrodes such as l and 9 of the crystal 5. The values of the capacitance C01 and the inductance L01 depend upon the dimensions of the crystal and upon its piezoelectric and elastic constants. These elements may be evaluated, in terms of the dimensions of the crystal 5, from the following formulas, assuming that the crystal is of the X-cut variety described above and that the electrodes cover substantially the entire area of the two major faces:

in which I, w and t are, respectively, the length, width and thickness of the crystal 5 measured in centimeters. The values of the elements L02, C02 and C02 in the equivalent circuit for the crystal 5 may be found from the same formulas the dimensions of the crystal 6 are substituted for those of the crystal 5. It will be observed that these elements have twice the impedance of the corresponding elements in the equivalent circuit for a crystal of the same type having only a single electrode on each side.

As-shown in Fig. 3 the equivalent lattice comprises two similar line impedance branches Z1 and two similar diagonal impedance branches Z2. It is assumed that the four-electrode crystal 5 has a lower resonance than the three-electrode crystal 6 and therefore, as pointed out above, the in ductorsL1, L1 of Fig. 1 are connected in the series-opposing relationship. Each line branch is made up of an inductance equal to (1-K1)L1 in series with a parallel combination consisting of a capacitance equal in magnitude to the sum of 2 C1, C2, C01 and C02 shunted by a branch comprising the inductance L01 in series with the capacitance C01. Each diagonal branch consists of an inductance equal to (1+K1)L1 in series with a parallel combination comprising a capacitance equal to the sum of C2, C01 and C02 shunted by an arm made up of the inductance Lcz in series with the capacitance Ccz. For the sake of clarity in this figure and also in Fig. '7 only one line branch and one diagonal branch are shown in detail, the corresponding line and diagonal branches being indicated by dotted lines connecting the appropriate terminals.

The image impedance ZK of the lattice network of Fig. 3 is given in terms of the impedances of the line and diagonal branches by the expression K l 2 and the propagation constant P may be found from the expression of the same sign, with peaks of attenuation occurring where these impedances are equal. By

- virtue of the equivalence of the two networks these expressions also give the impedance and propagation constant of the filter of Fig. 1. Due to the'series end inductances L1, L1 the filter will have an inherently low image impedance.

Fig. 4 gives the reactance-frequency characteristics of the line and diagonal branches of the lattice network of Fig. 3. Each branch will have two resonances with an intermediate antiresonance. To provide a band-pass filter the lower resonance of the one branch is made to coincide with the anti-resonance of the other branch, and the anti-resonance of the one branch is made to coincide with the upper resonance of the other. Assuming that the line branch has the lower first resonance the two branches will have the reactance characteristics shown, respectively, by the solid-line and the dotted-line curves of Fig. 4. The line branch Z1 has its resonances at the frequencies f2 and f4 and its anti-resonance at the frequency is, while the diagonal branch Z2 has its lower resonance at is, its anti-resonance at f4 and its upper resonance at ft. The transmission band will be located between the frequencies f2 and f5 and peaks of attenuation will occur at the frequency f1 below the band and the frequencies is and f1 above the band where the 'reactances are equal.

in Fig. 5. If the crystal 6 has a lower resonance and in and a resonance at I14.

than the crystal 5 the inductors L1, L1 should be connected series aiding to obtain the type of attenuation characteristic shown. If the coemcient of coupling K1 is made zero the upper attenuation peak occurring at 7 will be moved out to infinite frequency. If the end inductors are omitted entirely from the circuit the peak at f7 will disappear, leaving only the peaks at f1 and f6. These peaks may be placed both on the lower side of the band or both on the upper side if desired. However, without the end inductors the maximum band width obtainable is of the order of 0.8 per cent of the mid-band frequency.

The chief function of the capacitor C1 in the circuit of Fig. l is to permit the arbitrary location of the attenuation peaks occurring at f1 and f6. As the magnitude of C1 is increased these peaks are moved in toward the transmission band limits f2 and is. The function of the shunt capacitors C2, C2 is to decrease the width of the transmission band. The widest band is obtained when these capacitors are omitted. As their value is increased the band is narrowed.

The values of the various reactance elements in the lattice network of Fig. 3, including the electrical elements equivalent to the crystals, can be found from the resonant and anti-resonant frequencies of the Z1 and Z2 impedance branches by a direct application of R. M. Fosters reactance theorem given in the Bell System Technical Journal, vol. III, No. 2, April 1924, pages 259 to 267. The values of the component elements in the network of Fig. l are found by applying the numerical factors indicated.

If an inherently high image impedance is desired for the filter the inductors are connected in shunt at the ends of the network. In Fig. 6 the inductors L2, L2 are connected in this way and are inductively coupled with a coefiicient of coupling K2. It is assumed that the four-electrode crystal 5 has the lower resonance and therefore the inductors are connected in the series-aiding relationship. The arrangement of the .othercomponent elements is the same as in Fig. 1. The equivalent lattice network is shown in. Fig. 7. It is the same as the lattice of Fig. 3 except that the inductances (1K2)Lz and (1+Kz)L2 are in parallel with the crystal impedances instead'of in series with them, and the smallerinductance appears in the diagonal branch instead of in the line branch.

As shown by the reactance characteristics of Fig. 8 each branch of the equivalent lattice has two anti-resonances and an intermediate resonance. To provide a band pass filter the lower anti-resonance of one branch is made to coincide with the resonance of the other, and the resonance of the one branch is placed at the upper anti-resonance of the other. If the line branch Z has the lower, first anti-resonance its reactance will be as shown by the solid-line curve with anti-resonances at the frequencies In As shown by the dotted-line curve the diagonal branch Z2 will have anti-resonances at In and f16 and a resonance at ha. The frequencies fix and he mark the limits of the transmission band and attenuation peaks occur at hi and I12 below the band and. at in above the band where the reactances are equal.

Fig. 9 gives a typical attenuation characteristic. If the three-electrode crystal 6 has the lower resonance frequency the inductors are connected series opposing to obtain the type of characteristic shown. It the coemcient' of coupling K2 is zero the peak at in moves down to zero frequency. As in the circuit of Fig. 1, the function of the bridging capacitor C1 is to determine the location of the peaks at in and fll, and the function of the shunt capacitors C2, C2 is to regulate the width of the band. These capacitors may, of course, be made variable, both in the circuit of Fig. 1 and that of Fig. 6, as indicated by the arrows.

What is claimed is:

1. A wave filter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, and two piezoelectric crystals, one of said crystals having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, an electrode on one face and a diagonally opposite electrode on the opposite face of said one crystal being connected respectively to the terminals of said bridging branch, the other of said crystals having a pair of electrodes on one face and a single electrode on the opposite face, said pair of electrodes on said other crystal being also connected respectively to the terminals of said bridging branch, the remaining electrodes on said one crystal and said single electrode on said other crystal being connected to the remaining input and output terminals of said filter, and the dimensions of said crystals and the values of the reactance elements constituting said bridging branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission hand between said frequencies.

2. A wave filter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, two inductors connected at the respective ends of said filter, and two piezoelectric crystals having different frequencies of resoonance', one of said crystals having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, an electrode on one face and a diagonally opposite electrode on the opposite face of said one crystal being connected respectively to the terminals of said bridging branch, the other of said crystals having a pair of electrodes on one face and a single electrode on the opposite face, said pair of electrodes on said other crystal being also connected respectively to the terminals of said bridging branch, the remaining electrodes on said one crystal and said single electrode on said other crystal being connected to the remaining filter terminals, the impedance measured between said first-mentioned input and output terminals having a different reactance-frequency characteristic from that of the impedance measured between said first-mentioned terminals strapped together and said remaining terminals strapped together, and said two measured impedances being proportioned with respect to each other and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

3. A wave filter in accordance with claim 2 in which said inductors are connected in series at the ends of said filter.

4. A wave filter in accordance with claim 2 in which said inductors are connected in shunt at the ends of said filter.

5. A wave filter in accordance with claim 2 in which saidinductors: are inductively coupled.

6. A wave filter in accordance with claim 2 in which said inductors are inductively coupledin the series-aiding relationship.

7. A wave filter in accordance with claim 2 in which said inductors are inductively coupled in and are inductively coupled in the series-aiding relationship.

10. A wave filter in accordance with claim 2 in which said four-electrode crystal has the lower frequency of resonance and said inductors are connected in shunt at the ends of said filter and are inductively coupled in the series-aiding relationship.

11. A wave filter in accordance with claim 2 in which said three-electrode crystal has the lower frequency of resonance and said inductors are connected in. shunt at the ends of said filter and are inductively coupled in the series-opposing relationship.

12. A wave filter in accordance with claim 2 which includes two capacitors connected 1 in shunt at the ends of said crystals.

13. A wave filter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, two inductors connected in. series with said bridging branch one on either side thereof, a pair of capacitors connected between the respective terminals of said bridging branch and the remaining filter terminals, and two piezoelectric crystals having different frequencies of resonance, one ofsaid' crystals having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, an electrode on one face and a diagonally opposite electrode on the opposite face of said one crystal being connected respec[ tively to the terminals of said bridging branch, the other of said crystals having a pair of electrodes on one face and a single electrode on the opposite face, said pair of electrodes on said other crystal being also connected respectively to the terminals of said bridging branch, the remaining electrodes on said one crystal and said single electrode on said other crystal being connected to said remaining filter terminals, and

the dimensions of said crystals and the values of said inductors and capacitors being proporioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

14. A wave filter in accordance with claim 13 in which said inductors are inductively coupled.

15. A wave filter in accordance with claim 13 in which said four-electrode crystal has the lower frequency of resonance and said inductors are inductively coupled .in the series-opposing relationship.

16. A wave filter in accordance with claim 13 in which said three-electrode crystal has the lower frequency of resonance and said inductors are inductively coupled in 17. A wave filter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, two inductors connected in shunt at the ends of said filter, a pair of capacitors also connected in shunt at the ends of said filter and two piezoelectric crystals having different frequencies of resonance, one of said crystals having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, an electrode on one face and a diagonally opposite electrode on the oppothe remaining electrodes on said one crystal and said single electrode on said other crystal being connected to the remaining filter terminals, and

the dimensions of said crystals and the values of said inductors and capacitors being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

18. A wave filter in accordance with claim 17 in which said inductors are inductively coupled.

19. A wave filter in accordance with claim 17 in which said four-electrode crystal has the lower frequency of resonance and said inductors are inductively coupled in the series-aiding relationship.

20. A wave filter in accordance with claim 1'? in which said three-electrode crystal has the lower frequency of resonance and said inductors are inductively coupled in the series-opposing relationship.

21. A wave filter in accordance with claim 2 in which said inductors are connectors in series at the ends of said filter and said inductors are inductively coupled.

22. A wave filter in accordance with claim 2 in which said inductors are connected in shunt at the ends of said filter and said inductors are inductively coupled. I

WARREN P. MASON.