US1974081A - Piezo-electric wave filter - Google Patents

Description

. P w. P. MASON 1,974,081

PIEZO ELECTRIC WAVE FILTER Filed March 28, 1933 2 Sheets-Sheet 1 FIG. 2

FIG. 3

II I l' I l FIG. 4 U I a I E0 u I FREQUENCY :5 I t I I I I I I l I 'l l FIG. 5

F IG. 6

c c INVENTOR M! MASON A TTORNEV Sept. 1 8, 1934. w, v so 1,974,081

PIEZO ELECTRIC WAVE FILTER Filed March 28, 1933 2 Sheets-Sheet 2 INVE NTOR W P MASON ATTORNEY Patented Sept. 18, 1934 mmsms l 1 i 1,37 i',081

ris'zo nriic r n c Ways .rnxrisrz' This invention relates to broad band wave filters in which piezoeelectric crystals are .used as":

impedance elements and has for itsmprincipal object'to extend the range of transmissionzchar- 5 acteri'sti'cs'that can be obtained with filters of this type. Another object is to reduce the niimber of crystals required for a desired selectivity;

The electrical impedance of a quartz piezoelectric crystal, as is well known, is characterized Ma resonance and an antieresonance at frequencies very close to each other andby 'a high capacitive reactance elsewhere. This characteristic makes" it difiicult to combine crystals in a filter circuit to. obtain .a reasonably :wide transmission band and at the same time toprovide a high attenuation level outside the band. The problem is discussed' in my earlier application, SerialNo/653522 filed January 26, 1933, where-' in one arrangement is described for obtaining relatively wide transmission bands by combining crystal of] the filter." With this arrangement, band widths'as 'greatas' 14 percent of the mean 2 frequency .are obtainable without sacrifice of the further extension of the bandwidth consistent with a high attenuation levelis made possible L31; and a capacity C31.

by theuse of inductances connectedbothin series with and in shunt toeach' crystal of a filter. Two

separate inductances may be associatedwitheach crystal but in the preferred formsot .theinven tion the inductances are arranged to tormjrans formers through which the crystals 'areicoupled. to the ,filteribranches This arrangement has the advantage that in .manyfcases the transformer ratios may be adjusted'to permit th'e'us'e of more practical crystal dimensions than would obtain with directly connected crystals. In one form of the inventionthe same crystal is coupled simultaneously into two branches of the filter network by means of a special transformer, there'- by reducing the niunber ofcrystals required to a 4 minimum.

As the number of inductance elements asso-I ciated with the crystals of a filter is increased the v the'line branches, obtained: by substituting the effects of energy dissipation in the coil resistances become more important and the advantagesarising from'the substantially dissipationless character of the piezo-electric crystal tend-te disappear. In the circuits of the'inve'ntion the re.-

sistance of one of the added inductancesin each capacity. C21. The other elements are designated-;

ofthezother. partially compensated so, thatzthej to correspond. to Fig.1.. Since the electrical 5 branch can be completely compensated and that ductance L32 and capacity C32.

bination iL, 9G,. representing the-piezo-,elec.tric7r 'p'acity C.

ifilterselectivity is substantially' that of ads tsipationless network;

The invention will be more fully understood' 'from the following detailed :description'of repr e-r sentative circuits and from the appendedzdrawes ings, of which:

Fig. 1 shows in schematic form oneembodimentg;

of the invention; 1

Figs. 2 to 6, inclusive, are'diagrams explanatory of the invention;

of the filter of Fig. 1;

Fig. 7 shows a preferred form Fig. 8 is explanatory of the filter of Fig. 7';

Fig. 9 shows amodified form :of'the network of.

Fig. 7, and

Figs. 10 to 12, inclusive, show additional err.-

amples of filters in accordance with the invention.

impedancesconnected betweeninput terminals 1,;-

an inductance in series or, in shunt-with 'ea c'h' Y 2, and-'output- terminals 3, 4;; In" this .andfin subsequent figures only one :line impedance and";

one lattice impedance is shown invdetail for the i sake ofz'clarity, the other corresponding branches attenuation level at frequencies remote 'from 'the v having identical elements.

"each comp-rise a piezo-electric crystal X1 shunted In accordance with the presentinvention] by a small capacity C21, preferably an adjustable The line 'impedances.

The lattice impedances; are of similar construction comprisinga-crystal X2 shunted byan inductance Lzz'and a capacity" C22 and-including the series combination, of in- The'lcrystals are preferably of quartz, :cut'and; mounted in the rnanne'r described in my-eaflier: co-pending application, Seria11No...65'3,622 'filed impedances correspond accurately to that of the electrical system of Fig Thisequivalent electrical impedance comprises a series resonant com- January 26, -1933,'in which'case theirelectricalaf;

prop'ertiesxof, the crystal, shunted by a capacity Co, repr'esentingtheelectrode capacity; which has a minimum value. of about 125 times the. c-a-j The complete electrical equivalent of one of" impedance. of Fig. 2 for the crystal; is ShOWIlmv in Fig. 3 inwhich the'combination' L11, C11, rep

electrodecapacity plus the external shunting resonant.

equivalent contains six elements its reactance will be characterized by five critical frequencies of finite values, that is, there will be five frequencies at which the impedance is resonant or anti- The variation of the reactance with frequently is illustrated by curve 10 of Fig. 4, the critical frequencies being designated ii to is in ascending order. The reactance of the lattice branches of Fig. 1 will have a similar frequency characteristic with the same number of critical frequencies.

The general rules for the proportioning of impedances in a symmetrical lattice with respect to each other to provide desirable transmission characteristics are described in U. S. Patent 1,828,454 issued October 20, 1931 to H. W. Bode and their application to piezo-electric crystal filters is discussed in my above mentioned co-pending application. In accordance with these principles one way of proportioning the lattice reactances in Fig. 1 is illustrated by curve 11 of Fig. 4, which shows the lattice branch reactance characteristic, the critical frequencies being allocated with respect to those of the line branch reactance' to provide a single transmission band. In this arrangement the lattice branch has resonances coinciding with the anti-resonances of the line branch at frequencies f2 and f4 and antiresonances coinciding with is and f5. The highest -:resonance occurs at an additional frequency f6 and the transmission band extends from ii to is.

In my above mentioned co-pending application it is pointed out that in filters of simpler structure it is desirable that the several critical frequencies should form a geometric series or should approximate thereto, this type of spacing permitting the attenuation to be maintained high'at frequencies outside the band. The same rule is applicable to the present types of filter, abut in many cases it is preferable to modify the distribution of the frequencies somewhat particularly in the direction of spacing them closer together towards the edge of the band. For the case in. which the critical frequencies form a. geometric series the proportioning of the impedances is simple. Considering the structure of Fig. 3, the inductance L21 should be made to resonate with the capacity Czi at the crystal resonance frequency. The combination of the crystal. and the shunt inductance will then have a reactance characteristic of the type represented by curve 12 of Fig. 5. This curve exhibits a resonance at frequency is, which is the crystal resonance, and two anti-resonances f2 and I4 spaced geometrically above and below is. The separation between the anti-resonance frequencies is determined by the ratio of the capacities C11 and Czi and is given by the formula If the additional elements L31 and C31 are adjusted to resonate also at frequencyfa their reactance will have a frequency characteristic of the type illustrated by curve 13 of Fig. 5/ It is clear that the addition of such a reactancewill not disturb the resonance at frequency is or the anti-resonances at f2 and f4, but will simply introduce additional resonances above and be- 1O Wf2 and f4, which, due to the symmetry of the circuit will likewise'be spaced geometrically about the frequency is. The proportioning of the crystal and shunt inductance combination thus determines three of the critical frequencies of the total impedance and also the ratio of the successive frequencies. To make the additional critical frequencies fall into the series, I find that the capacity C31 of the added resonant circuit should be given the value C 31= ll( +2 73 and the inductance L31 proportioned accordingly.

Since the ratio of Cu to 0'21 determines the separation of the frequencies f4 and f2 it follows that, in the case described, the total band is controlled by this ratio. For crystals of the preferred type the electrode capacity has a minimum value about 125 times the piezo-electric capacity, corresponding to a value of the frequency interval 14-12 equal to 9 per cent of is for the case where the frequencies are in a geometric series. The addition of the external shunt capacity C21 permits the reduction of this interval as much as may be desired, thus making possible a band width range from about zero to 25 per cent of the mean band frequency. I

In the more general case in which the critical frequencies do not lie in a geometric series the computation of the elements may be carried on as follows:

The impedance, Z1, of the line branches may be expressed in terms of L31 and the critical frequencies as r and the impedance Z2 of the lattice branches as in which w denotes 211' times frequency.

By thedirect application of Fosters reactance theorem, described in the Bell System Technical Journal Vol. III, No. 2, April 1924, page 259, the

elements of an impedance of the type shown in.

Fig. 6 may be calculated from the expression for Z1 and a corresponding impedance for Z2. impedance shown in Fig. 6, while equivalent electrically to the filter line branch impedance is different from it structurally since it contains,

two series connected anti-resonant combinations The.

LaCa and LbCb instead of the inductance shunted.

and to have a value Km at the mean frequency of the band given by a If L31 is made equal to Liz the common value is determined by Equation 6.

For the case in which the critical frequencies form a geometric series it will be noted thatthe external capacity C31 of the line branch is approximately'three times the piezo-electric capacity of the crystal.

is inconveniently small and the inductance L31 is inconveniently great. Alternativelygif C311 and k Since the latter is frequently verysinall it may be found that the capacity C31 which vary through a wide range of values, reach- L31 are proportioned to'give desirable values of the characteristic impedance it may be found that the crystal capacities are such that can-be obtained only With excessively thin crystals. These difficulties are avoided in a modified form of the invention illustrated in Fig. '7 in which the crystals are coupled to the lattice branches through step-down transformers. 1

The line branches in the filter of Fig. "I each comprise a capacity C31 in' series with an inductance Lpl to which is coupled a'secondary inductance LS1; Across the terminals of this in ductance are connected the piezo-electric crystal X1 and the band controlling shunt capacity C21. The lattice branches are similar in structure comprising series capacity C32 inductance L132 and a secondary system made up of inductance L52, crystal X2 and capacity C2.

The branches of this filter differ structurall from those of the filter of Fig. 3, but, since they contain the same number of elements and since their reactances'at zero and infinite frequencies are the same asfor the branches of Fig/.3, the two filters are potentially equivalent. By known methods the line branch impedance of the filter of Fig. '7 may be transformed to the type shown in Fig. 8, which comprises the capacity C31, un-. changed in value, a series inductance of value (Lpl- Lsl), and the. parallel combination of an inductance L5 a capacity C21+ and a crystal of impedance ZX1, where Zxl is the impedance of crystal X1. The factor appearing in these values is an impedance transformation ratio having the value where M1 is the mutual inductance between inductances L 11 and LS1. The resistances of the inductance coils are shown in Fig. 8, the resistance r 11 being that of inductance Lpl and the resistance 1'51 being that of inductance L51. The latter appears in series with the crystal and its shunt capacity, its value being modified in accordance with the transformation ratio.

Since the impedance shown in Fig. 8 corresponds, except for the location of the resistances, to the branch impedance of Fig. 1 it follows that the design procedures outlined above in connection with that figure can be applied to the circuit of Fig. 8 and hence to the filter of Fig. 7. The impedance ratio may evidently be made as small as may be desired by properly proportioning the coupling between the inductances. The effec tive impedance of the crystal may thus be brought to any desired value; so permitting the capacity C31 and its associated inductance (Lp1 Lsl) to be kept within practical values.

The effects of the coil resistances may now be considered. The resistances of the series coils Lpl and Lpz may be made equal in which case their effects balance each other so that the selectivity of the filter is not disturbed. Equal series resistances in the four branches of a symmetrical lattice have the same effect as a resistance of the same value added in series external to the lattice at each end. That is, the effect is simply that which would arise from a slight change in the resistances of the impedances between which the lattice is connected. The secondary coil resistances cannot be made to balance each other completely but they do so partially. Since they appear in the branch impedances as part of an anti-resonant loop circuit they will produce effective series resistances ing maximum values. at the anti-resonance frequencies of the impedance.

'To maintain the sharpness of selectivity characteristio of dissipationless structures it is desirable principally that the effective resistance should be negligibly small at the cut-off frequencies and at frequencies in theattenuation range close thereto. In the filters of the types described above two factors help towards the realization of this condition. The first is that the anti-resonance frequencies lie within the band some distance from the cut-off frequencies so that the effective resistance at the cut-off frequencies tends to be fairly small-and diminishes in the attenuation ranges. The second factor lies in the proportions of branch impedances due to inherent relationships of the effective capacities of the crystals which have .a minimum ratio of about 125., In connectionwith the filter of Fig. 1 it was'pointed out that for geometric spacing of the critical frequencies the series capacities C31 and C32 have valuesaboutB times the piezoelec+ tric capacity of the crystal. .Since the series inductances Lz1-and L32 are, proportioned to resonate with these capacities at, the crystal resonance and since theshunt inductances L21 and L22 are proportioned to resonate with the total shunt capacities of the crystals at the same frequency, it follows that. the series inductancesmust be at leastAO times as great as the shunt inductances. This relationship is, of course, accurate only for the case of the geometric arrangement of the critical frequencies, but it holds substantially for most practical filter designs. The effective resistances due to, the dissipation in the low inductance shunt coils therefore appear in series with the very large reactances of the series coils and condensers which representqthe dominant part of the total impedance outside the band. The effect of the shunt coil dissipation thus becomes negligibly small at frequencies. quite close to the cut-off. From experiment and calculation I have found that the unbalanced effective resistance corresponds to less than 20 per cent of the series coil resistance. Since similar relationships are involved in the filter of Fig. 7 the effects there are of like character and magnitude.

A modified form of the filter of Fig. '7 is shown schematically in Fig. 9, the feature of this network being that instead of having a separate crystal for each arm of the lattice only two crystals are used one of which is coupled by a double primary transformer to the two line branches, and the other of which is similarly coupled to the two lattice branches. The designation of the elements in Fig. 9 corresponds to the designations in Fig. 7. This circuit has the advantage that, besides reducing the number of crystals by half, the necessity for balancing the line and the lattice arms to secure symmetry is largely eliminated.

Additional examples of filter networks in accordance with the invention which are obtained by changing the location of the external capacities are illustrated by Figs. 10, 11 and 12, the elements being designated to correspond to Fig. '7. The filter of Fig. 10 is a band pass filter in which the primary coils are tuned by means of shunt condensers rather than series condensers. Fig. 11 represents a low pass filter obtained by omitting the series condensers from the line branches of the network of Fig. '7. Fig. 12 illustrates a high pass filter obtained by omitting the shunt tuning condensers from the line branches of the filter of Fig. 10. The capacities in shunt to the crystals are not shown in these figures, but it will be understood that such capacities may be employed as desired. It will be evident also that these networks may be modified in accordance with Fig. 9 to reduce the number of crystals.

What is claimed is: l

1. A broad band wave filter comprising a plurality of impedance branches interconnecting a pair of input terminals and a pair of output terminals, said branches having reactances ofdiverse frequency characteristics proportioned'with respect to each other to provide a single transmission band, each of said branches including a piezo-electric crystal, an inductance in parallel with said crystal, and a second inductance contributing a reactance. effectively in series with said parallel combination.

2. A broad band wave filter comprising a plurality of impedance branches interconnecting a pair of input terminals and a pair of output terminals, said; branches having reactances of diverse frequency characteristics proportioned with respect to each other to provide a single transmission band, each of said branches including a primary inductance, a secondary inductance coupled thereto and a piezo-electric crystal con.- nected in parallel with said secondary inductance.

3. A broad band wave filter comprising two pairs of similar impedance branches connected between input terminals and output terminals to form a symmetrical lattice network, a primary inductance included in each of said branches, secondary inductances coupled to said primary inductances, and a piezo-electric crystal connected across the terminals of each of said secondary inductances, the impedances of said crystals cooperating with the reactances of said inductances to provide a continuous transmission band.

4. A wave filterin accordance with claim 3, in

which the primary inductances are coupled in pairs to singlesecondary inductances. I 5. A broad-band wave filter comprising a plurality of impedance branches interconnecting a pair of input terminals and a pair of output terrality of impedance branches similar in pairs connected between input terminals and output terminals to form a symmetrical lattice, a primary inductance and a tuning condenser. therefor included in each branch, secondary inductances coupled to said primary inductance, and a piezoelectric crystal connected across the terminals of each of said secondary inductances, the im-, pedances of said crystals co-operating withthe reacta'nces of saidinductanes and said tuning condensers to provide acontinuous transmission band. V f

'7. A wave. filter in accordance with claim 6 in which the said tuning condensersare connected in series with the said primary inductances.

8. A Wave filter in accordance with claim 6 in which the said tuning condensers are connected in parallel with the said primary inductances.

WARREN P; MASON.

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