US 2406796 A Abstract available in Claims available in Description (OCR text may contain errors) Sept 351946o F. R. BIES l 2,406,796 WAVE FILTER Filed March 2s. 1944 2 sheets-snm 1 r Ly n (C11 l 2 /zl/ f3 vv/avro@` F. R. B/ES A TTORNE Patented Sept. 3, 1946 gaan WAVE FILTER. 'l Frank R. Bies, Springfield, N. J., assigner to Bell |Iielephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application March 23, 1944, Serial No. 527,764 17 Claims. 1 This invention relates to wave filters and more particularly to those of the impedance-transforming variety. The principal object of the invention is to provide impedance transformation in a wave filter of the lattice type. A further object is to employ piezoelectric crystal elements,V in the impedance branches of an impedance-transforming lter of the latticetype. 1 Y The wave lter in accordance with the invention comprises a lattice network andtwo inductances, one of which is connected in series at one end of the lattice and the other of which is connected in shunt lat th-e other vend. If certain design limitations are observed the impedance branches of the lattice may be constituted by piezoelectric crystals. Variable shunt capacitances may be provided at the ends of the lattice to facilitate the Iadjustment of thetransmission characteristic of the filter. The nature of the invention will be more fully understood from the following detailed description and by reference tothe accompanying drawings, in which like reference characters refer to similar or corresponding parts and in which: Fig. 1 is a schematic circuit of a wave filter in accordance with the invention; Fig. 2 shows the initial network comprising a central lattice and two three-element ladder-type end sections, from which Vthe circuit of Fig. 1 is derived; . Fig. 3 shows the combination of the right-hand ladder section and an ideal transformer; Fig. 4 is an impedance-transforming section equivalent to the combination of Fig. 3;r Fig. 5 shows the network of Fig. 2 with the right-hand ladder section replaced bythe iin pedance-transforming section of Fig. 4 to provide equal series and equal shunt capacitances external to the lattice; Fig. 6 is the network of Fig. 5 withthe external capacitances taken into the lattice; Fig. 7 is a network equivalent to the one' of Fig. 10 shows thefilter of Fig..` each shunt capacitance constituted b-y a iixed portion and. avariable portion.- Y ' are given hereinafter. `band extending between'selected frequencies, has Taking `up the figures in more detail, Fig. 1 is a schematic circuit of an impedance-transforming wave filter in accordance with the invention. The filter has two pairs of terminals I, 2 and 3, 4, either pair of which may be considered the input and the other pair the output. The network comprises a lattice having two equal series impedance branches Z11 and two equal diagonal impedance branches Z12. kFor the sake of simplicity, in Fig. 1 and also in Figs. 2, 5, 6 and 7 onlyrone series impedance branch and vone diagonal impedance branch of the lattice are shown in detail, the other branches being indicated by dashed lines between the appropriate terminals. At the right-hand end of the' lattice is a shunt inductance of value L1. At -the left-hand end there is a series inductance, alsoof value L1, which may be equally divided, as shown, and L1/2 connected in'each side of the line to provide a balanced structure. At each vend of the lattice there is a variable shunt capacitance of value CX, provided for adjusting the transmission characteristic of the filter. Each series branch Z11 of the filter is made up of a capacitance of value C12 shunted by the series-connected combination 0f an inductance of Value L11 and a capacitance of value C11. Each diagonal branch Z12 comprises a capacitance of value C14 shunted by the series-connected combination of an inductance of value L12 and a capacitance of value C13. It will be understood, of course, that in some cases the end shunt capacitances CX may be incorporated in the lattice by increasing the value of each of the capacitances C12 and C14 by an amount equal to CX. Formulas for evaluating the various elements of the filter The filter transmits a peaks of attenuation only at Zero frequency and at infinite frequency and provides an impedance step-up'from left to right which at the mid-band frequency is equal to the ratio R2 to R1. The derivation of the filter of'Fig, 1 will now be taken up. Fig. 2 shows schematically the initial network, comprising a central lattice section 5 with ladder-type half sections 5 and 1 connected one at each end. The latticer has the same configuration as the lattice in Fig. 1 but will have different element values, as indicated by the use of the different subscripts. It has a transmission band extending between a lower cut-off frequency f2 and an upper cut-ofi frequency f3 andr an image impedance R4 at the mid-band frequency fm, which is the geometric mean of f2, and f3. For the case where peaks of attenuation occur onlyat zero and innite frequency, which is the one most frequently used, the values of the component reactance elements may be found from the following formulas: The capacitances are given in farads and the inductances in henries. The proper value to use for R4 is derived hereinafter and is given by Equation 27. Each of the end ladder half sections 6 and 'l transmits a band extending betweena lower cutoff frequency f1 and an upper cut-off frequency f4, with the same mid-band frequencyvfm as the lattice 5. The band may be of the same width as that of the lattice or it may be Wider, as explained below. The section 6 to the left is of the type designated III1 in Fig. 168B on page 316 of Sheas Transmission Networks and Wave Filters, published by D. Van Nostrand Company. The series impedance branch comprises an inductance'Lr and a capacitance C1 connected in series andthe shunt impedance branch consists of a capacitance C2. designated III4 byV Shea in the above reference. The series impedance branch is a capacitance CA and the shunt impedance branch comprises a capacitance CB and an inductance LB connected in parallel, These elements may be evaluated from the following formulas: where R1 is the mid-series image impedanceY at mid-band for the section 6 and R2 is the midshunt image impedance at mid-band for the section 1. Each of these half sections 6 and 1 introduces an impedance transformation which, in terms of the cut-off frequencies f1 and f4, may be expressed as where R3 is the mid-shunt image impedance at mid-band for the section 6 and R5 is the midseries image impedance at mid-band for the. secr.. tion 1. The mid-shunt image impedance of the section 6, and the mid-series image impedancel of the section 1, which face each other, will match perfectly throughout the band, and alsowill VThe section 1 to the 4right is of the type match the image impedance of the lattice 5, if the impedance levels are properly chosen. In accordance with the invention it is desired that the lattice 5 have at its right end a shunt capacitance equal to the capacitance C2 shunting the left terminals 8, 9 and a series capacitance equal to the capacitance C1 at the left, in order that .these external capacitances may be taken into the lattice 5 either in Whole or in part. In order to accomplish this an ideal transformer T is inserted between the capacitance CA and the vterminals I0, Il of the lattice 5, as shown in Fig. 3,V giving a new mid-band image impedance equal to The network ofv Fig. 3 is now transformed into the equivalent network I2 shown in Fig. 4 by replacing the transformer T and the capacitance CA by the equivalent 1r comprising the shunt capacitance C2, the series capacitance C1 and the shunt capacitance CY which have the values where 11 is the square root of the impedance transformation ratiofrom right to left in the transformer T. In this connection reference is made to the United States patents to E. L. Norton 1,681,554, issued August 21, 1928, and 1,708,950, issued April 16, 1929. From Equations 12 and 13 i is found, in terms of C102, to be Substituting in Equation 15 the values of C1 and C2 from Equations 5 and 6 gives li in terms of the cut-off frequencies f1 and f4 as The next step is to determine R2 in terms of R1, f1 and f4. This may be done by substituting in Equation 12 the Values of C1, CA and as given respectively by Equations 5, 8 and 16. The re sult is R1f1f4 R2 (f4-fw (17) Now, by substituting this value of R2 in Equation 9, CB is found to have the value frfl C19-27mm! (18) But from Equation 14, by the aid of Equations 5, 12 and 16, it is found that zffR, (19) It is seen from Equations 1,8 and 19 that the sum of CB and CY is zero. These capacitances may, therefore, be omitted from the network I2. From Equations 10 and 17 it is found that R3 at the left end and Re at the right end. These Will be found in terms'of R1 and the cut-oir frequencies f1 andV f4. We know that But from Equation 1,1 Y 122)4 V Y R5-f1-Ff4 Now from Equation 21, using Equations 16, 17 and` 22 From Equation V11 Faofa (24) Dividing Equation 23 by Equation 24 gives @nu R374 (25) If the end sections 6 and I2 have a comparatively narrow band (f4-f1) the impedances R3 and Rs will not differ much from each other. if the image impedance R4 of the lattice 5 is taken as the geometric mean of the impedances R3 and Rs the lattice 5 will be terminated substantially n in its image impedance and the reflection losses at the junctions 8, 9 and I0, ll will be negligible. The value of R4is, therefore, taken as RF1/12T@ (26) and by the am of Equationszs and 24 1410111111 to be This value of R4 is used in Equations 1, 2, 3 and 4 to evaluate the component elements of the lattice 5. From Equation 1'7 the over-all impedance stepup of the filter at the mid-band frequency is Since the mid-band frequency fm does not change, it is apparent that the impedance ratio is inversely proportional to the square of the band` width (f4-f1) of the end sections. The Width of 53 the band may, therefore,`be chosen to correspond to the desired impedance ratio. For exam-ple, a ve per cent band will give a ratio of 400 and a two per cent band a ratio of 2500. In some cases it may be desirable to make the band oi the end sections wider than that of the lattice in order to get a more suitable image impedance outside of the band. This is of importance where two or more filters are to be operated in parallel. However, as the band width of the end sections is 'l o :c 021012 (zo) l 13 (C11-02+ C21) (01+ 02+C21+04 In Fig. 7 the elements C11, C13, L1, L11 and L12 are thev same as the ones shown in Fig. 1. The capacitances C41 and C42 will be the same as C12 and C14 if the end capacitances Cx are zero. However, it is sometimes desirable to have variable shunt capacitances such as Cx available to adjust the transmission characteristic of the illter.r They may be provided by reducing the value of C41 and C42 each by an amount equal to CX and connecting Cx at the ends, as shown in Fig. 1. It is seen that each of the lattice branches Z41 and Z42 of Fig. 7 has the configuration of the Yequivalent circuit of a piezoelectric lcrystal element. If the ratio of the capacitances in these branches does not exceed a certain Value K, that is, if snag, the branches may be constituted by crystals. Fig. 8 shows the branches Z41 and 242 replaced, re- vspectively,` by the crystal elements -X1.and X2. The series inductance L1 is also divided, as in Fig. 1. For quartz crystals K has a Value of approximately k140. The limitation expressed in Equation 33 also placesl a limit on the maximum band width of the end sections 6 and 1 which, in terms ofthe mid-band frequency ,fm and the band I fir-f1: fm f1+f4 K (f3-f2)- lf K is taken as iI it is found from Equation 34 that for a two per cent band for the lattice the maximum band for the end sections will be approximately seventy-six per cent and for a six per cent band for the lattice this maximum band for the end sections will be approximately twentyiive per cent. For approximately a twelve per cent band for the lattice the maximum band for the end sections will just equal theband of the lattice. Therefore, if quartz crystals are used the maximum band that can be transmitted 4by the filter as a whole is twelve per cent. If the lattice section is designed to have a wider band than this the band of the end sections will be narrower and thus limit the over-all band. Of course, if a type of crystal having a smaller value of K is used the maximum band of the end sections and the maximum band for the filter as a whole are correspondingly increased. It is assumed that the filter of Fig. 8 has the maximum possible band width and therefore no shunt capacitances, such as Cx in Fig. 1, are required. However, if the lter has a band width less than maximum additional shunt capacitances are required. These may be added in shunt at the ends of the network as the capacitances Cx in Fig. 9 and may be made variable, as indicated, for adjustment. The crystals X1 and X2 of Fig.,8 will, of course, have to be replaced by slightly different crystals X3 and X4. The lter shown in Fig. 10 is the same as the one of Fig. 9 except that each of the end capacitances Cx is replaced by two capacitances Cv and Cw of such value that One of these capacitances, for example Cv, is made variable for adjusting the filter. This circuit may be used Where it is inconvenient to make the entire capacitance CX variable, as is done in Fig. 9. What is claimed is: 1. An impedance-transforming wave lter comprising a lattice networkand two ind'uctances of equal value, one of said inductances being connected in series at one end of said lattice and the other of said inductances being connected in shunt at the other end of said lattice. 2. A wave filter in accordance withclaim 1 in which said lattice is symmetrical. 3. A wave lter in accordance with claim 1 having a band Width which is small compared to the mid-band frequency. 4. A wave filter in accordance with claim 1 in which the impedance branches of said lattice comprise piezoelectric crystal elements. 5. A wave filter in accordance with claim 1 which has peaks of attenuation only at zero and infinite frequency. 6. A wave filter in accordance with claim 1 which has peaks of attenuation only at Zero and infinite frequency and a band Width which is small compared to the mid-band frequency. '7. A Wave lter in accordance with claim 1 in which said lattice is symmetrical and the band Width is small compared to the mid-band frequency. v 8. An impedance-transforming wave lter comprising two pairs of piezoelectric crystal elements and two inductances of equal value, said crystal elements being arranged to form a lattice net- Work, one of saidinductances beingV connected in series .at one end of said lattice network and the other of said inductancesbeing connected in shunt at the other end of said lattice network. 9. A wave filter in accordance with claim 8 having a band width which is small compared to the mid-band frequency. 10. A Wave filter in accordance with claim 8 which has peaks of attenuation only at zero and infinite frequency. 11. A wave filter in accordance with claim 8 which has peaks of attenuation only at Zero and infinite frequency and a band width which is small compared to the mid-band frequency. 12. An impedance-transforming Wave filter comprising a lattice network, two inductances, and two' variable capacitances, one of said inductances being connected in series at one end of said lattice, the other of said inductances being connected in shunt at the other end of said lattice, and said capacitances being connected in shunt at the respective ends of said lattice. 13. A wave lter in accordance with claim 12 in which said lattice is symmetrical. 14. A wave lter in accordance with claim 12 having a band width which is small compared to the mid-band frequency. 15. A wave filter in accordance with claim 12 in which said inductances are equal. 16. A Wave filter in accordance with claim 12 in which the impedance branches of said lattice comprise piezoelectric crystal elements. 17. A wave filter in accordance with claim 12 which has peaks of attenuation only at zero and infinite frequency. FRANK R. BIES. Referenced by
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