US2081861A - Band-pass filter - Google Patents

Description

May 25, 1937. H. AIWHEELER BAND PASS FILTER Filed June 10, 1935 2 Sheets-Sheet 1 5144 0 P4615 F/L TEE BAA/D P mm INVENTOR.

42040 A. WHEEL 5/2 ATTORNEY.

May 25, 1937. H. A. WHEELER BAND PASS FILTER 2 Sheets-SheetB Filed June 10, 1935 m 2 X f F f2 y E E of,

I INVENTOR.

ATTORNEY.

30 comes difiicult, if not impossible, to design a ouencies having a ratio on the order of 40 to 1.

Patented May 25, 1937 PATENT- OFFICE 2,081,861 BAND-PASS FILTER Harold A. Wheeler, Great Neck, N. Y., assignor to Hazeltine Corporation, a corporation of Dela ware Application June 10, 1935, Serial No. 25,737

16 Claims.

My inventionrelates to band-pass filters and more particularly to composite filters including a plurality of separate band-pass filters cooperating to pass a more extended band than any of the filters individually.

While my invention is of general application, it is especially suitable for coupling portions of an antenna system of a radio-frequency signaling system adapted to receive or transmit a wide band, or a plurality of bands, of the radiofrequency spectrum.

In many installations, particularly in radiofrequency receiving and transmitting circuits, it is desired to pass a wide band of frequencies, or selectively to pass any of .a plurality of frequency bands aggregating a wide portion of the radio-frequency spectrum. For example, such awide frequency band may be bounded by' fre- However, certain difliculties are presented in the design of a band-pass filter operating between extreme frequency limits, both as to the complexity or number of filter elements required and theactual circuit design, and as to the procurement of reasonably uniform responsiveness over the band. More-particularly in the case of a wide band filter which must include a transformer to separate the input and output circuits or to match their respective impedances, it besingle transformer capable of passing such a wide band of frequencies, for such a transformer would require a coeflicient of coupling very near unity. In other words, agiven coeflicient of coupling in a transformer places a limit on the ratio of the boundary frequencies of. the band which can be passed by a filter utilizing the transformer. It is an object of my invention, therefore, to provide a composite band-pass filter capable of passing a wide band of frequencies, which will overcome the above-mentioned difficulties of the arrangements of the prior art, and which will require a minimumof circuit elements.

More specifically, it is an object of my invention to provide a composite band-pass filter capable of covering a wide band of frequencies and including a plurality of band-pass filters each having a transformer section and designed individually to pass a plurality of frequency bands separated by intervening frequency bands, the co-operating filters being proportioned and poled so as to pass a resultant continuous band comprising the pass bands and the intervening bands.

In accordance with my invention, there are provided two or more constant-k derived bandpass filters each comprising at least two bandpass half-sections of any of several suitable types and including a transformer section, said filters being of similar type and termination and being similarly connected to common terminal circuits. Both terminal sections of each individual filter are of such type and are so proportioned that correspondin terminal sections of all the filters may bev directly interconnected I both at the input end and at the output'end of 'the'resultant network. The several filters-are designed individually to pass a plurality of bands separated by intervening bands and to co'-operate in passing the frequencies of the intervening bands, resulting in an image impedance characteristic similar to that of a single constant-k continuous-band filter passing the extended frequency range.

In the drawings, Fig. 1 is a schematic diagram of a complete antenna system including a composite band-pass filter employing my invention; Figs. 2 and 3 are approximately equivalent simplified'circuit diagrams of the system of Fig. 1 when operating in the short wave and long wave bands, respectively; Figs. 4a4b are circuit diagrams illustrating the circuit transformations in developing the high-frequency filter component; Figs. 5a5'b are corresponding diagrams for the low-frequency component of the filter of Fig. 1; Fig. 6 is a composite equivalent circuit diagram of the networks of Figs. 4 and 5; Fig. 7a is a graph representing the individual image impedance characteristics of the filters of Figs. 4b and 5b; 'while Fig. 7b is a graph of the image impedance characteristic of the composite filter of Fi 6.

Referring now more particularly to Fig. "1, there is shown schematically a wave-signalcollecting system to which my invention is particularly suitable and in which it is embodied as a composite filter for coupling a transmission line from the antenna to a signal' translating or load device, such as a' radio receiver. The general system of Fig. 1 is disclosed and claimed in my copending application Serial No. 25,735, filed June 10,. 1935, and patented December 15, 1936 as U. S. Patent No. 2,064,774 so that a detailed description thereof is considered unnecessary.

In: general, the system includes an antenna l lla-'i0b,-preferably designed as a doublet for band to be covered, and for operation as a simple, fiat-top antenna over the low-frequency portion of the band. The antenna l0al0bis by means of a composite filter l3 designed in accordance with my present invention. The composite filter I3 is designed and proportioned to pass an extended band of frequencies, for example, from 0.5 to megacycles. It is desired that the composite filter l3 shall approximately match the constant image impedance of the line [2 with the impedance l5 of the input circuit of the load device M. It is also desirable that the composite filter shall include transformer sections which avoid direct connections between the primary and secondary circuitsof the filter and permit impedance transformation, since, .in general, the image impedance of the line will have a value different from thatof the load device l4.

The composite filter l3 comprises a'plurality of filters of similar type and termination, similarly connected between common terminal circuits and designed individually to pass certain frequency bands spaced by intervening frequency bands. While my invention is applicable to a composite filter in which the boundary frequencies defining the individual pass bands and in tervening bands are related in any predetermined manner, it is particularly useful in such a composite filter in which the boundary frequencies are related approximately in an arithmetic or geometric progression; that is, the width of each of the intervening bands is the arithmetic or geometric mean of the adjacent bands. When the arithmetic relationship between the boundary frequencies obtains, the resultant filter is characterized 'by very nearly equal velocities of propagation for all frequencies within the aggregate band, which is the condition for minimum distortion of a complex wave. For the purposes of explanation and calculation it will be assumed that the complete frequency band, for example, 0.5-20 megacycles, is divided into three hands by the boundary frequencies f1, f2, f3, and f4 having values, respectively, of 0.5, 1.7, 5.8 and 20 megacycles, these frequencies being related approximately in a geometric progression in which the mean constant of progression, which is also the ratio of the upper to the lower boundary frequency of each band, is 3.4. In fact, in order fully to utilize the advantages of my invention, it is desirable that each component band shall be relatively wide, that is, that the ratio of its upper to its lower boundary frequencies shall be substantially greater than unity-in the example given. having an average value of 3.4, as stated above. v

It has become common practice in the design of band-pass filters to base the design on afilter section of a standard type. preliminary computations, an arbitrary value may be assumed for the nominal inputand output image impedances. A type is generally cho For the purpose of" v 2,081,861 operation in the high-frequency portion of the sen the input and output impedance characteristics of which are similar and have the same nominal value, which is the value at the frequency for which the slope of the image impedance curve is zero. This nominal value is indicated by the symbol R which may be assumed to be 100 ohms.

for the purposes of preliminary computation. A particular filter section found to meet the requirements of this invention is shown in Fig.4a and referred to hereinafter as type A. (For a more complete description of the several types of symmetrical band-pass filter sections suitable for use in the preferred embodiment of this invention and discussed herein, reference is made to a textbook of T. E. Shea-Transmission Networks and Wave Filters, D. Van Nostrand Co., 1929). The type A filter section is referred to at page 316 of the Shea reference as of the type 1113, which, it will be noted, is a-constant-k derived type having a. mid-shunt-image impedance similar to that of'the basic constant-k type.

The type A filter section of Fig. 4a com-prises a mid-shunt condenser I6 and inductance H, a full-series inductance l8 and a mid-shunt condenser I9 and inductance 9. Such a half-section permits the insertion of a transformer, since it includes both series and parallel inductances circuit reactances maythen be computed, in'

terms of R and the boundary frequencies of the band which the section is to pass, either from the formulas given by Shea on page 316 or by such formulas modified for a single section with mid-shunt termination, such as the type A section, as given in the appended table for Fig. 4a, type A.

By the use of well-known equivalent-circuit transformations, section A of Fig. 411. can be converted into the section illustrated in Fig. 4b, hereinafter referred to as a type B section. In this transformation the inductances I1, [8 and 9 are converted into the equivalent inductances 2| and 23 and mutual inductance therebetween, these inductances constituting primary and secondary windings of a transformer. In the computation of the values of the circuit elements of the section B, however, it is necessary to multiply all the reactances of the primary circuit of this section by the ratio of the image impedance R1. of the line 12 to the assumed image impedance R of the filter section of Fig. 4a. Similarly, in order to match the secondary circuit of the section B to the input impedance l5, it is necessary to multiply the several reactances of the secondary circuit by the ratio of the impedance RA of the curve X of Fig. 70, from which it is seen that 4 the minimum image impedance is equal to the image impedance Rx, of the line l2. The characteristics'of the filter section B are-the same respective filter sections both have substantially on the secondary side except that the .actual values are modified to match the impedance RA of the input circuit l5. This curve has the shape of the well-known constant-k mid-shunt image impedance curve, and may therefore be so designated. v The component band-pass filter for operation over the low-frequency band f1fz, for example, 0.5 to 1.7 megacycles, may be similar to that described, as modified for the different boundary frequencies. The theory of design of the lowband filter is the same as that of the-high-band filter described above. Referring to Fig. a, the

' starting point is again a filter section of type A having a constant-k image impedance of nominal value R, say 100 ohms. The section A of Fig, 5a comprises a mid-shunt condenser 24 and inductance 25, a full-series inductance 26, and a midshunt condenser 21 and inductance 23. The fortransformed. There results a type B filter section comprising a primary condenser 29 and inductance 30 and a secondary condenser 3| and inductance 32. circuit transformation the primary and secondary reactances are multiplied by the ratios RL/R and RA/R, respectively. The formulas for the circuit constants of the type B section of Fig. 5b, including the circuit transformations and the factors for matching the primary and secondary impedances, are given in the appended table for Fig. 5b, type B.

The image impedance characteristic of the primary circuit of the filter section of Fig. 5b is represented by the curve Y of Fig. 7a, from which it is seen that the minimum image impedance is equal to the image impedance R1. of the line l2. As in the case of the high-band filter, the characteristics of the filter section are the same on the secondary side, but the actual values are modified to match the impedance RA of the input circuit I5;

Curve Y, like curve X, is a constant-k mid-shunt image impedance curve.

The high-band and low-band filter sections of Figs. 4b and 5b may be combined into the composite filter section of Fig. 6, hereinafter-referred to as type C, in which both the primary and secondary circuits are similarly connected individually between common terminal circuits, By the term similarly connected" is meant that both filters are connected to each terminal circuit with being connected in series.

the same polarity and that the circuits of both filters on both the primary and secondary sides are similarly related to each other, in this case In addition, the in ductance 2| of the primary circuit is split into two sections Ma and Mom order to maintain the- 'balance of the line i2. .type shown in Figs. 4b and 5b having character- Two band filters of the These for- In this case, also, in effecting the infinite values at the cut-off frequencies 12 and fa bounding the intervening band. This relationship enables the high-band and low-band filters to be combined to secure the resultant image 1111- pedance characteristic Z,'Fig. 7b, which is a constant-k mid-shunt image impedance curve for the band jif4. It will be seen from this curve that the resultant image impedance is approximately uniform not only over the pass bands i-h and fa-f4, but also over the intervening band fa-f3. While the formulas given above for computing the reactance values of the circuits of Figs. 4b and 5b may be used with approximate accuracy for th; type C composite filter of Fig. 6, there is a certai amount of interaction between the circuits, and

'more exact formulas 'are given in the appended table for computation of the reactance values of the type C composite filter, Fig. 6. In these formulas, attention is called to thefact that the inductance L21 is the total inductance of the combined coils 2m and 2| b.

Whilethe formulas given above for the computation of the individual band-pass filters may be used in the design of the composite filter with approximately the characteristics described, the two band filters have a certain amount of mutual interaction and for exact results it is preferable to compute the entire system as a single filter. Such computations may. be based upon the. fundamental short-circuitopen-circuit methods of filter design described at pages 75-84 and 179- 208 of the 'above Shea reference, The resultant modified formulas for 'the type C composite filter of Fig. 6 are given in the appended table under such heading. It will be noted that the formula forv the parameter h of these formulas is the reciprocal of the constant of the geometric progression of theboundary frequencies of the component bands; it follows that It should have a value much less than unity-in the example given being 0.29.

By the use of my invention, as described, it is possible to design a band-pass ,filter to pass any required wide range of frequencies, and including several transformers of reasonable coupling. While individual filter sections of the type described are particularly suitable because of their relatively low attenuation outside their respective I bands, other filter sections having generally similar characteristics may be substituted therefor,

provided that they have at each common terminal circuit similar extreme values of image impedance at the cut-off frequencies bounding each intervening band.

3 While I have shown a composite filter comprising only two band-filter sections, it is clear that the principles involved may be extended to any number of filter sections. For'example, the inductance 30 may be split for the insertion of the primary circuit of a third band-filter, while the lower connection between the inductance 32 and condenser 3| may be broken to insert the secondary circuit of a third band-filter, and this procedure may be repeated to include as many sections as desirable for any particular installation.

It is to be noted that the shunt condensers'2ll the high-frequency filter inductances 2| and 23,

respectively. In case of the extension suggested in the preceding paragraph, the same relationship would obtain. In other words, in a composite filter of the type described, if all the condensers and inductances on each side are numbered serially in their order of increasing inductance and capacitance, respectively, and the elements of the same serial number are connected to form individual band-pass filters, the inductances of each of the primary and secondary circults being all in series,-each condenser will be connected in shunt with its respective inductance of like serial number and, in addition, with only those inductances of higher serial number. this arrangement, the condensers of the highband filter sections serve to by-pass from the low-band filter inductances, frequencies whichmight correspond to natural frequencies of the coils of greater inductance, and therefore might otherwise be affected abnormally.

The composite filter of Fig. 6 is identical to the filter l3 of Fig. 1, save only that thecondenser of Fig. 1 has been split into two equal as that marketed under the name Ferrocart.

It is believed that the general principles of operation of the above-described system will be clear from the foregoing detailed description of the circuit arrangements and the principles involved in its design. However, the operation in the several frequency bands may be summarized by reference to Figs. 2 and 3, each of which in cludes only the circuit elements primarily activein its respective frequency band. It will be clear that the inductances oi. the low-band filter have such high impedances over the high-frequency band that their admittances may be neglected, while the condensers of this filter have such low impedances that they may be considered as short circuits, so that the low-band filters have very little effect on the high-band operation. Similarly, the inductances and capacitances of the high-band filter have little efiect on the operation over the low-frequency band. In the intervening frequency band. f2-f3, the reactance elements of the two component band filters are all effective in determining the operation.

Referring specifically to Fig. 2, it will be seen that the high-band filter component is effective in the high band fa-h to transfer signals received from the line l2 to the input circuit ii, at the same time substantially matching the impedance of the line l2 with that of the input impedance ii. In Fig. 3.the low-band filter similarly operates over thelow band 11-4: to couple the line l2 and the input circuit ii. In Fig. 1 the two individual band-filters cooperate over the intervening frequency band f:fa to couple the transmission line I! to the input impedance It, at the same time matching the impedances of these two devices. With the arrangement described above, each of the transformers Zia, 2| b, 23 and 30, 32 may have a coeflicient of coupling that may be readily realized in practice, while the composite filter is effective to pass a frequency band for which a single transformer couldbe'designed only with difii culty, if at all.

while the composite band filter above-def1- f2= Ta= f.= 20 megacyclcs Line image impedance RL= 500 ohms resistance Load impedance R4=400 ohms resistance Elements: 210 21b= 27 microhenrios 23= 21 microhenrios 30=262 microhenries 32=210 microhenries 20= i6 micromicrofarnds *22=- 20 micro-inicrofnrnds 29a, 29b=386 micro-microfarnds each 31=242 micro-microfarads 0.6 megacycic 1.7 megacycles 5.8 megacyclcs "Capacitance 22 was physically a part of the inherent capacitance. between coil 23 and ihe adjacent shield.

Transformer 21a, 21b, 23 Coeflicient of coupling-84%. Transformer so, 32

Coefilcient of coupling-84%.,

While I-have described what I at present consider the prefered embodiment of my invention, it will be obvious to'those skilled in the art that various changes and modifications may be made K therein without departing from my invention, and I, therefore, aim in the appended claims to cover all such changes and modifications as fall 7 within the true spirit. and scope of my invention.

TABLE, or DESIGN FORMULAS' Fromm 4A Type A 1 ran tance means eiiectively in parallel therewith, cor-1,

responding inductances of all said filters bein connected in; series across their respective terminal circuits, said band-pass filters being adapt-- ed individually to pass frequency bands spaced by intervening bands, the boundary frequencies pi said bands being related approximately in a get- 1. A- continuous-band filter comprising the combination of a plurality of constant-k derived band-pass filters of similar type and termination connected individually between common terminal circuits, the several filters being similarly connected to both terminal circuits, said band-passfilters' being adapted individually to pass frequency bands spaced by intervening bands each having a width equal to a mean value of the widths of the adjacent pass bands, and said bandpass filters belng' relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

2. A continuous-band filter comprising the combination of a plurality of constant-k derived band-pass filters of similar type and termination connected individually between common. terminal circuits, the several filters being similarly connected to both terminal circuits 'said band-pass filters being adapted individually to pass frequency bands spaced by intervening bands, the boundary frequencies of said bands being related approximately in a geometric progression, and said band-pass-filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

3. A continuous-band filter" comprising the combination of a pluralityoi constant-k derived band-pass filters of similar type and termination connected between common terminal circuits, each of said band-pass filters comprising at least two inductively coupled inductances efiectively connected, respectively, vto said terminal circuits and each having capacitance means efi'ectively in parallel therewith, corresponding inductances of all said filters being connected in series across their respective terminal circuits, saidband-pass filters being adapted individually to pass frequency bands spaced by intervening bands each having a width equal to a mean value of the widths oi the adjacent pass bands, said band-pass filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

4. A continuous-band filter comprising the relatively poled and proportioned to pass a resultant continuous bandcomprising said pass bands and intervening bands.

5. A continuous-band filter comprising a primary circuit and a secondary circuit, a plurality of inductively coupled sets of primary and secondary inductances of which each set may be identified by a serial numberin the order of increasing inductance, and a plurality of sets of primary and secondary condensers of which each set may be identified by a serial number in the order of in-- creasing capacitance, said primary inductances being connected in series across-the primary circuit and each of said primary condensers being connected in parallel with certain of said primary inductances'including that identified by the same serial number and in series with those identified bylesser serial numbers, said secondary inductances and capacitances being similarly connected across said secondary circuit, all the elements identified by each serial number being proportioned to form an individual band-pass filter, the

, respective pass bands of all such individual filters being spaced by intervening bands each having a width equal to a mean value of the widths of the adjacent pass bands, and said band-pass filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

6. A continuous-band filter comprising a primary circuit and a secondary circuit, a plurality of inductively coupled sets of primary and secondary inductances of which each set may be identified by a serial number in the order of increasing inductance, and a plurality of sets of primary and secondary condensers .of which each set may be identified by a serial number in the order of increasing capacitance, said primary inductances being connected in series across the primary circuit and each of said primary condensers 'being connected in parallel with certain of said primary inductances including that identified by the same serial number and in series with those identified across said secondary circuit, all the elements identified by each serial number being proportioned to form an individual band-pass filter, the respective pass bands of all such individual filters being' spaced by intervening bands, the'boundary frequencies of said bands being related approxieach set may be identified by'a serial number in the order of increasing capacitance, said primary inductances being connected in series across the primary circuit and each of said primary capacitances being connected in parallel only with all those of said inductances identified by equal and 'greaten serial numbers, said sec-- ondary inductances and capacitances being similarly connected across said secondary circuit, all the elements identified by each serial number being proportioned to form an individual band-, pass filter, said individual filters being of the same type and the respective bands of all such individual filters being spaced by intervening bands, the boundary frequencies of said bands being related approximately in a geometric progression, and said band-pass filters being relatively poled and proportionedto pass a resultant continuous band comprising said pass bands and intervening bands.- A

8..A continuous-band filter comprising the combination of a plurality of band-pass filters of similar type and termination connected between common terminal circuits, said band-pass filters being adapted individually, to pass frequency bands spaced by intervening bands,'the boundary frequencies of said bands being related approximately in a geometric progression, each of said band-pass filters being of type B and proportioned approximately according to the formulas for type B, and said filters being relatively poled to pass a resultant continuous band comprising said pass bands and intervening bands. v

9. A continuous-band filter comprising the combination of apair of band-pass filters of similar type and termination connected between common terminal circuits, said band-pass filters being proportioned individually to pass a pair of frequency bands spaced by an intervening band, the boundary frequencies of said bands being related approximately in a geometric progression and said filters co-operatingto form a composite .filter of type C and proportionedapproximately according to the formulas for type C to pass' a resultant continuous band comprising said pass bands and intervening bands. 1 I a 10. A continuous-band filter comprising the combination of n/2 band-pass filters of similar I having capacitance means effectively in parallel therewith, corresponding windings of all of said filters being connected in series across their respective terminal circuits, said band-pass filters being adapted individually to pass alternate frequency bands spaced by intervening bands, said bands being bounded by frequencies 11, f2 In related approximately in a geometric progression, the coefiicient of coupling of each of said transformers being determined by the formula where the' value of It being muchless than unity and said band-pass filters being relatively poledand proportioned to pass a resultant continuous band intervening comprising said pass bands and bands.

11. A continuous-band filter comprising the I combination of a pair of band-pass filters of similar type and termination connected between com- ,mon terminal circuits, each of said band-pass filters comprising a transformer having primary arid secondary windings, a winding of the transformer of the higher-band filter being divided into sections with the corresponding winding of the lower-band filter being interposed therebetween,

and having a lower-band filter condenser connected in shunt thereto, said serially connected windings being connected across a common terminal circuit and having a higher-band filter condenser connected in shunt thereto, the other windings of said transformers being serially connected across the other terminal circuit and having a higher-band filter condenser connected in shunt thereto and a lower-band filter condenser connected in shunt to its respective winding, said band-pass filtersbeing adapted individually to pass frequency bands spaced by intervening bands, the boundary frequencies of said bands being related approximately in a geometric progression, said band-pass filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and in-' tervening bands.

12. A continuous-band filter comprising the combination of a plurality of constant-k derived band-pass filters connected individually between common terminal circuits, the several filters being similarly connected to both terminal circuits, said band-pass filters being adapted individually to pass frequency bands each bounded by cut-of! frequencies having a ratio much greater than unity, said frequency bands being spaced by intervening bands each having a width equal to a mean value of the widths of the adjacent pass bands, and said band-pass filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

13. A continuous-band filter comprising the combination of a plurality of band-pass filters connected individually between common terminal circuits, said band-pass filters being adapted individually to pass frequency bands each bounded by cut-off frequencies having a ratio much greater than unity, said frequency bands being spaced by intervening bands each having a width equal to a mean value of the widths of the adjacent pass bands, said band-pass filters having individually at either terminal circuit similar extreme values of image impedance at the cut-off frequencies bounding each intervening band, and said bandpass filters being relatively poled and proportioned substantially to secure over said intervena,oe1,so1

' widths of the adjacent pass bands. and said band-.

ing bands a uniform resultant image impedance at each common terminal circuit.

14. A continuous-band filter comprising the combination of a plurality of constant-k derived band-pass filters connected individually between common terminal circuits, the several filters being similarly connected toboth terminal circuits. said band-pass filters being adapted individually to pass frequency bands each bounded by cut-offfrequencies having a ratio much greater than said frequency bands being spaced by inunity, tervening bands each having a width not exceeding the arithmetic mean value of the widths of the adjacent pass bands, and said band-pass filters being relatively poled. and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

15. A continuous-band filter comprising the combination of a plurality of band-pass filters connected individually between common terminal circuits, each of said band-pass filters comprising at least two inductively coupled inductances effectively connected, respectively. to said terminal circuits and each having capacitance means connected therewith, said band-pass filters being adapted individually to pass frequency bands each bounded by cut-ofl frequencies in a ratio much greater than unity, said frequency bands being spaced by intervening bands each having a width equal to a mean value of the pass filters being relatively poled and proportioned to pass a resultant continuous band comprising said pass bands and intervening bands.

16. A continuous-band filter comprising the combination of a plurality of constant-k derived band-pass filters; of similar type and termination connected between common terminal cir-.

cuits, the several filters being similarly connected to both terminal circuits, and each of said bandpass filters comprising only primary and secondary inductances coupled only inductively and eflectively connected, respectively, to said terminal circuits and each having capacitance means eifectively in parallel therewith, correspondinginductancescofali said filters being connected in series across their respective terminal circuits, said band-pass filters being adapted individually to pass frequency bands each bounded by cut-oi! frequencies having a ratio much greater than unity, said frequency bands being spaced by intervening' bands each bounded by frequencies having a ratio on the order of the geometric mean value of the cut-oi! frequency ratios of the adjacent pass bands, and said band-pass filters being relatively poled and proportioned to pass a continuous band comprising said pass bands and intervening bands.

HAROLD A. W.

resultant

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