US2064775A

US2064775A - Band-pass filter

Info

Publication number: US2064775A
Application number: US25736A
Authority: US
Inventors: Harold A Wheeler
Original assignee: HAZCLTINE CORP
Current assignee: HAZCLTINE Corp
Priority date: 1935-06-10
Filing date: 1935-06-10
Publication date: 1936-12-15
Anticipated expiration: 1953-12-15
Also published as: FR807235A; GB462874A

Description

D 1936. H. A. WHEELER BAND PA's s FILTER Filed June 10, 1935 3 Sheets-Sheet 1 RECEIVER BAND P/IJS FILTER i- -o I 1 {7-49 64w PASS mm? INVENTOR. 054mm A WlfELfR BY RIM/HM ATTORNEY.

Dc. 15, 1936. H, A. WHEELER I 2,064,775

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24 W 6 a RD 27 3: 28 121; I l BL i E i L was; 3,3 6

26 I 5.9 F} {a Jfcz 4 4 9 J0 J2 J68 ATTORNEY.

$3 (J7 INVENTOR- i {2" #49040 A. WHEELER BY W Dec. 15, 1936. H. A. WHEELER BAND PASS FILTER Filed June 10, 1935 3 Sheets-Shee't 3 INVENTOR. flma'om A WHEEL 2 ATTORNEY.

* arrangements of the prior art, and which will re- Patented net. is, case new , attests asa -ease rnrr'sn Application June 10, test, Serial he. 2553s it iliaims.

My invention relates to band-pass filters and more particularly to composite filters including a plurality of separate band-pass filters co-oper ating to pass a more extended hand than any oi the filters individually.

While my invention is or general application, it is especially suitable for coupling an antenna, adapted toreceive or transmit a wide band or a plurality of bands of the radio-frequency spec= trum, to a signal-translating circuit.

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 oi frequency bands aggregating a wide portion of the radiofrequency spectrum. However, certain dimmities 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 the actual circuit design and as to the procurement of reasonably uniform responsiveness over the band.

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 dimculties oi the quire a minimum otcircuit elements.

More specifically it is an object of my invention to provide a composite band-pass filter capable oi covering a wide band of frequencies and including a plurality of co-operating band-- they may be directly interconnected, as by a series connection, without substantially affecting the operation of either filter over its respective band. The terminal sections, of the other end of the filters are of a type and so proportioned that they may be connected in difierent manners to an input circuit, and these latter sections include impedance elements efiective substantially to isolate each input section from the other over its respective band. I

For a better understanding of my invention, together with other and further objects thereof, reference is had to the following description ticularly applicable and in which the invention megacycles.

or riee (or, ire-ssh taken in connection with the accompanying drawings, and its scope -vrill be pointed out in the appended claims.

In the drawings, Fig. 1 is a schematic 511cm of a complete antenna system including a com- 5 posite band-pass filter employing my invention; Figs. 2 and 3 are approximately equivalent sim plified circuit diagrams of the system oiFia. i when operating in the short wave and long wave bands, respectively; Figs ioid are circuit 10 diagrams illustrating the circuit transiormations in developing the high-frequency filter component; Fiasco-Edam corresponding diagrams for the low-frequency component of the filter of Fig. 1; Fig. s is a composite equivalent circuit diagram oi the networks of Figs. i and 5; Figs. "Ia-7d are graphs representing certain operating characteristics of the primary side of the composite band-pass filter of Fig. 1; while Figs. tic-8c are graphs of certain operating characteristics of the secondary side of the filter oi Fig. 1.

Referring now more particularly to Fla. 1, there is shown schematically a wave-signal collecting system, to which my invention is pariii is embodied as a composite filter for coupling an 25 antenna, for operation over an extended frequency hand or a pluralityaof individual frequency bands, to a sianal-translatmg or load device,such as a radio receiver, either directly, or indirectly by means of a transmission line. The generalsystem of Fig. 1 is disclosed and claimed in my co-pending application Serial No. 25,735, filed June 10, 1935, so that a detailed de scription thereof is considered unnecessary,

In general, the system includes an antenna lea-4th, preferably designed as a doublet for operation in the hiehirequency portion of the band to be covered but including connections for converting it into a fiat-top antenna tor oporation over the low-frequency band. The antenna ltd-4th is coupled to a transmission line it by a high-band filter tie to! balanced operation of both the doublet antenna and the line over a high-frequency hand which may, tor errample, extend from 6 to 18 megwyfiles. Similarly, the low-hand filter iib couples the antenna, for unbalanced operation asa fiat-top antenna, with the balanced line, for operation over a low-frequency band, for eizample, of 9.55 to 6 so The two filters areuncoupled on the antenna side because of the balanced and unbalanced operation oi the antenna over the high and low-frequency bands, respectively. They are joined together-on theline side and as their operation is interdependent at frequencies in the neighborhood of the dividing frequency, for example, 6 megacycles. The two filters Ha, I lb are designed independently and then combined, as will be explained more fully hereinafter.

The other end of the line I2 is coupled by a band-pass filter l3, which may be of any of several types well-known in the art, to a signaltranslating or load device H having an input circuit the impedance of which is represented at l5. One type of composite extended-band-pass filter particularly suitable for this purpose is disclosed and .claimed in my copending application, Serial No. 25,737, filed June 10, 1935. I

It is desired that the composite filter shall match the impedance of the doublet antenna to the constant image impedance of the line over the high-frequency range of operation, and that it shall connect the antenna as a fiat-top antenna and match its impedance to that of the line over the low-frequency portion of the operating band. It is also desirable that the composite filter cir- I cuit shall include a transformer section which avoids direct connections between the primary and secondary circuits of the filter and permits impedance transformation. The impedance of the antenna lilal0b, operating as a doublet, is shown in Fig. 7a, in which a value of impedance somewhat greater than the geometric mean of the antenna impedance over the high-frequency band is indicated by the value Rn.

For the purpose of explanation, the characteristic of Fig. 7a is divided into portions separated by the frequencies f1, f2, fa, f4, which arbitrarily divide the entire frequency band to be covered into three component bands. For example, f1, h, is and f4 may have approximately the values 0.55, 1.8, 6 and 18 megacycles, respectively. With respect to the antenna filter circuits Ila, llb,

the lower frequency band is from fi-h, while.

the upper frequency band is from fa-f4.

The antenna impedance, as shown in Fig. 7a, over the band fs-f4 is approximated by' the image impedance of a constant-k half-section with mid-series termination facing the doublet antenna. (Fora more complete description of the several types of band-pass filter sections utilized in the preferred embodiment-of this invention and discussed herein, reference is made to a textbook of T. E. SheaTransmission Networks and Wave Filters, D. Van Nostrand 00., 1929.)

It has become common practice in the design of band-pass filters to make certain of the computations on the basis of a constant-k filter halfsection of a standard type, which is adopted as a conventional reference standard and in terms of which the formulas for some of theother types are derived and expressed, even though, in certain instances, sections of this standard type are impedance at each junction -of the sections or' half-sections. For the type generally used as a standard, the input and output image impedances have the same value at the frequency for which. the slope of their characteristic curves. is zero. This value is indicated by the symbol R, which may be taken as 100 ohms, for example, for the purposes of computation. Such a filter section will be referred to hereinafter as type A. (This type is referred to' at page. 315 of the Shea reference as type IVK.)

In Fig. 4a is illustrated a constant-k filter halfsection of type A, just described, indicated at A. This filter half-section comprises a mid-series condenser l6 and inductance l1 and mid-shunt condenser l8 and inductance I9. Such a halfsection permits the insertion of a transformer since it includes both series and parallel inductances, which may be realized by a transformer in an equivalent network. In computing the circuit constants of the section A, it wil be assumed that it is to be designed for equal values of R of 100 ohmsat both input and output terminals. The values of the circuit reactances may then be computed, in terms of R and the boundary frequencies of the band which the filter is to pass, from the formulas given by Shea for the IVx type on page 316. These formulas are for the so-called full-series and full-shunt" arms and must be modified in the well-known manner for computation of the mid-series" or mid-shunt arms employed at the'input and output terminals of a filter. Alternatively, the circuit constants may be computed by such formulas as modified for a half-section (the mid-series termination reactance one-half the full-series reactance; the

mid-shunttermination reactance twice the fullshunt reactance), and for the particular boundary frequencies, as given in the appended table of formulas 'for the type A filter section of Fig. 4a. In order to connect adjacent band filters together at one end to form a composite filter, it is desirable to. include at that end of each com-' ponent filter a half-section terminated in a mid- I series reactance arm for which may be substituted reactance elements of the other adjacent band filter. There is represented at B, Fig. 4a, a type of half-section filter by which these characteristics can be procured. The filter halfsection B includes the parallel-connected midseries condenser 20 and inductance 2i and midshunt condenser 22 and inductance 23. In this type of filter, for the purposes herein described, the values of the mid-series elements 20, 2! are not critical and these elements can be replaced by reactance elements forming a part of, and critically proportioned for, a band filter designed for an adjacent band, without substantially affecting the operation of this type of filter. The filter halfsection B has at its left-hand terminals .a constant-k mid-shunt image impedance similar in form to that at the right-hand end of the filter section A, so that if .these two image impedances are made equal, the two sections may be directly interconnected. The circuit constants of the filter section B may be computed by assuming for R the same valueas for the section A, for example, 100 ohms, and by using the formulas given by Shea for filter sections of thesame type or by such formulas modified for a half-section and for the particular boundary frequencies of this case, as given in the appended table for type B of Fig. 4a.

It will be noted that the formulas for the circuit co nstants of the type B filter section are in terms of, the parameters m1 and ma. Theoretically, the larger of the parameters mi'and m2 is a function of the cut-ofi' frequencies of the filter and the frequency of infinite attenuation. For the purposes of this application, however, the larger of the values m1 and m: is chosen rather to secure the desired shape of 'the mid-series image impedance characteristic and to determine the approximation of the major portion of this characteristic to a level value. These parameters have no effect on the cut-off frequencies hectare of the filter. In the designing of a type B filter for the higher of two adjacent bands (of the type 1V4 in Shea), the parameter ma is the greater, while in the case of a type B filter for the lower 'oftwo adjacent bands (type IV: inShea) m1 is the greater. In either .case the value .of the a value of m onthe order of (Lite 0.5 has been found to he the optimum.

Byithe use of well-known equivalent circuit transformations, the half-sections A and B of Fig. in can be combined into the high-band filter lie of Fig. i. For example, the adjacent termi nals of the sections A and B may he interconnected, and the condensers i8 and 22 combined intoa single condenser and the inductances it) and it, into a single inductance 2Q, since these elements are all connected in parallel. This transformation is shown in Fig. 4b. Similarly, it is well-known that the inverted-L connection of inductances ii and 2d of Fig. 4b is the equivalent of a transformer in which the inductances ii and 2% provide the self-inductance of the primary circuit, and the inductance 2% provides the mutual inductance andthe self-inductance of the secondary circuit, in this case the two latter inductances being of equal value. The result of this transformation is the circuit of Fig. 4c, in which the inductances 2'! and ti are proportioned as just described.

In the computation of the values of the circuit reactances of the circuit of Fig. 40, however, it is necessary to multiply all of the reactances of the primary circuit by the ratio of the-nominal arrtenna impedance R1) to the assumed image impedance R. The maximum image impedance of the filter at the antenna end will then have the value Rn, as indicated in Fig. 7b, which, as stated above, is somewhat greater than the mean value of the antenna'impedar ice over the band, so that the image impedance of the line reasonably ap proximates the antenna impedance over the hand. Similarly, in order to match the secondary circuit to the line 82; it is necessary to multiply the circuit reactances\ of the secondary circuit by the ratio of the image impedance of the line 02, R1,, to the assumed image impedance R. The formulas for the circuit constants of the circuit of Fig. 4c. referred to hereinafter as a type C filter section, including the circuit transformations and the factorsfor the matching of the primary and secondary impedances, are given in the formula for type C of Fig. 4c, in the appended table. The

similarly, by dividing the condenser 30 and informulas for type pfilters may be derived from the formulas for types A and B by well-known algebraic transformations.

The circuit oflFig. 40 may be rearranged as shown in Fig. 4d, for balanced operation, by 4 giving to the induct ances 21a and 21b a combined value equal to that of the inductance 2i and,

ductance 3! into two portions represented by the elements 80a, Ma and 30b, 3"); In general, the inductancesl'la, 211; will not each have a, value half that of the inductance 21, nor the inductances flu, Slb, half thatof the inductance 3!,

because of the mutual inductance between con-e sponding portions. Similarly, the component band-pass filter ilb, for operation over the low-frequency band, for

example, 0.55-6 megacycles, may be designed to couple the antenna lilo-4GB, operating as a simple, unbalanced, flat-top antenna, to the balanced transmission line it and to match the impedances of the antenna and line over the low-frequency band. The antenna characteristic impedance over this band is shown in Fig. 7c.

The design of the component low-band filter lib is approached from the same standpoint as that of the high-band filter described above. Referring to Fig. 5a, the starting point is again a standard filter half-section of type A having a constant-k image impedance of nominal value R,

for example, 1% ohms. The half-section A of Fig.

512 comprises a mid-series condenser 32 and inductance t3, and a mid-shunt condenser 34 and 1 inductance 35. The formulas for the circuit constants of the half-section A of Fig. 5a are given in the appended table, Fig. 5a, type A.- It is seen that these formulas are identical with those for are similarly applicable to the selection of the right-hand type B half-section of the low-band L- fllter 6 lb. As shown in Fig. 5a, the type B section is similar to the type B section of Fig. 4a, and comprises the parallel-connected mid-series condenser 38 and inductance 31, and the mid-shunt condenser 38 and inductance 39. The only difference between the type B halfsection of. Fig. 5a and that of Fig. 4a is that in the type B the parameter m1 is greater than me. while in the latter ma is greater than m1 (parameter m1 is greater or less than ma, depending on whether the natural frequency of the mid-shunt elements is greater or less than that of the midseries elements). The formulas for the type B half-section of Fig. 5a are given in the appended table under'this heading.

While the sections A and B of Fig. 5a could be merged directly into an equivalent network in-' 'cluding a transformer section, as was done in the case of the high-band filter, for the particular disclosed herein, this transformer would require a coefficient of coupling very close to unity in order to cover the entire 'low-frequency-band f1- is. This requirement may be made less severe by the addition of a transformer filter section such as the section E of Fig. 5a. The half-sections A 1 denser 63, and inductance M. The formulas for computing the. circuit constants of the type E section of Fig. 5a are given in the appended table.

The components A, Band E of Fig. 50. can be mergedinto their electrical equivalents, as indi-' cated in Figs. 5b, 5c and 5d. In Fig. 5b the midthe single condenser 45, the mid-shunt inductances 35 and II into the inductance 46, the midshunt condensers 38 and 43 into the condenser 41, and the

mid-shunt inductances

39 and 44 into the inductance 48.- It is seen that the inductances 46, J2 and comprise a pi-section which may be replaced by an equivalent transformer. 'Such shunt condensers :34 and 40 are. combined into operating frequencies and circuit characteristics a transformation is'shown inFig. 5c, inv which these inductances areconverted into a transformformer 50-52 is effective to match the impedances of the antenna and the line over the lowfrequency band ;f1fa. ,The circuit of F18. 5c is also modified in that the values of the reactance elements of its primary circuit are multiplied by such a factor that the condenser 53 has a capacitance equal to that of the flat-top antenna, efiective at the lowest frequency 11. The nom-' inal value of the, antenna impedance and the image impedance of the antenna end of the filter of Fig-5c is then determined by multiplying the assumed nominal image impedance R by the ratio of the capacitance of the condenser 53 to that of condenser 32. The image impedance characteristic of the antenna end of the filter of Fig. 5c is shown. in Fig. 7d, in which the nominal value RE is seen to be slightly greater than the mean antenna. impedance over the band .fij3, as shown in Fig. 7c.

The circuit of Fig. 5c is modified to that of Fig. 5d in order that the secondary circuit may operate into a balanced line. To this end the midseries condenser 55 and inductance 56 are each divided into equal parts represented by the condensers 55a and 55b and the inductances 56a and 56b of Fig. 5d. In Fig. 5d isshown also a modiflcation of the primary circuit of Fig. 5c, in which the capacitance 58, representing the value of antenna capacitance effective, at the lowest frequency ii, is substituted for the mid-series condenser 53, and in which the inductance 59,'representing the inductance requiredto tune with capacitance 58 to the fundamental frequency is of the antenna, is substituted for a portion of the mid-series inductance 54 of Fig. 5c. The inductance 51, thus, represents the difference between the inductance 54 and the inductance 59.

The formulas for computing the equivalent filter circuit of Fig. 50, which is referred to hereinafter as type D, are given in the appended ta.- ble. These formulas are derived from the formulas for sections A, B and E of Fig. 50,, taking into consideration the circuit transformations and multiplying the primary circuit reactances' by the ratio of the nominal antenna impedance Ra to 'the assumed nominal image impedance R and by multiplying the secondary circuit reactances by the ratio of the image impedance of the line R1. to the assumed nominal image impedance R of the section B of Fig. 5a.

It is seen that the arrangement of Fig. 5d is the equivalent of a filter section with constant-k mid-series termination'on short circuit. As indicated in Fig. 7d, the image impedance of this arrangement is zero at the cut-off frequencies, so that the cut-off frequencies of the'circuit are. not affected by the short-circuit and the filter properties of the circuit are not destroyed.

In Fig. 6 is shown the combination of the highband filter of Fig. 4d and the low-band filter of Fig. 5d. The primary circuits 'are unchanged, but the secondary circuits are combined in a particular manner.- The

mid-series elements

28 and 29 of Fig. 4d are replaced by elements 5i and 52, respectively, of the low-band filter, as shown in Fig. 6, while the mid-series elements 55a, 56a, v

55b, 56b of the low-band filter are replaced by the elements 30a, 3|a, 30b, 36b, respectively, of the high-band filter. In other words, each filter circuit proper operates as a mid-series reactance arm for the other filter. While the circuit constants of each of the filters may not be ideal for terminating the other; the values of these terminating reactances are not critical, so that these siderably more abrupt than that of'a constant-k section and is characteristic of the mid-series termination of the type B filter. Similarly, the image impedance characteristic of the type B section of Fig. 5a is shown in Fig. 81). It is seen that these two filter characteristics are substantially complementary for the entire band fif4. The effect of connecting together the highand low-band filters at the terminals of the line l2, as'shown in Fig. 6, is to merge the image impedance curves of the two filters into a single curve substantially continuous over the band f1--j4, as shown in Fig. 8c. The characteristic of Fig. 8c is similar to that of a continuous band filter with constant-k mid-shunt termination, but the composite filter just described secures this characteristic by the merging of two separate adjacent band filters at one end. Y

The type B filter is fundamentally characterized by having only one frequency of infinite attenuation in an adjacent band and none outside of the composite band. I This frequency of infinite attenuation is the natural frequency of the mid-series reactance arm comprising the parallel resonant circuit. For the purposes described herein, the values of the mid-series reactance elements are not critical, so that an adjacent band filter may be substituted therefor, as de-,

scribed above. This characteristic of a frequency of infinite attenuation in only one adjacent band is fundamentally associated with the above-described properties of the mid-series image impedance 'of this type of filter, as shown in Figs. 8a and 812. These properties enable two bandpass filters designed for adjacent frequency bands to be combined into a composite filter having a resultant image impedance characteristic as shown in Fig. 80.

It will be seen that the derived circuit of Fig. 6 is equivalent to that comprising the high-band and low-band filters liar-l lb of Fig. 1, the input terminals of the high-band filter being connected to the terminals of the doublet antenna, which are interconnected through an inductance M. The input terminals of the low-hand filter are connected, respectively, to the mid-point of the inductance 64 and to the junction of

coils

52a and 52b, into which the coil 52 of Fig. 6 is divided to provide a ground connection through the line for the antenna Ina-lob when operating as a simple fiat-top antenna in the low-frequency band. As an alternative this latter connection may be independently grounded, preferably in the immediate neighborhood of the antenna, as directly underneath. The transformer comprising the windings 50 52a and 52b of the low-band filter 7 preferably is provided with a core of finely divided iron.

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 inductances of the low-band filter lib have such a high impedance that their admittance may be neglected, while the condensers of this filter have such a low reactance that they may be considered as short circuits.- Similarly, at the lower frequencies of the low band, the reactance elements of the high-band filter may be neglected. Thus,.the primary circuits of the two'filters efiectively have separate input circuits of difierent impedances, even though they are. connected in a conjugate manner to the same antenna structure.

Referring specifically to Fig. 2, the antenna Eda-lilo operates as a balanced doublet and the high-band filter lie is efiective to couple the balanced antenna currents to the balanced line it as balanced circulating currents therein, at the same time approximately matching the impedance of the doublet antenna with that of the line over the lot-frequency fs-fc. The circulating currents in the line it are coupled by the filter l3 toinduce unbalanced currents in the input circult to of the receiver M.

en operating in the low-frequency band, as illustrated in Fig. 3, the low-band filter No serves to couple the unbalanced currents of the antenna lilo-lob, operating as a simple flat-top antenna, as balanced circulating currents in the linel2. The filter 83 similarly couples the balanced circulating currents of the line l2 into the unbalanced input circuit to of the device to. In this hand the line 62 may serve also as a ground leadfor the simple antenna, the connection being made at the junction between coils 52a and. 52b so that the unbalanced ground currents flow in parallel through the conductors l2.

While the filter sections of my invention have been described with reference to primary or input circuits and secondary or output circuits, it will be clear that these designations are by way of illustration only, and that power may be transferred through the filters in either direction, so that either end may be considered as the input or output" circuit.

e the composite band filter above-described may be designed for operation over a wide range of conditions. there are given herewith, by way of example only, the circuit constants of a particular composite filter embodying myinvention in the form described iii-.1. e iollo 1-1;; circuit values were re rive-L as closely as possible and include such efiects as erent capacitance or inductance of other related circuit elements:

' System f1= h=1a mecycles i =6 rnycles f6=18 megacyclee dome filter Ito-1500 ohms v Rr=1080 ohms I Element =45 mlcrohenries fila+fill1=9 microhenries 8lc+tib=5 microhenries tl= microhenries 52a+52b=l2e microhenries 59=3 microhenries 25:44.2 micro-microiarads 363a, tob=63 micro-microiarads each l=59 micrmmicroiarads 5 i =98 micro-microtarads ta=2ao micro-microiurads Transformer 22770., 2%, cm, 86o Coemcient of couplina=ii7.8%

Transformer to, 2%, 2th Coefiicient of coupling=89.3%

characterized by a constant-k image impedance at its non-terminal end and by one frequency of infinite attenuation in only each adjacent one of said bands, each of said half-sections normally including a reactance arm at its terminal end resonant at each of its respective frequencies of infinite attenuation, each said reactance arm.

being replaced by reactance elements of the filter passing the band including its resonant frequency, and said filters being relatively proportioned to present across said terminal circuit a resultant image impedance approximating that of a constant-7c continuous-band filter passing the band comprising said contiguous bands.

2. A composite band-pass filter comprising a plurality of individual band-pass filters passing respectively a series of contiguous frequency bands and connected at one end to a common terminal circuit, each of said filters being terminated at said end in a half-section of a type characterized by a constant-7c image impedance at its non-terminal end and by one frequency of infinite attenuation in only each adjacent one of said bands, each of said half-section's normally including a reactance arm *at its terminal end resonant at each of its respective frequencies of infinite attenuation, each said reactance arm being replaced by reactance elements of the filter passing the band including its resonant frequency, each of the terminal half-sections of the filters passing the two extreme frequency bands being of type B and proportioned substantially in accordance with the type B formulas, the two corresponding frequencies of infinite attenuation being each predetermined to give a value within the range 0.25-0.75 for the greater of mi and m: in the said formulas, and said filters being relatively proportioned to present across said terminaleircuit a resultant image impedance approximating that of a constant-k continuous-band filter passing the band comprising said contiguous bands.

3. A composite band-pass filter comprising a plurality of individual band-pass filters passing respectively a series of contiguous frequency bands and connected at one end to a common terminal circuit, each of said filters being terminated at said end in a half-section of a type characterized by a constant-7c image impedance at its non-terminal end and by one frequency of infinite attenuation in only each adjacent one of said bands, each of said half-sections normally including a reactance arm at its terminal end resonant at, each of its respective said frequencies of infinite attenuation, each said reactance arm being replaced by reactance elements of the filter passing the band including its resonant frequency, each of the terminal half-sections of the filters passing the two extreme frequency bands being of type B and proportioned substantially in accordance with the type B formulas, the two corresponding frequencies of infinite attenuation being each predetermined to give a value on the order of 0.4 to 0.5 for the greater of mi and m: in the said formulas, and said filters being relatively proportioned to present across said terminal circuit a resultant image impedance aproximating that of a constant-k continuous-band filter passing the band comprising said contiguous bands.

4. A composite band-pass filter comprising a plurality of input circuits of different impedances and a common output circuit, a plurality of individual band-pass filters passing respectively a series 'ofcontiguous frequency bands and connected to said common output circuit, each of said filters being terminated at said common end in a half-section of a type characterized by one frequency of infinite attenuationin only each adjacent one of said bands and normally including a reactance arm at its terminal end resonant at each of its respective frequencies of infinite attenuation, each said reactance arm being replaced by reactance elements ofthe filter passing the adjacent band including its resonant frequency, each of said filters including also one or more impedance matching filter half-sections interconnecting its respective input circuit and said first-named half-section, adjacent half-sections of each filter having at their connecting terminals substantially equal constant-k image impedances, and said filters being relatively proportioned to present across said output circuit a resultant image impedance approximating that of a constantk continuous-band filter passing the band comprising said contiguous bands.

5. A composite band-pass filter comprising a plurality of input circuits of different impedances and a common output circuit, a plurality of individual band-pass filters passing respectively a series of contiguous frequency bands and connected to said common output circuit, each of saidfilters being terminated at said common end in a half-section of type B and proportioned according to formulas of type B, each of said filters including also one or more impedance matching filter half-sections interconnecting its respective input circuit and its first-named half-section, adjacent half-sections of each filter having at their connecting terminals substantially equal constant-k image impedances, and said filter halfsections adjacent said input circuits being of the type A and being proportioned according to formulas of type A, whereby said filters present across said output circuit a resultant image impedance approximating that of a constant-k continuous-band filter passing the band comprising said contiguous bands.

being terminated at said common" end in an equivalent half-section, each of said filters nor-" mally including a reactance arm at its termina' end resonant at a frequency of infinite attenuation, each said reactance am being replaced by reactance'elements of the other filter, each of said filter! including also one or more impedance matching equivalent half-sections interconnecting its respective input circuit and its first-named half-section, the equivalent half-sections of .each filter being K combined to form composite filter sections for the high and low bands of the types C and D, respectively, andproportioned according to the formulas of types C and D, respectively.

7. A composite band-pass filter comprising a pair of individual band-pass filters passing respectively two contiguous frequency bands and connected at one end to a common terminal circuit, each of said filters including a transformer provided with primary and secondary windings,

a transformer winding of the higher band filter being divided intosections with the corresponding winding 0! the lower band filter being interlosed therebetween, condensers ccnnectedrindivlduaily across each oi. said higher band winding sections and across said lower band winding, whereby said higher band filter constitutes terminal reactance arms for said lower band filter, and the lower band filter constitutes the equivalent of a terminal reactance arm for saidhigher band filter, said transformer windings and associated condensers being proportioned to approximate a constant-k mid-shunt image impedance of a continuous-band filter over said contiguous bands.

HAROLD A. WHEELER.