Wave filter

April 30, 1940.

G. W. GILMAN

2,199,221

WAVE FILTER

Filed Aug. 20, 1938

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FIG. 6

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ATTORNEY

Patented Apr. 30, 1940

2,199,221

UNITED STATES PATENT OFFICE

2,199,221

WAVE FILTER

George William Gilman, London, England, assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York

Application August 20, 1938, Serial No. 225,901 (CL 178—44)

Claims.

This invention relates to wave filters and more particularly to wave filters for high frequencies in which the selective transmission properties are obtained by the use of sections of uniform trans⁸ mission lines of low dissipation.

Heretofore it has been the practice in the construction of transmission line wave filters to use open-circuited or short-circuited line sections as two-terminal impedance elements, appropriate 10 elements being combined in series-shunt or in other configurations in accordance with the kind of selective characteristic desired.

In the present invention, a novel configuration is employed according to which open-circuited J⁸ or short-circuited line sections are electromagnetically coupled to each other along their lengths, whereby wave energy is transferred from the input terminals of one line to the output terminals of another with a band frequency se²⁰ lective characteristic which is determined by the character and degree of the coupling.

The lines may be open-wire types or they may be of the shielded conductor type and the coupling is preferably effected by running the con125 ductors parallel to each other along their length. The degree of coupling may be modified by the interposition of partial electrostatic screens between the conductors or by proportioning their dimensions and separations. _

The filters of the invention are characterized by multiple pass-bands spaced at harmonic frequency intervals. The width of the bands and the amount of attenuation in the intervening frequency ranges is controlled by the degree of &lt;35 coupling between the lines.

Other features of the invention and the principles underlying its operation will be more fully understood from the following detailed description and by reference to the attached drawing, 40 of which pigs. i and la are schematic diagrams illustrating one general form of the invention;

Fig. 2 shows an alternative general form of the invention;

Figs. 3 and 4 are schematic diagrams illustrating tandem arrangements of the forms shown in Figs. 1 and 2, respectively; and

Figs. 5, 6 and 7 are illustrative of mechanical constructions used in modifications of the in50 vention.

Referring to Figs., 1 and la, elements I and 2 represent two elevated conductors of equal lengths lying parallel to each other at a height h above ground and separated by a distance d. ⁵⁵ Between one end of line I and ground is connected a high frequency generator 3 and a load resistance 4 is connected from the remote end of line 2 to ground. Conductors 1 and 2 and go the common ground return constitute a pair of open-circuited transmission lines coupled electromagnetically to each other along their lengths by virtue of their juxtaposition. Transmission takes place in the system from the generator 3 to the load 4 through the distributed coupling · and, because of the character of the coupling and the current and voltage distributions in the two lines, exhibits a definite band selective characteristic. The center of the first transmission band lies at the frequency for which the lengths of the two conductors are equal to a quarter of the propagation wave-length, that is, for which the conductors become quarter wave lines. The other transmission bands are located at certain equally spaced harmonic frequencies above the ¹first band.

The manner in which the transmission bands are formed and the dependence of the selective characteristics upon the line parameters is explained by the following mathematical analysis. ^MIt will be assumed that the effects of resistance in the two conductors and the return path are negligibly small so that the wave propagation velocity in the system may be taken as equal to the velocity of light. Fields other than radial ²⁵fields may be disregarded and the steady distribution of oscillatory currents in the lines may be represented by the equations

Ιιω^-Αιο-”—Biet* ' 30 and (1) wherein Iiw and Lu) are the currents in conductors I and 2 respectively at points distant (a:) from the generator, the A’s and the B’s are factors determined by the terminal or boundary conditions and the impressed voltage, and 7 is the propagation constant of the individual lines. The quantity 7 is a pure imaginary in the absence of resistance and has the value (2) where ω is 2?r times frequency and v is the velocity of light.

The voltages at any point along the conductors are related to the densities of the electric charges on the conductors by the equations ₅₀

Vite — P11Q1+P12Q3 and (3)

V2(x)—P12Q1 + P22Q2 gg where Vi(x> and V2(x) represent the voltages at point x, Qi and Q2, the charges per unit length on lines I and 2 respectively at the given point, and pn, P12, and P22 are the Maxwell potential coefficients of the system. 60

2,199,221

By means of the general steady state relationship ⁽⁴>

which states that the charge density is proportional to the rate of diminution of the current along the line, Equations 3 can be written in terms of the current differentials and, with the help of Equations 1 may be transformed to ⁼^·[(ΡιιΑ.ι+Pi2A2) e^-71-/ (p22B,+^12¾) e⁷¹] and (5) ^2te) =^-[(pi241 + P11A₂) 6-^+ (P12B1 “Γ P22B2) e^TX]

When the two conductors are similar and the system is symmetrical, the coefficients pu and P22 are equal. Hereinafter, symmetrical systems will be assumed and the notations p and p_mwill be used in place of pu, P22 and P12, respectively.

Since the system is symmetrical longitudinally, its general image parameters can be determined by solving Equations 1 and 5 for the particular case in which the load terminals are short-circuited. The establishment of the boundary conditions corresponding to this case permits the determination of the appropriate values of the A’s and the B’s and thereafter of the shortcircuit input impedance at the generator end and the short-circuit transfer impedance from the source to the output terminals. These latter quantities suffice for the computation of the image impedance and the image transfer constant of the symmetrical system.

The boundary conditions when the load terminals are short-circuited are

Vi = E and Z₂=0 when a:=0 and

U₂=0 and Z,=0 when x=S

S denoting the whole length of the lines and E the terminal voltage of generator 3. The application of these boundary conditions to Equations 1 and 5 gives a new set of equations; namely,

A_le~f^s—B_le'r^s=0

A₂-B₂=O

/. . (6) p^+B^+p^+B^E^ (p_m A, + p A₂) e~r^a+ (p_mBi+pB₂) ei^s=0

These equations can be solved for the A’s and B’s, the values of which are found to be ¹ 2 7 p¹· cosh² 7&lt;S-p^2w

A---BiE.______Pm______(O\ ² 2 7 p² cosh² yS-pi,

PCoAtyS ¹ 2 7 p² cosh² yS-pi, and

B₂=A₂ (ΐθ)

The determination of the significant parameters of the complete system, namely, the image transfer constant and the image impedance requires only the knowledge of two impedances, namely, the input impedance at the generator end when the output of line 2 is shorted and the transfer impedance from the generator to the short-circuited output of line 2. Denoting the input end impedance by Zc and the transfer impedance by 5 Zt, their values are found from Equations 1, with the help of Equations 7 to 10, to be . 4ir,S pv sin —7— (11) ¹⁰ and (12) wherein / being the frequency, and denotes the wavelength of the current in the line.

The image impedance K, which is the same 25 for both ends of the system, is given by

ZgZ_T^Jzy—zy and has the value ~v . 2ttS sm —r— Λ

The transfer constant Θ is given by (13) (14) tanhe=yi-(gy(15) and has the value40 _C0SW J tanh LXSz-----£_/(16) p2ττο

COS ——— ^λ45

The transmission bands are located in the ranges for which K is real and tanh β imaginary and the band limits are determined as the frequencies at which these quantities change from reals to imaginaries. From the character of ⁵⁰Equations 14 and 16 it is evident that the band limits are defined by the relationship

P 2~S — COS -rr— = ± 1

Pm λ (17) ss DO

The potential coefficients p and Pm are of the nature of inverse capacities and are related to the capacities of the system as follows. As shown in Fig. la, the system of conductors has three significant capacities, namely, the direct ⁶⁰mutual capacity between conductors 1 and 2, which is designated Cm, and the direct capacities of each wire to ground, which in the example illustrated are equal and are designated C. ,-. These capacities are the capacities per unit ⁶⁵length of the line. The values of the potential coefficients in terms of the capacities are given by and 1 C ⁽¹⁹⁾₇₅

2,199,221

The lowest frequency band has its center at the frequency for which &lt;S= that is, for which the conductors are quarter wave-length lines. The other bands are centered at the odd harmonics of this frequency. The cut-off frequencies in terms of the line capacities are given by

27rS 2vfS , C_m^cos~^=cos-v^=±c+c;

(20) from which it is evident that the smaller Cm is with respect to C, the narrower will be the resuiting band. A band width of about ten per cent of the mid-band frequency is obtained by proportioning the size and spacing of the conductors so that Cm is about one-twelfth of C.

₂₀ The image impedance is zero at the band edges and rises to the value Km, given by ^Km~_vc(C+2C_my ⁽²¹⁾ at the center of the band. Absolute or c. g. s. ²⁸ units are assumed in all of the preceding formulae, the value of v being 3χ10¹⁰ centimeters per second. The capacities C and Cm are the capacities per centimeter length of the conductors. If these capacities are measured in micro³⁰ microfarads per centimeter, Equation 21 becomes ^Km~ 3 C(C+2C_ro) °^{hms (22)}

The modified filter circuit shown in Fig. 2 ³³ corresponds to that of Fig. 1 except that the free ends of the two conductors are short-circuited instead of being open-circuited. In both types the free ends of the conductors are terminated to provide full wave reflection. The transfer 40 constant of the filter of Fig. 2 is the same as that of Fig. 1 and has the value given by Equation 16. The image impedance is the reciprocal of the expression in Equation 14 except for a constant multiplier. Its value becomes infinite at 45 the edges of the transmission band and at the mid-band frequency drops to a minimum which is inversely proportional to the coupling as measured by Pm or Cm.

The open-circuit type shown in Fig. 1 has an 50 impedance characteristic of the form exhibited by mid-series terminated filters and is characterized by a relatively low impedance in the transmission bands. The modified form shown in Fig. 2 resembles a mid-shunt terminated filter 55 and is characterized by a relatively high image impedance in the transmission bands.

Since the filters are symmetrical longitudinally, similar sections may be connected in tandem to provide increased discrimination. The 60 tandem connection of two sections of the type shown in Fig. 1 is illustrated in Fig. 3. The resulting structure comprises two quarter wave open-circuit wave conductors 5 and 7 paralleled by a half wave-length open-circuit conductor 6. ⁶⁵ A corresponding arrangement of two sections of the short-circuited type is shown in Fig. 4. Manifestly, additional sections may be added in any desired number.

Instead of using open wires with a common ground return, the filters of the invention may comprise a pair of conductors symmetrically disposed within a surrounding tubular conductor which constitutes the common return path. A cross-section of a line of this type is shown in re

Fig. 5. The line conductors I and 2 may be solid or may be tubular as shown and are disposed symmetrically within an enclosing cylindrical conducting tube 8, preferably of copper. The inner conductors are held in position by suitable 5 insulators not shown. Tandem connections of multiple sections may be employed as shown in Figs. 3 and 4 by dividing the inner conductors or short-circuiting them to the shield at appropriate intervals. ¹⁰

To secure narrow transmission bands, the direct capacity between the inner conductors must be small relatively to the capacity of either to the shield. For this purpose, it is desirable to separate the conductors as widely as practicable 15 and to keep their diameters small. The reduction of the direct capacity may, however, be secured more advantageously by the use of a partial shield interposed between the conductors, as shown in Fig. 6. 20

In Fig. 6 the outer shell is composed of two flanged channel sections 9 and 10 which are welded or soldered to a perforated copper screening plate 11 coextensive in length with the conductors. Plate 11 is solid except for a series of 25 perforations such as shown at 12 in Fig. 7 extending along its axis. These perforations should be close together and uniform in size to maintain a substantially continuous longitudinal distribution of the mutual capacity. The size of the 30 apertures may be determined experimentally to provide a desired relationship between the mutual capacity Cm and the shield or ground capacities C.