US2199221A - Wave filter - Google Patents

Description

Patented Apr. 30. 1940 UNITED STATES WAVE FILTER George William Gilman, London, England, as

signor to Bell Telephone 'porated, New York, N. Y.,

New York Laboratories, Incora corporation 'of' Application August 20, 193s, Serial No. 225,901 8 Claims. (01. 17844).

openr-circuited transmission lines coupled gelectro- 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-transmission 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 elements being combined in series-shunt or in other configurations in accordance with the kind of selective characteristic desired.

In the present invention, anovel configuration is employed according to which open-circuited 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 selective 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 conductors 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 coupling between the lines.

Otherfeatures of the invention and the principles'underlying its operation will be more fully understood from the following detailed descrip tion and by reference to the attached drawing, of which Figs. 1 and 1a are schematic diagramsillustrating 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 invention. e I I Referring to Figs.,1 and 1a, elements I and 2 represent two I elevated conductors; of equal lengths lying parallel to each other at a height 71. above ground and separated by a distance d. Between one end of-linel 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 l and 2 and the common ground; return constitute a pair of magnetically to each other along their lengths by virtue of their juxtaposition. Transmission takes place in the system from the generator 3 to the load 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 first band.

The manner in which the transmission bands are formed andthe dependence of the selective characteristics uponthe line parameters is explained by the followingmathematical analysis.

It 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 fields may be disregarded and the steady distribution of oscillatory currents in the lines may be represented by the equations and v 1 wherein I1(x) and I2(x) are the currents in conductors I and 2 respectively at points distant (at) from the generator, the As and the Bs are factors determined by the terminal or boundary conditions and the impressed voltage, and 'y is the propagation constant of the individual lines.

The quantity '7' is a pure imaginary in the absence of resistance and has the value where w is 2-- times frequency and'b is the veloo- I point :0, Q1 and Qz,-the charges per unit length on lines I. and 2 respectively at the given point, and p11, p12, and .1122. are the Maxwell potential coefl lcientsof the system.- 1

.55 where V101) and V2(x) represent the voltages at By means of the general steady state relationship and (5) When the two conductors are similar and the system is symmetrical, the coefficients p11 and 1 22 are equal. Hereinafter, symmetrical systems will be assumed and the notations p and 1 m will be used in place of p11, p22 and. p12, respectively.

Since the system is symmetrical longitudinally, its general image parameters can be determined by solving Equations 1 and for the particular case in which the load terminals are short-circuited. The establishment of the boundary con ditions corresponding to this case permits the determination of the appropriate values of the As and the Bs 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 suflice 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 V =E and 1 0 when x=0 and V =O and I1='0 when=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,

These equations can be solved for the As and Bs, the values of which are found to be 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-cir cuited output of line 2. Denoting the input end impedance by Z0 and the transfer impedance by ZT, their values are found from Equations with the help of Equations 7 to 10, to be 41s (11) p1) sin and 2 ie 1 Z 2' J p n 229 1) s1 7 X wherein I) .21r f 'Y I being the frequency, and denotes the wavelength of the current in the line.

The image impedance K, which is the same for both ends of the system, is given by The transmission bands are located in the ranges for which K-is real and tanh 0 imaginary and the band limits are determined'as the frequencies at which thesequantities change from reals to imaginaries. From the character of Equations 14 and 16 it is evident that, the band limits are defined by the relationship p 21i-S E 008 T :l: 1

The potential coefficients :0 and 20m 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 mutual capacity between conductors l' 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 length of the line. The values of the potential coefi'icients in terms of the capacities are'gi'ven by The lowest frequency band has its center at the frequency for which 7,

A 1 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-oif frequencies in terms of the line capacities are given by 27FS m cos -cos ic+cm from which it is evident that the smaller Cm is with respect to C, the narrower will be the resulting 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.

The image impedance is zero at the band edges and rises to the value Km, given by at the center of the band. Absolute or c. g. s. units are assumed in all of the preceding formulae, the value of 11 being 3x10 centimeters per second. The capacities C and Cm are the capacities per centimeter length of the conductors. If these capacities are measured in micromicrofarads per centimeter, Equation 21 becomes The modified filter circuit shown in Fig. 2 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 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 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 ohms (22) 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 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 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 I paralleled by a half wave-length open-circuit conductor 6. 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 the shield. For this purpose, it is desirable to separate the conductors as widely as practicable 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.

In Fig. 6 the outer shellis composed of two fianged channel sections 9 and Ill which are welded or soldered toa perforated copper screening plate ll coextensive in length with the conductors. Plate II is solid except for a series of perforations such as shown at l2 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 apertures may be determined experimentally to provide a desired relationship between the mutual capacity Cm and the shield or ground capacities C.

What is claimed is:

1. A band selective transmission system comprising a pair of similar transmission lines disposed parallel to each other and electrostatically coupled, a wave source connected to one end of one of said lines, and a load impedance connected to the remote end of the other of said lines, both of said lines being terminated at their free ends to produce full wave reflection and the lengths of the lines being equal to one quarparallel thereto and disposed symmetrically with respect to said conductors, terminal means for connecting a wave source between one end of one of said conductors and said common return, and terminal means for connecting a load impedance between the remote end of the other of said conductors and said common return, said conductors being terminated at their free ends for full-wave reflection, and their lengths being equal to quarter wave-lengths at an assigned frequency whereby the system has a finite transmission band centered about said assigned frequency.

5. A wave filter in accordance with claim 4 in which the direct mutual capacity between said conductors is small in comparison with'the capacity of each conductor to the return path, whereby a narrow transmission band is provided.

6. A wave filter in accordance with claim 4 in u capacity is made small with respect to their 'direct capacities to the shield.

8. A system in accordance with claim 1 including a partial electrostatic shield interposed between the said lines.

GEORGE WILLIAM GILMAN.

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