US1603329A - Tapered filter for alternating currents of varying frequency - Google Patents

Description

' E. DlEl-rzEi TAPERED FILTER FORALTERNATING.'CURRENTS 0F VARYING FREQUENCY l di g? VAVAVAV VAVVA'A p7 'fia/0' r www Filed Feb. 26, 192i 1200 /a'oo 20.00 24.00 '25;20 ,Jada

Patented oct. i9, 192e.

D/IETZE, OF BROOKLYN,

EGINHARD TELEGRAPE COMPANY, A; CORPORATION .OF NEW YORK.

NEW YORK, .ASSIGNORA TO AMERICAN TELEPHONE TAPEEED FILTER non. AnTEnNnEINe-CUERENTS on vnnYmG FREQUENCY. i

Application led February By the term wave-filter I refer to a network of'recurrent sections formed alike I -or according to some law of progressive change, and adapted freely to transmit currents of frequencies Within a certain range and to shunt out currents within a different frequency range. v The lprincipal object of my invention 1s to provide sucha lter of taper1ng-charac teristic impedance; Another objectfof my invention is to provide a filter adapted to be interposed without serious refiection loss or irregularit between lines or apparatus o f different c aracteristic impedance. Still anotherfobject is to provide a filter of this type, all sections of which shall have the same free transmission ranges land which shall have a definite and unvarying propa gation constant throughout its length.

In the following speciiication I have disclosed a limited number of specific embodiments of the invention, which I shall now proceed to describe with the understanding that the definition of the invention 1s given j in the appended claims.

Referring to the drawings, Figure 1 is a diagram illustrating a lter'embodying my invention. Fig. 2 is a diagram of a more specific example. Fig. 3 is a diagram showing characteristic curves for the .filter of Fig. 2. Figs. 4 and `5 are diagrams show ing modifications.

is known how to make filters of recurrent sections, all alike, each section comprising series impedance 'or impedances and shunt impedance or impedances. Fig. 1 can be looked upon as a filter of this type, pro.- vided the constant a appearing inthe legends is taken equal to 1. With this understanding, it will be, seen that the series impedances are each al and the shunt impedances z2. The theory of such a iilter is commonly' developed on the assumption that there is an infinite number of sections. The results obtained for the innite filter apply to a filter having only a initefnumber of sections, provided the proper terminal impedance is employed.` The Yimpedancesz, and a, are made with as little dissipative loss as practicable, and vfor most purposes ac. 1921. .seria11vo.`447,`a9s.

this loss can bev disregarded, and z, land a,

can be'lookedk upon as pure reactances.` The filter of Fig. 1 has mid-series vtermination at the left, that is, 'the initial series-impedance is 'only half that of the succeedingseries impedances. equal. 1 The foregoing discussion of Fig. 1 is on the express lassum tion that the constant a A1s equal to 1. y improvement involves making a: different from 1. Assuming that the'first mid-series section extending A to B is as given in Fig. 1, I form the next mid-series section from B to C by multiplying each of the component impedance elements by a. In the next section from C to D these elements are multiplied by a2, and so on. This delines the structure of my `improved filter. mine the value to be given-to w will be diss cussed later.. My improved -ilter has the following properties:

definite and the same, no matter what value is given to a; accordingly the 'same as for the non-tapered filter, corresponding to a=1.

2. The characteristic impedance from successive oints 0f junction of the sections is increase from section tosection by the factor ra, assuming a 1, orV decreased in.

this ratio if a 1.

3. The propagation constant ris identical The shunt impedances are l. Its critical or cut-off frequencies are from The conditions that detelw for all filter sections, both in the free trans-A mission and attenuated .frequency range.

I-Iaving the foregoing properties, it will be seen that my improved filter may be introduced between `two. lines or apparatus ofdiierent characteristic impedance, the Afilter beingdesigned so that its characteristic im- "pedance from section to section Ais graded between the two extreme values of impedance. My tapered .filter then serves in all respects as an ordinary filter, and 'in addition it obviates the" disadvantage of large 4reflection loss that wouldl be had with an yordinary non-tapered lter; In the freev transmissionranges o'f a filter the currents are displaced from section to section by a phase angle which varies from 0 at the one limit-in great extent these reflections annul one another. Perhaps this point may be made clearer by considering that the sum of a number of vectors of equal length and random direction will be decidedly ess than if they all had the same direction.

That the characteristic impedance of my improved lter varies in geometrical ratio from section to section with the factor a may he shown by the followinv Whatever the impedance i, at A, if each individual component impedance element of the whole network be. multiplied by a, the resultant impedance will be aZo. But now considerations.

the filter viewed from A will be identical with what it was before when looking to the right from B, for itis assumed always that the filter has an infinite number of sections. at B for thefilter as given in Fig. 1 must be aZo. By similar reasoning it may be shown that at C the characteristic impedance must, be a2Z, and so on.

will ynow proceed to obtain a formula for vthe input characteristic impedance Z0. From Kirchhoffs laws we 'get the equation The solution of this gives Knowing the impedance at vthe input end Z0, the lmpedance at any junction oint of the filter sections may be determine at once by the formula ZnIan--Zo where 71,:0 at the input end A, 1 at B, 2 at C, and so on.

That the propagation constant is the same at all points A, B, C, D, etc., may be shown as follows. By definition of the propagation constant I where the currents in the series elements of the successive nth and (n-l-l)th meshes are represented by In and IDH. Let the current in theintermediate shunt impedance element be I. Then we have the equations Inf n+1=I,n

and

I i n ana, Inn* allai anHZo) From thesetwo equations we obtain the solution Thus the value of the current ratio in successive sections lof the filter is seen to be independent of n, showing that P has the same value, whatever the value of n that is taken. This proves the constancy of theI propagation constant throughout the length ofthe filter.

In the ordinary filter to which the filter of Fig, 1 reduces when a=1, if We represent the propagation constant by F0, We have the a- 1 cosh 1"=cosl1 PMI-0Wl smh I (7) and cosh 1"=cosh Io-l--q-l (8) From equations (7) and (8), the propagation constant of the tapered filter can easily be compared with that of the non-tapered filter. In order to keep reflection effects b etween successive sections small, a value of a should be taken differing only slightly from 1.

It will be seen that my improved filter involves making the characteristic impedance vary in geometrical ratiofrom section to section. I have tried other laws ,for the progression of value of the characteristie impedance and I find that the law disclosed in this specification gives ap unique result.` Under other laws, a value ofthe propagation constant is obtained that can not be freed from fn., which defines the position of the section in the lter. 'l In Fig. 2 I have illustrated a simple lowpass filter o f three sections designed for a specific purpose and embodying thetapering construction heretofore disclosed in this specification. The filter of Fig. l2 is intended to make connection between a` low mpedance line of 600ohms and another line Hence the characteristic impedancel vas lis desired at a fre having an impedance of 2000 ohms. Thev critical or cut-off frequency of the filter is to be 2,500, and the maximum transmission uency of 800 cycles. With three sections t ere will be fourpoints of discontinuity: hence we have for the determination of a, the equations Z0=600, @4Z :2,000, from which a, is readily computed to be 1.35. I shall not take s acel here to give the steps by which the va ues of e, and z2 are etermined as they are practically the same non-tapered filter having the characteristic impedance Z.I of the lter the two series impedances shown separately on either side of a junction oint such as B in Fig. 1 will be consolidated and inthe case of the low-pass filter of Fig. 2 their combination in a single coil 1s shown. The resultant inductance values of the coils appear as legends on Fig. 2. The' shunt impedances vary by `the factor a -.1.35; and accordingly the capacities of the condensers 2', 3 and C2 vary inversely by the same factor. v

In Fig; 3 the heavy line shows, plotted against frequency, the current received over the tapered filter per Avolt a plied at the sending end. The diagram-s ows how the filter cuts off at a frequencylof 2,500. For comparison Il have shown, in the light, continuous line,` the corresponding characteristic that might be obtained witha nontapered filter inserted between two lines of equal im edance, thatis when there are no reflection losses, and in the dotted line I have shown the characteristic for the nontapered filter vinserted between a G-ohm line and a 200G-ohm line.v The number of sections in Fig. 2' is rather small; for a larger number of sections the transmission characteristic of the tapered filter would bev lim roved. i

e foregoing discussion is based on mid-series# geometrical law of progres'- sion is equally applicable for other sections and filterv terminations.

asin the case of the In the actual constructionv sections and filter termination,y but the sameI Thus-alY lter may be terminated at :1J-series section and all the sections ma vbedivided accordingly. This is illustrate -in Fig. 4. It will be seen that the lter' of Fi.` 1 is a special case of Fig', 4, with w=i in ig; 1

Instead of .fr-series and mid-series sections one ma have -shunt sections. In this case a: times the shunt admittance is considered to belong` to the section that follows and the remainder to the section that precedes.' To make this clear on Fig. 5 the shunt im edances have been replaced bypairs of impedances with appropriate legends. By making w=i, we special case of mid-shunt sections and termination.

1. The method of reducing the total reflection loss in a sectional alternating current filter between lines or apparatus of different characteristic impedance, which consists in partially reflecting the currents' at eachl successive section of the "filter, whereby' the vector sum of the partial reflections will be less than the total reflection would be if the impedance irregularity were all at one place.

2. The method of reducing yreilection losses in Ia filter Ainterposed between `lines Nor apparatus of different characteristic impedance, which consists in dividin up the reflection at different points in iferent phase throughout the filter, and thereby largely neutralizing the reflection effects.

3. n the operatlon of a filter of recurrent section type, the method of ltering alternating currents of a certain frequency rangefrom a circuit of'one impedance value to a circuit of another impedance value, which' consists in producing partial reflection effects at the respective sections due to ave the corresponding differences of limpedance between them.

In testimony whereof. I have signed myA name to this specification .this'18th day of February, 1921.

EGINHABD DIETZE.

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