US1559638A - Wave filter - Google Patents

Description

Nov'. 3, 1925. 1,559,638'

W. H. MARTN "WAVE FILTER Filed April 26, 1920 (Wwf/arl] x 6, 52x52 l ATTORNEY IN1/'EN TOR.

'Patented Nov. 3, 1925.

WILLIAM H. MARTIN, or NEW YORK, N. Y.,

TCELEGRAPH OMPANYQACORPORATION 0F N EW YORK.

Application led April 26, 1 920. Serial No. 376,763.

To all who-m t may concern:

Be it known that I, IVILLIAII residing Bronx and State of New York, have invented certain Improvements in fave Filters, of which the following is a specification.'

-My invention relates to wave filters for use in electric circuits where 'it is desired to transmit frequencies and to suppress, or partly suppress, currents of other frequencies.A More particularly, general typeillustrated and described vin the atents to George A.. Campbell, 1,227,- 113 and 1,227,1145iss'ued May22, 1917.

The presentl invention proposes a filter which freely transmits all frequencies in a range between certain pre-assigned limits, neither of' which is zero or infinity, and which attenuates frequencies outside this range; The filter of the. presentinvention is characterized by having theoretically infinite attenuationyat a finite frequency other than zero and lying in the attenuated range.' It may consequently be so designed that it vwill effect substantially complete suppression of anyv desired .frequency outside the H. MARTIN.

transmitted band, or it may be so propor-4 tioned, that the frequency of infinite attenuation is close to either limit ofthe transmitted band, so that a very sharp cut-off action may be attained at the said limit. vAs in the Campbell filters, all frequencies. within the attenuated range-can be suppressed to any desired degree by use of a sufficiently large number of sections. The -special feature of this filter, however, lies in the fact that the attenuation per section is substan-4 tially infinite for one frequency which can be freely chosen within the specified limits. A good understanding of the invention may now be had from the following description of one form of embodiment thereof, reference being had to the accompanying drawing in which,

Fig. 1 is a diagrammatic View showing one form of embodiment of the invention;

Figsf 2 and 3, diagrams showing graphically the attenuation characteristics of the filter ofFig. 1; and l Fig. 4, a diagrammatic view showing one form of termination of the filter. I

at New York, in the county of alternating current of selected it concerns 'wave filters of the C, and that of Fig.

AssIGNon To AMERICAN TELEPHONE AND.

Similar characters of reference designate similar partsin each'of the several views. In the form shown in Fig.` 1l the filter comprises a number of sections or elements each of which consists of a lumped impedance Z1 1n 'series wlth the line 1 and a lumped impedance Z', in .shunt to the line. i

The impedances Z1 and ZZ* are shown as comprlsed of inductances L, and ll.,2 in series withcapacities C, and (G2, .'respectively.

lBothserie's and shuntl impedancesfare thus constituted of like types -of resonant circuits, a feature. which distinguishes them from the filt'ersidisclosed in the Campbell patents hereinbefore referred to,'in certain of which filters theseries imnedances con'- sist of one type'of resonant. circuits (i. e.. series) and the shunt impedances, 'of an# other type of resonant circuits, (i. e., parallel or anti-resonant). f i f I have found that the. type of filter of this invention has certain advantageous charaeteristics which I shall presently explain with reference to Figs. 2 and .3, whichshow graphically the' attenuation characteristics of filters similar to that of Fig;l 1, the abseissae representing frequencies and the ordinates, values of attenuation. The 'curve of Fig. 2' shows the attenuation for the genera-l case in which the numerical product of L1.

timesI C1 is'greater than that ofL2 times the reverse is true. It will be observed that the attenuation is nil only for the band of frequencies lying between fo and f3, this be-v ing the transmitted band. 'The attenuation y is a maximum at the'frequency f2, being theoretically equal to infinity. When f2 is close to f3, theslope of the attenuation curve through f3 is very steep, showing that 4the lter discriminates sharply against frequencies just Byso designing the filter that f2 is above f3, (Fig. 2) for the upper limit of the transmitted band. and by so proportionin the impedanees that f2 is below f8 (Fig. 3 the same property may be secured for the lower limit. More- 2, the attenuation when' outside the transmitted band.v

the sharpcut-off may be attairnxdv over, where it is desired to' discriminate parv ticularly against some pre-determined fre-l quency outside the transmitted band, the filp ter may be so designed that it has infinite stants but independent of eachother, chosen at will. Two of these may be takenl attenuation for this frequency provided there is no energy dissipation in the filter.

I shall now give certain convenient mathematical formulae by means of which any one skilled in the art may design a filter of the type disclosedherein, tol meet the requirements in any' particular practical case.

The design of the filter involves the derivation of the values of the four constants L1,

L2, C1 and C2. These values may, of course,

be chosen at will, and the properties of Vthe filter computed therefrom, but in the general case thereverse procedure will be 4 venient, i. c., to choose the properties of the filter (according to the conditions under which it' is to 4be employed) and to calculate the values which the constants of the filter must have to give it these properties. t Since therearefour independent constants to be determined, it follows that anyfour properties of the filterv dependent upon the conas the frequencies fo and fsthus defining the range of free transmission',- the third as f2,

the frequency of infinite attenuation, and

the fourth, as the impedance of the filter, this factor being of importance because it is desirable to make the saine substantially equal to that of 'the circuit into which the filter is placed, in order that reflection losses may be avoided. The relations which exist 'between the above-mentioned properties of the filter and the quantities L1, L2, C1, C2, will now be set out in mathematical form.

'In the Campbell patents hereinbefore mentioned, it was shown (equations 3 and 4) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z1 and the shunt impedance persection is Z2, there is unattenuated transmission for all frequencies of currentfor which the value,of,-f

i/zla so that the limiting values fsandffo) of the +1 lies betweeni 1,.- (1) frequencies for free transmission may be determied from the following equations:

. In the present case the values of Z1 and Z2 in terms of frequency are'- zzfile-CQ (4) Where i is the imaginary operator 1/ 1 and p, the angular velocity, is written for 2wf, for. sake of convenience.

. equation (2) the resultant mentioned may be vention is not limited to any I of termination.

When', therefore, the values of Z1 and Z2, as given by (3) and (4), are substituted in vexpression may be solved for p, one of the roots, p2, deter- `mining one limiting frequency, f3, and the other, p0, the other limiting frequency, fo:

IIlhe relation which exists between the' valuessof -tlic constants of the filter and the frequency, f2, at which the attenuation is infinite, may be determined by placing the expression (eiation 2 of thev hereinbeforeampbell patent) for cosh Where is the propagation'constant, equal to infinity:

Thefrequencies fo, kf1 and f2 are thus expressed `in terms of the constants of the lter. It remains to' evolve an expression for the impedance of the filter.

This impedance varies With frequency, and it has been found convenient in the art to specify in design the' impedance at the frequency, termed mid-frequency, which is the geometric mean of the limiting frequencies of the transmitted range, i. e.,

A filter is defined to have mid-'series termination when it is terminated by a series impedance of half that of the normal series section. This is illustrated in Fig. 4 in which the normal series impedance is ZJ and the left terminal impedance is 1/2Z1,

1. e., composed of 1/2L1 and 2C1.` The filter may be assumed to have an 4infinite number of sections toward the -ri-ghtso that the impedance at any other mid-series section, such as that which extends to .the right from line l-I is the same as the impedance measured at the terminals Lf-b. Consequently, if Zms designates theniidseries section impedance,

substituting for and Z2, their values as given by equations (3) and (4), and simplifying, it will be found that the impedance at the frequency is given by the expression inid-series. v

Equations (5), (6), (7) and (10) are four simultaneous equations 1nvolving the factors p2, p0, p3 and Zms, the values of which may be assumed, and the factors L1, L2, C1 and C2, the values of which are to be determined. These equations may therefore be solved for the values of the last mentionedquantities,

I and when this is done itwillhe found that @Fm-P5' (12) @Femm (14) ZmsPZ2 l p0) The constants of the filter may' consequently l be determined by merely substituting the assumed values of p0, p2, p, and Zms in the above equations.

For example, where, it is desired to construct a filter whose band of free transmission shall extend from 400 to- 2000 cycles, whose maximum (theoretically infinite) attenuation shall be at 2300 cycles and whose impedancezat mid-'frequency shall be 800 ohms,I (when terminated by a mid-series section) so that the filter' may be inserted in a line of #14 N. B. S. gauge open wire line (the characteristic impedance of which is, roughly, 800 ohms) we have, according to the notation used herein:

@Fac (4o0)=25ia )93:27: (2000) :12570. @Fae (2300) :14451. Zm=soa Substituting thesevalues in equations (11) to (la), and solving gives:

L1: .0798 henries,

L2=.0594 henries,

(3l-:1.98 microfarads,

02:.0807 microfarads,` as the constants of the normal filter section.

'With tlie'mid-series termination assumed herein the values of the first and last series inductance and capacity are, respectively, .0399 henries and 3.96 microfarads.

Although I have herein shown and described only one form and arrangement of apparatus embodying my invention it is readily understood that various changes and modifications may be made'therein with the scope of the following claims without de-x parting from the spirit and scope of the invention.

1What I claim is: l 1. A wave filter for an electric circuit,

said filter having a plurality of like recurrent sections,- each section comprising lumped impedance in series with the circuit and lumped impedance adj acently in shunt thereto,fboth of said impedances being like types of resonant circuits' and so proportioned that the filter approximately suppresses all frequencies lying 'outside a pre-assignedband extending ibetween two frequencies 4other than zero or infinity and substantially completely suppresses 'a certain pre-assigned finite frequency other .than zero. 2. A recurrent' section .wave filter for an electric circuit, each section consisting' of lumped impedance .in seriesv with the circuit and lumped impedance of like-type adja- `cently in shunt thereto, whereby said filter transmits freely all frequencies lying within two finite limiting frequencies, but approximately suppresses the frequencies outside of the said frequency range and dis criminates sharply against frequencies close to one of said limits.

3. A wave lfilter for an electric circuit, said filter having a Aplurality^of like recur.- rent sections, each section consisting ofv a lumped inductance and capacity'-in series with each other inserted in series with the circuit andI a 4lumped induc'tance and ca# 'pacity in series with each other connected in shunt to the circuit, adjacently to said first-mentioned inductance and capacity.

4; A wave filter for an electric circuit,

consisting of a resonant circuit in series with the circuit and a like type of resonant cir- 'cuit in shunt to the circuit, each of` which determined by a finite frequency other than zero at which the attenuationof the "filter is approximately infinite, the impedance of the'filter, and the limiting frequencies of a pre-assigned band of free transmission, which limiting frequencies are other than zero or infinity.

5. A Wave filter for an electric circuit, said filter having a plurality of like recurrent sections, each section consisting` of lumped impedance in series with the circuit and lumped impedance in shunt thereto, the said impedances being so proportioned that the attenuation of the filter has a finite value at a chosen finite frequency and decreases, as the frequency is changed in one direction, until it is substantially equal to zero at `a certain other finite frequency, remains at this value until stillanother finite frequency is reached, then.A increases until it becomes approximately infinite at still another finite frequency and then decreases with further change of frequency in the same direction.

6. A Wave filterv for an electric circuit, said filter having a plurality of like recurrent sections, each section consisting of lumped inductance land capacity in series Witheach other and in series in the 'circuit and resonant at a certain frequency, and each section also consisting of lumpedl inductance and capacity in series with each other andI in shunt to the circuit and resonant to a certain other frequency.

7. A Wave filter for an electric circuit, said filter having a plurality of like recurrent sections, each section consisting of lumped impedance in series with the circuit and lumped impedance of like type adjacently in shunt thereto, one such impedance being resonant at one frequency and the other such impedance being resonant at another frequency.

8. An electr-1c Wave filter'consistlng of a connecting line of negligible attenuation containing lumped impedance in series with the line and lumped impedance pf like type in shunt 'across the line, said impedances having precomputed values dependent upon the upper limiting frequency and the lower limiting frequency of a range of frequencies itmis desired to transmit Without attenua-A ing frequencies.

Y9. Anelectric wave filter consisting of a approxiline composed of a plurality of sections, each section including a condenser and an inductance coil constituting an impedanceI in series with the line and a condenser and an inductance coil associated in like manner and constituting an impedance in shunt across the line, said condensers and inductance coils having precomputed values dependent up`on the upper limitingffrequency andthe lower limiting frequency of a range of frequencies it is desired to transmit Without attenuation, the lvalues of said` condensers and said inductance coils being so proportioned that the structure transmits with practically negligible attenua-tion sinusoidal currents of all frequencies lying between two limiting frequencies, While attenuating and approximately extinguishing currents of y`neigh,boring frequencies lying Outside of said limiting frequencies.l

In testimony whereof, I have signed my name to this specification this 23rd day of April, 1920.

WILLIAM H. MARTIN,

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