US1568141A - Frequency selective circuits - Google Patents

Description

Jan. 5 1926. 1,568,141

H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 15, 1920 3 Sheets-Sheet 1 [1190mm .A arz'o'ua Positive y)? INVENTOR ATTORNEY Jan. 5 1926. 1,568,141

H. w. ELSASSER FREQUENCY SELECTIVE CIRCUI TS Filed August 13, 1920 3 Sheets-Sheet 2 w M m 6' 3V6. c, :EVQ 6 I [p INVENTOR ATTORNEY Jan. 5 1926.

H. w. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 13, 1920 3 Sheet's-Sheet 3 figiljmmel' ATTORNEY mama Jon. 5-, 1m

UNITED STATES ma W. nmsaln, 0! m YORK, 17. Y.,

ABSIGNOB TO AMERICAN Tm AID mnomx comm; a coarom'rron or NEW YORK.

name! mnc'rm moons.

Application filed August 18, 1020. Serial No. 403,367.

To all whom it may cmwern:

Be it known that I, HENRY W. Emassnu, a citizen of the United States, residing at New York, in the county of New York and State of New York, have invented certain Improvements in F1 uency Selective Circuits. of which the fol owing is a specification.

This invention relates to frequency-selective circuits.

It contemplates a network of impedances having a period of series resonance and a period of parallel resonance, so that its impedance for a certain frequency of current is very low and for another, very high.

The invention pro ses, further, the use of a. network of this 0 aracter in combination with other impedance elements in a periodic structure of the type illustrated and described in the patents to G. A. Campbell, 1,227,113 and 1,227,114 of May 22, 1917. Certain new and useful types of wave filters are thus arrived at, the characteristics of which are explainedhereinbelow.

This application is related to certain copending cases, Serial Numbers 403,368, 403,- 369, 403,370, filed of even date herewith.

A good understanding of the invention may now be had from the following description' of certain specific embodiments thereof, having reference to the accompanying drawing, in which,

Figure 1 1s a diagrammatic view showing one form of network-embodying the invention,

Figs. 2 to 5 inclusive,- are di ammatic views showing varlous types of ters comprising the network of Fig. 1,

Fig. 1 is a graph showing the variation with a frequency in the impedance of the network of Fig. 1, and

Figs. 2 to 5", inclusive are gra hs showing the variation in attenuation of t e filters of Figs. 2 to 5, respectively.

Similar characters of reference designate similar parts of the several views.

The network of Fig. 1 consists of a condenser C in series with a pair of parallel paths, one of which contains an inductance L, and the other of which a condenser (1,. The impedance of the condenser G, is-

f being the frequency of the current. The

impedance of the parallel resonant path is 10L, 1 wiry-w, (1)

Place for convenience where f, is the frequency at which L and C, are resonant. Substitute equation 2 in equation 1 and simplify. Then where The expression in the brackets of the above equation may be placed equal to K. Then where The variation in the value of K with frequency is shown by the curves of Fig. 1*, in which the valuesof K are ordinates and the ratios of to' f, are abscissee. These curves indicate the manner in which the impedance of the network changes with frequency, as may be seen by an inspection of equation 4. At low frequencies the impedance of the network is negative, but as the frequency is raised, the impedance changes from negative to positive, the point of crossing of the axis of abscissae denoting series resonance of C and the combination of G, and L or zero impedance of the network. The impedance then increases until, at the frequency at which L, and O, are in arallel resonance its value is infinite. The impedance t on chan s sign and thereafter decreases, Tapproac ing zero at infinite frequency. 6

network, therefore, has two periods of reso- 11o nance, a period of series resonance at one frequency and a period of parallel resonance at a higher fre uency. The period of parallel resonance depends on the relative value 6 of only two impedance elements, namely L and O and the period of series resonance is governed by the values of all three reactances. The curves of Fig 1 are drawn for an ideal network containing no resistance or other dissipative elements, but in an actual case, the resistance may be made so small that its efiect is practically negligible. It thus a pears that the network of Fig. 1 may e used as a selective circuit for passing current of series resonant frequency and preventing the passage of current of parallel resonant frequency.

I have found, moreover that by employing the network as a shunt and series impedance in a periodic structure like that discussed in the Campbell patents hereinbefore mentioned, certain new types of wave filters are arrived at, which filters have certain new and valuable characteristics which I shall 95 now describe.

Figs. 2, 3, 4 and illustrate four types of filters employing the network of Fig. 1, the first two of these views showing the network as a shunt impedance element and the last two as a series impedance element of the filter section. Figs. 2 and 3 show an inductive and a capacity reactance, respectively as the series impedance element, and Figs. a and 5 show the same reactances, respectively, as the shunt impedance element.

The properties of the above filters may be determined from certain mathematical expressions which set forth the relations existing between the frequency of current and the impedance elements of the filters. In the Campbell patents hereinbefore mentioned, it was shown (equation 2) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z and the shunt impedance per section is Z the attenuation per section of the filter may be derived from the relation cosh '=1/2 +1 (6) naeem in which denotes the propagation constant of t e structure. The variation of the attenuation of any filter with frequency of current may, therefore, be deduced from equation 6, when the corresponding values of Z and Z are substituted therein. For the filter shown in Fig. 2, the value of Z, is

2 is a graph showing the variation of the attenuation of the filter of Fig. 2, as computed from equation 9. The axis of the abscissae is laid ofi in ratios of f to f and the axis of the ordinates in values of the attenuation constant per filter section. An inspec-- tion of the curves shows that the attenuation is nil for two ranges of frequencies, f, to f, and f, to f,. The filter, in other words,passses Without attenuation, only such frequencies as lie below 7, or between f and f,. It is, therefore, a combined low-pass and band filter and performs the functions of both. It is characterized, moreover, by having infinite g5 attenuation at a frequency f which is close to f,, and it discriminates, consequently, with particular sharpness against frequencies just above the upper limit of the lowpass range.

The frequencies f f and f, may be evaluated as follows: it was shown in the said Campbell patents, that for unattenuated transmission, must be a pure imaginary, and that, therefore, the value of cosh must lie between *1. The frequencies which limit the ranges of free transmission may consequently be determined by placing equation 9 equal to +1 and 1 respectively, and solving for 7. When this is done, it will be found that the roots are respectively,

Lee a z L202 4 4) 16 214 C;

is infinite, may be evaluated by placing nation 9 equal to co and solving f,

.WODOQ i 1 -r m/ The attenuation characteristics of the remaining filters may be arrived at in a similar manner, The curves of Fig. 3

show that the filter of Fig. 3 passes without substantial attenuation only a single band, the limiting values of-which are 1 and f The filter is further characterized. y having infinite attenuation per section at a freuency f below f This frequency may be 'c osen within the lower attenuated range, but preferably so as to lie close to f ,.so

' that the filter has a sharp cut-ofi at the lower limit of the transmitted band.

The frequencies f f,,, and f... may be evaluated similarly as the limiting frequencies'of the filter of Fig. 2. The expression for cosh in the present case is, since Z is acapacity reactanoe,

cosh P a/2 m 14 By placing equation 14 e ual res tively to' +1 and -1, simplifying, and solving for f, the roots will be found to be i which is similar to equation9 exce t that 1 Tm When nation 14 is placed equal to co and solved or f, the frequency of maximum attenuation, f.,,, is found to be derived from the expression.

cosh f" 1/2 the value of Z and Z are interc anged, the shunt impedance of Fig. 2 being the series im ance of Fig. 4, and vice, versa. The limltin frequencies are obtained, as before, by p acing cosh equal to +1 i pd -1 respectively and solvlng for f.

enoe

1' 1 fI- T +6 The expression for the frequency of maxiinum attenuation, f is obtained by placing c lsfih equal to on and solving for f.

. 1 r 22 mitt The curves of Fig. 5 show that the filter of Fig. 5 is of the single band type and similar to that of Fig. 3, difiering therefrom, however, in that the frequency of infinite attenuation lies in the u per attenuated range. This filter, may caused to have a sharp cut-ofi at the upper limit of the band. The attenuation curve of Fig. 5 is derived from the expression,

and the values of f and f and f are obtained by placing the above expression for cosh equal to +1 and 1 and co, respectively:

It should be noted that the attenuation curves herein illustrated refer to the ideal structure in which the resistance of the im pedance units is zero. In a practical filter there is a departure from these curves, owing to energy dissipation. In any case, however, the resistance may be madeso small that the departure from the ideal .is practically negligible.

The formulae 1013, 15-17, 19-22, and 2e25, given above, may be used in designing filters to meet any specified sets of conditions. Since there are four independent impedance elements in each filter section,

any four properties of the filter dependent upon the values of the impedance elements but independent of each other may be chosen at will. For example, in the design of a filter of the type illustrated in Fig. 2, two of. the design conditions may be taken as the frequencies f, and f and the third as f thus defining the ranges of free transmission. This leaves one condition open to choice, and this may be taken as the impedance of the filter at any desired frequency, or as the value of any one of the elements of the filter section. In the design of a filter of the type of Fig. 3, two of the design conditions may be chosen as the frequencies f and f and the third as 7%,, thus wearer leaving the fourth to be chosen in accordance with any other condition that may prevail. Similar considerations apply to the remaining types of filters.

As an example of the application of the formulae, let it be re uired to design a filter of the type illustrate in Fig. 3, which shall transmit frequencies between 4:00 and 2500 cycles, and which shall have maximum, ideally infinite, attenuation at 360 cycles, so that it has a particularly sharp out-ofi at the lower limit of the freely transmitted range. Frequencies f f and f are thus specified as 400, 2500 and 360 cycles respectively. As a fourth design factor let it be assumed that certain considerations dictate that the value of L shall be .5 henry. Applying formula (16), we find that 0 1100810 microfarads. Substituting in (17) we have hence hence Therefore C =.398 microfarads.

All the constants of the filter are thus determined. It will readily be seen that, instead of-the above-mentioned set of conditions, any others involving 'the filter impedances may be imposed, it being understood that the above example is merely a simple illustration, and in no way limits the invention.

Although only certain forms of filters embodying the invention are shown and de-' scribed herein, it is readily understood that various changes and modifications may be made therein within the scope of the following claims, without departing from the spirit and scope of the invention.

What is claimed is: H

1. A wave filter of the type having like recurrent sections and in which each section consists of a series element and a shunt element, one of these elements consisting of a capacity reactance in series with a plurality of paths in parallel with each other, one of said paths comprising inductive reactance and the other of said paths comprising capacity reactance.

2. A wave filter of the type having like recurrent sections and in which each section consists of a series element and a shunt element, one of these elements consisting of a reactance in series with a plurality of paths in parallel with each other, one of said paths comprising inductive reactance and the other of said paths comprising capacity reactance.

3. A filter for an electric circuit, consisting of an impedance in series with the circult and an impedance in shunt thereto, one of said impedances consistin of a single reactance element and the ot er of a network comprising a capacity reactance in series with a pair of parallel paths, one of which consists of a capacity reactance and the other of an inductive reactance.

4. A filter for an electric circuit consisting of an impedance in series with the circuit and an impedance in shunt thereto, one of said impedances consisting of a single reactance element and the other of a network comprising a reactance in series with a pair of parallel paths, one of which consists of a capacity reactance and the other of an inductive reactance. k

5. The method of discriminating among alternating current components according to their frequency which consists in passing currents of frequency from zero to a certain finite frequency, then attenuating currents of higher frequency1 up to another certain finite frequency wit a maximum of attenuation close to the lower of these two frequencies, and then passing currents whose frequency ranges from the upper limiting frequency previously mentioned to a thir 10 frequency still higher and attenuating all currents of frequency higher than the last mentioned f uency.

6. A wave ter of the type having like recurrent sections and having a series ele- 6 ment and a shunt element in each section, 'said filter embodying means in said elements to provide two separate ranges of frequencies for free transmission, one lying between finite boundin frequencies and the other bounded by a i nite frequency and extending thence over the whole remaining frequency range on that side.

7. A wave filter of the type having like recurrent sections and having a series element and a shunt element in each section,

said filter embodying means in said elements to provide two separate ranges of frequencies for free transmission, one lying between finite boundin frequencies and the other range lyin be ow the first mentioned range and exten ing between a finite frequency and zero.

8. A filter of recurrent sections having 1 four reactances in each section and iving two free transmission bands, one band having bounds at finite frequencies, the other extending from another finite frequency bound over the whole frequency range on that side, the values of the reactances being determined as functions of the said three finite bounding frequencies and of the characteristic impedance of the filter at the extreme of the free transmission range for which there is only a single finite frequency bound.

In testimony whereof, I have signed my name to this specification this 10th day of August, 1920.

HENRY w. ELSASSER.

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