Title:
Electric filter circuit
United States Patent 2298177


Abstract:
This invention relates to electrical filters with particular regard to improving the degree of attenuation at a predetermined frequency or predetermined frequencies. The principal object of the invention is to improve the performance of resistance-capacitance filters used for smoothing the...



Inventors:
Hosmer, Scott Hermon
Application Number:
US27572139A
Publication Date:
10/06/1942
Filing Date:
05/25/1939
Assignee:
GEN RADIO CO
Primary Class:
International Classes:
H03H7/06
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Description:

This invention relates to electrical filters with particular regard to improving the degree of attenuation at a predetermined frequency or predetermined frequencies.

The principal object of the invention is to improve the performance of resistance-capacitance filters used for smoothing the output of rectifiers by increasing the attenuation in the low-frequency region. According to this invention, the attenuation of such a filter may be made substantially infinite at any predetermined frequency, and this predetermined frequency may be varied by merely varying one resistance in the filter network.

Other important objects of the invention are to provide a peak of very high or substantially infinite attenuation in the characteristic of any type of filter circuit through the addition of a relatively simple auxiliary circuit or network, which in many cases may consist of only a single resistance. A further object is the provision of filters for power-supply smoothing or other purposes, having a high degree of suppression but containing no inductances, thus eliminating undesirable resonance effects or magnetic interaction between the inductances and other electrical equipment.

A brief inspection of the diagrams will disclose similarities in general arrangement to circuits which have been used in the prior art. It should be noted, however, that the auxiliary networks or resistors shown in the diagrams are of a different order of magnitude compared to the other circuit elements and perform a different function than in the prior art circuits. Resistors have been used in connection with filter circuits to compensate for losses in the other circuit elements. In the circuits constructed in accordance with this invention some of the resistors or auxiliary networks or circuit elements may perform this function to a certain degree, but the main object of their inclusion in the circuits is to provide a peak of very high or substantially infinite attenuation which, in contrast with the prior art circuits, would not be present without the inclusion of these auxiliary networks or circuit elements, even though all other circuit elements had no losses whatsoever.

Some of the applications for which this invention is best suited have previously been met by the use of a so-called parallel-T network, which consists essentially of two resistance-capacitance filters connected in parallel, one of the filters being of the high-pass type and the other of the low-pass type. In contrast to this prior art circuit, a circuit according to this invention comprises essentially two filters of like character, that is, high-pass, low-pass, etc., connected in parallel or one filter connected in parallel with an all-pass network.

The invention will be described in connection with the diagrams, of which Fig. 1 represents a particular and preferred application, providing partial balance in accordance with this invention. Fig. 2 is a diagram of a modified similar circuit, which provides complete balance. Figs. 3 and 4 are further simplified diagrams indicating circuits which will provide, respectively, partial and complete balance according to this invention. Figs. 5 and 6 show the difference in operation between circuits constructed according to this invention and similar circuits from the prior art but lacking the particular features of this invention.

Fig. 7 is an elementary block diagram illustrating the principle upon which the invention operates. Fig. 8 shows a circuit which may provide balance at all frequencies, and Fig. 9 shows how interaction between the two parallel transmission paths, which are required by this invention, may be eliminated if desired. Figs. 10 and 11 show diagrams of a character similar to I and 2, respectively, or to 3 and 4, respectively, but involving other arrangements of circuit ele:;0 ments including inductances. Figs. 12 and 13 show arrangements similar to Figs. 3 and 4, respectively, but with the substitution of a second network in place of the single balancing resistor.

Figs. 14 and 15 show high-pass circuits compris:;, ing resistors and condensers. Fig. 16 presents the invention in a more elaborate application involving more complex filter structures, in order to illustrate the broad application of the invention. Fig. 17 shows the application of the invention to a high-pass filter.

Referring to Fig. 3 and neglecting resistor 10, the circuit consisting of series resistors II, 12, and 13 and parallel condensers 21 and 22 presents a common type of low-pass filter which may be used for power-supply smoothing or other applications. The most serious disadvantage of a filter of this type is that the resistance of the series arms I , 12, and 13 must be kept high compared to the impedance of condensers 21 and 22 at frequencies where substantial attenuation is required. This results in appreciable attenuation of those frequencies which it is desired to transmit and, in particular, in the case of powersupply smoothing filters it results in a voltage 5 drop through the filter which may, in many cases, be serious. As the current-handling requirements of the filter are increased, it therefore becomes necessary to decrease the size of the resistors 11, 12, and 13 and to increase the size of capacitors 21 and 22 in order to provide adequate filtering while maintaining an acceptably low direct-current voltage drop through the filter. The use of electrolytic capacitors has made practical the use of this type of filter in many applications where the cost or size of other types of capacitors has hitherto been prohibitive.

The filter shown in Fig. 3, however, providing connecting leads 47 and 48 are opened so that resistance 10 is left out of the circuit, has a frequency characteristic like curve a in Fig. -that is, the attenuation increases as the frequency increases. In contrast to this, the ripple voltage on the output of the rectifier generally has its strongest components in the low-frequency region, and the higher-frequency components are present at only relatively low amplitudes. In order to produce the lowest effective ripple voltage on the load, therefore, it is desirable to use a smoothing filter having ite a maximum attenuation in the low-frequency region.

The applicant has discovered that by adding the resistance 10 to the circuit, as shown in Fig. 3, this result may be obtained at a low cost and without other necessary changes in the circuit.

The circuit shown in Fig. 3, including the resistance 10, has an attenuation characteristic of the general shape shown by curve b in Fig. 5.

The inclusion of resistance 10 provides two separate transmission paths between the input circuit and the output circuit of the filter, which 3 circuits consist respectively of leads 41 and 42 and leads 43 and 44. In order to provide the desired results, resistance 10 should be so proportioned that the voltage transmitted through it between the input circuit and the output cir- 4 cuit should be approximately equal in magnitude to the voltage transmitted through the main section of the filter 2 at or near the frequency , which represents the peak of maximum attenuation caused by the addition of this resistor. For 4 conditions of good filtering, the impedances of the shunt arms of the illustrated ladder-type network, whether low-pass or high-pass filters are considered, must be low compared to the impedances of the series arms. When the two trans- 51 mission paths through the parallel-connected networks, namely, the ladder network and the resistor 10, are terminated together in the output circuit according to this invention, furthermore, the actual attenuation through each path at the 5. null frequency must be equal in magnitude.

In actual practical circuits, therefore, it follows that the resistance of the resistor 10 must be large compared to that of each of the seriesresistive arms 11, 12, 13, etc., of the ladder-type 6C low-pass filters illustrated, for example, in Figs. 1 and 3. In the case of the high-pass filter, illustrated, for example, in Fig. 14, the resistance of the resistor 10 must similarly be considerably higher than that of the capacitive series arms 65 111, I12 and 150. It follows also that the resistance of the resistor 10 will be considerably higher than the total resistance of the series arms of the ladder network.

Because of the phase-shift characteristics of 70 the main section of the filter 2 as compared to the auxiliary parallel transmission path through resistance 10, there will be a net difference between the voltages transmitted through these paths of approximately 180 degrees. The equal 75 voltages transmitted through these paths will oppose each other due to this phase difference, with the result that transmission at the predetermined frequency f is substantially cancelled.

It is obvious that for the correct phase relationship to take place in the circuit shown in Fig. 3 the condensers in the shunt arms 21 a nd 22 must have a low impedance with respect to the resistors in the series arms II, 12, and 13 at the frequency i. In many practical cases this condition does not exist due to practical limitations in the size or cost or other characteristics of the circuit components. Under such conditions the phase shift through the main filter 2 may not be sufficient to provide satisfactory cancellation of transmission at frequency f. The circuit shown in Fig. 4 indicates how the invention may be applied to this condition also. In contrast to Pig. 3, the circuit shown in Fig. 4 includes the additional condenser 23 and the resistance 52. The function of these components is to provide the additional phase shift necessary at frequency f so that the voltage transe mitted through the main section of the filter 2 and the auxiliary parallel transmission path 10 will oppose each other by exactly 180 degrees, thus providing complete cancellation and infinite attenuation.

10 It will be seen, therefore, that, in accordance with this invention, the circuits shown in Figs. 3 and 4, which would, without the inclusion of resistance 10, have an attenuation-versus-frequency characteristic similar to a in Fig. 5, have, by ;3 the inclusion of resistance 10, been made to have an attenuation-versus-frequency characteristic similar to curve b in Pig. 5. In contrast to prior art circuits having a similar diagram, the inclusion of resistance 10 has produced a 0 type of characteristic entirely different from that of the circuit without this resistance. In case the capacitances in the network arms have appreciable losses or residual capacitance or inductance, the values of resistances 10 and 52 may 5 be varied somewhat from the values which would be used in case all of the other circuit elements were perfect. Such compensation would, however, be only an incidental function of these resistances, their main purpose being to produce )a type of attenuation-versus-frequency characteristic which the main section of the filter 2 would not otherwise possess, even though all of its component parts were perfect and had no losses. Also, the addition of resistance 10 actu5 ally lowers the IR drop through the circuit at direct currents.

In connection with the invention, it should be noted that in the case of Fig. 3 the frequency of the peak attenuation-that is, f-may be varied by merely varying resistance 10. In the case of Pig. 4, either resistance 10 or resistance 52 may be used to vary the frequency I over a narrow range, while simultaneous variation of both resistances will produce a variation over wide ranges of frequency.

Figs. 1 and 2 illustrate typical applications of the principles of this invention in a filter for smoothing the output of a rectifier. In such an application it is generally desirable to have the frequency of maximum attentuation f coincide approximately with the strongest component in the ripple frequency, which is generally equal to the line frequency in case a half-wave rectifier is used or twice the line frequency in case a fullwave rectifier is used. Of course, other consid2,29 erations regarding the amplitude and frequency of the ripple components which can be tolerated at the load may sometimes govern the choice of the filter characteristics.

It will be noted that the circuits shown in Figs. 1 and 2 include in the section marked 2 an input condenser 20 and an output condenser 25. These are not essential to the functioning of the invention and do not, in general, affect the balance at frequency /, but are included for reasons peculiar 1 to the application. In regard to condenser 20, inclusion of such a circuit element across the output circuit of a rectifier is conventional practice, to provide a higher direct output voltage for a given transformer voltage in the rectifier. 1 Also, condenser 25 is generally desirable to provide a low-impedance by-pass across the connecticns between the load and the rectifier. Also, both condensers 20 and 25 function to increase the attenuation of higher harmonics. e Curve a in Fig. 6 shows the general attenuation characteristic of filter circuits as designated by 2 in Figs. 1 and 2 without the inclusion of the resistances designated as 10. In contrast to curve a in Fig. 5, curve a in Fig. 6 has a steeper 2 slope dued to the additional capacitances 20 and 25. The addition of the resistance 10 to these circuits produces the characteristic shown by b in Fig. 6, which, because of the inclusion of condensers 20 and 25, has an improved attenuation 3( characteristic at the higher frequencies when compared with curve b in Fig. 5.

In Fig. 2 resistance 52 is shown as a part of series resistance 14. The exact value of 52 may be adjusted by varying a slider or tap 49 on re- 3; sistance 14. It will be noted that, with the exception of the resistance 10, the filters shown in Figs. 1 and 2 are of the conventional resistancecapacitance coupled type and that the inclusion of resistance 10 provides an extremely simple 4C and inexpensive means of improving the performance of these filters. The inclusion of resistance 10 also allows the lowering of the series resistances in the filters, with a consequent decrease in the direct voltage drop, or a lowering 4t of the capacitance of the shunt condensers, which has various economic and practical advantages, while still maintaining a high degree of suppression to the ripple components.

An analysis of the circuits shown in Figs. 1, 60 2, 3, and 4 indicates that the condition of balance is obtained at that frequency where the transfer impedances of the two parallel transmission circuits are equal in magnitude but opposite in sign. Transfer impedance is defined 55 as the ratio of the input voltage of a circuit to the current flowing in the output circuit, providing the output circuit is short-circuited. In Figs. 1 and 4, inclusive, the two parallel transmission paths consist of the filter circuits desig- 60 nated as 2 and the resistances designated as 10.

An analysis of the circuits in Figs. 1 and 3 indicates that an approximate condition of balance can be obtained, and the degree of suppression at the frequency f is satisfactory for most prac- 65 tical applications. An analysis of the circuits shown in Figs. 2 and 4 indicates that a complete balance may be obtained, so that the attenuation at frequency / will be substantially infinite.

Choice between the conditions of absolute and 70 approximate balance will in practice depend upon practical and economic considerations.

Fig. 7 shows a further analysis of the principle of the invention and presents it in a somewhat broader form than in the foregoing diagrams. 75 In Fig. 7 network B corresponds to the main filter which has been designated as 2, while network A corresponds to the auxiliary parallel transmission path which has been designated as 10. In the broadest scope of the invention these networks or filters may be of any desired construction, including resistances, capacitances, inductances, and transformers. For the purposes of describing this invention the word "filter" is 0 used to designate a network having transmission which varies with frequency.

In accordance with this invention, both of the networks or transmission paths should have transmission characteristics which vary with fre5 quency in the same sense through that range of frequencies in which the peak of attenuation obtained by means of this invention is located, or, as an alternative, one of the transmission paths may have constant transmission at all fre0 quencies within said range. In most practical cases, therefore, the networ th toks or parallel transmission paths should have similar transmission characteristics, the word "similar" in this case being intended to indicate that both circuits be 5 high-pass, low-pass, band-pass, or band-elimination filters or networks, excepting in the case where one path may be a filter and the other an all-pass network. It is also possible, in accordance with this invention, to combine a high- or 0 low-pass filter with a band-pass or band-elimination filter in order to obtain the desired results.

In any case, in order to provide operation in accordance wtih the principles of this invention a peak in attenuation or a point of infinite at5 tenuation may be obtained by operating the two networks as parallel transmission paths, and this peak may occur at a frequency where no peak exists in the characteristic of either network alone. In order to provide this result it is essential that the attenuation in the two filters should be equal in magnitude but that the phase shifts should differ sufficiently to provide cancellation of the output voltages of the networks. In accordance with the invention, therefore, it is obviSous that the phase shifts in the two filters should be in the same sense or equal to zero.

Assuming that at frequency I the attenuation in filter B is equal to aB and the phase shift is equal to oB, and assuming that the attenuation in network A is equal to UA and the phase shift equal to OA, the condition of exact balance will be obtained when !A-- AB and OA--OB=±+1800+3600 This condition provides an exact balance and consequently gives infinite attenuation at the frequency / where these conditions are obtained.

As previously mentioned, this condition of exact balance is not always required by the dictates of the application. An approximate degree of balance can be obtained when MPA-= approximately and OA-OB=-±1±_360o where o is any angle between 90 and 270 degrees.

Figs. 8 through 17 show various circuit arrangements where these conditions are obtained in accordance with this invention. In Fig. 8 the two filters A and B may be exactly alike, but are not necessarily so, and the transformer 57 is used to obtain the proper phase reversal. Condensers 55 and 56 are included in the circuit merely to prevent direct current from flowing through the windings of the transformer, which would be disadvantageous in many applications. If filters A and B are identical and transformer 57 is an ideal transformer, and if condensers 55 and 56 are large enough in capacitance so that their effect on alternating currents flowing through the circuit may be neglected, the circuit shown in Fig. 8 provides complete balance at all frequencies.

Such an arrangement is advantageous in powersupply smoothing applications, where complete 1 suppression of all alternating components is required, and only the direct current should be transmitted through the circuits.

It is obvious that in some cases the effect of filter A upon filter B or of network A upon net- i, work B caused by either the input or output circuits of these networks or filters being connected in parallel may affect the overall result. It is generally most economical to design the networks or filters with this in mind, so that, as, for in- 2( stance, in the cases of the circuits shown in Figs. 1, 2, 3, 4, and 7, the input and output circuits of the networks or filters may be connected directly in parallel. It is appreciated, however, that sometimes it is undesirable or uneconomical to design the filters or networks with this in mind, and some arrangement such as that shown in Fig. 9 may be necessary. In Fig. 9 amplifiers or isolation networks C and E are connected in the input and output circuits, respectively, of filter A, while amplifiers or networks designated as D and F are connected, respectively, in the input and output circuits of filter B. The amplifiers and networks C, D, E, and F are so designed that the characteristics of filter A have no effect upon filter B, and vice versa. It is obvious that Fig. 9 represents an extreme case, employing, as it does, four separate amplifiers or networks. In most practical applications one or more of these could be eliminated. The exact number required would, of course, depend upon the characteristics of filters A and B and upon the circuits with which they were to be used.

Figs. 10 and 11 show further variations of the invention, in which the main filter designated as 2 contains inductances as well as other types of circuit elements. In either case the addition of resistance 10 to the main filter 2 will produce a peak in attenuation which is not present in the characteristic of the filter 2 when used by itself, even though all of its circuit elements are perfect. In accordance with the invention, the filters or networks designated by 2 in the figures may consist of any desired combination of resistances, capacitances, and inductances, but need not consist of more than two of these types of circuit elements.

Many of the diagrams show the auxiliary transmission path 10 as merely a single resistance, since this presents the invention in one of its simplest and most practical forms. It is important, however, to remember that this auxiliary transmission path may consist of a more elaborate network or filter, the only requirements being that it meet the conditions in regard to transmission characteristics and phase shift previously set forth in this specification. Fig. 12, for instance, presents a circuit similar to Fig. 3, but with the important difference that 10 has been changed to a second network. Such an arrangement is sometimes desirable where better attenuation characteristics are desired at frequencies other than I. Similarly, Fig. 13 is much the same as Fig. 4, excepting that again resistance 10 has been replaced by network 10. In the cases of Figs. 12 and 13, the networks designated by 2 contain additions over the corresponding networks in Figs. 3 and 4, respectively, in order to provide the proper phase shifts in accordance with the conditions of approximate or complete balance, as previously set forth.

Figs. 14 and 15 show two typical high-pass arrangements involving resistors and capacitors, 0 although the circuit is not necessarily limited to these types of circuit elements. Because of the simplicity and low cost of resistances and capacitors as compared to inductances, however, and also the freedom from magnetic pick5 up which is a natural result of the elimination of inductances, filter circuits of the type shown in these diagrams are frequently of great value.

In either case, as in the previous figures, the addition of the auxiliary parallel transmission 0 path 10 provides a substantial null point in the transmission at a predetermined frequency. It will be obvious that the circuits shown in Figs. 14 and 15 are similar, respectively, to those shown in Figs. 3 and 13, but represent high-pass Scases. In this same manner the principle of the invention may be applied to any type of filter or frequency-discriminating network.

Fig. 16 presents a more elaborate arrangement than that shown in some of the previous diaSgrams in that an amplifier or network is included to provide isolation between the filter circuits and the proper relative level of transmission between the two filters. Some of the filter sections shown in Fig. 16 are of the Mderived type, which in themselves would provide a peak in attenuation. In accordance with the invention, however, the combination of filters A and B will produce in the net transmission characteristic a peak in attenuation which does not necessarily coincide with any of the peaks in the characteristics of the filters if they were used singly.

Fig. 17 shows a further modification of the invention, in which the proper phase relationship is obtained by means of capacitances. This particular circuit is of the high-pass type and consists essentially of the high-pass filter 2 and the auxiliary parallel transmission path 10.

It is understood that all of the circuits shown in the diagrams which do not contain unidirectional circuit elements, such as some types of amplifiers, will operate in either direction-that is, leads 41 and 42 may be considered as the input circuit and leads 43 and 44 may be considered as the output circuit, or leads 43 and 44 may be considered as the input circuit and leads 41 and 42 may be considered as the output circuit. Similarly, although the circuits present, in general, networks of the type commonly referred to as unbalanced, since all of the series elements are connected in one side of the circuit, the corresponding balanced circuits could also be used by merely dividing the series circuit elements equally between the two sides of the circuit. It should also be pointed out that, outside of those points in the circuit where the two parallel transmission paths are connected together, the existence of additional circuit elements does not affect appreciably the transmission at the point of balance, in accordance with this invention, but merely affects the transmission at other frequencies. For instance, in Fig. 17 capacitance 51 could be short-circuited and coil 39 opened without affecting the balance at frequency /, where substantially infinite attenuation occurs.

What is claimed is: 1. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

2. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

3. An electric filter having a peak of high 3 attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a 4 ladder-type network having capacitive series arms and resistive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor 4 and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency. 51 4. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, 5, one of the transmission paths comprising a ladder-type network having capacitive series arms and resistive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the 6( total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at (;, the said frequency.

5. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

6. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path comprising a resistor the resistance of which is large compared to the total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

7. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in ,0 parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms !5 being capacitive, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms 0 having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency, and means for varying the resistor to vary the said frequency.

5 8. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, 0 one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of 5 each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said Sfrequency, and means for varying the resistor and the resistance of one of the resistive series arms to vary the said frequency.

9. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency, and means for varying the circuit elements of the filter to vary the said frequency.

10. An electric filter having a peak of high attenuation at a predetermined frequency and provided with two circuits, namely, an input circuit and an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor connected between one of the said two circuits and an intermediate point of one of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

11. An electric filter having a peak of high attenuation at a predetermined frequency and provided with two circuits, namely, an input circuit and an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor connected between one of the said two circuits and an intermedaite point of one of the series arms, the resistance of the resistor being large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

12. An electric filter having a peak of high attenuation at a predetermined frequency and provided with two circuits, namely, an input circuit and an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor connected between one of the said two circuits and an intermediate point of one of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency, and means for varying the position of the intermediate point to vary the said frequency.

13. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel di- ( rectly to the input and output terminals, one of the transmission paths being constituted of a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of C arms being capacitive, and the other transmission path being constituted of a resistor, the resistor and the resistive arms having resistances and the capactive arms having capacitances such that the attenuation characteristic of the filter 7 contains the said peak of high attenuation at the said frequency.

14. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and 7 two transmission paths connected in parallel directly to the input and output terminals, one of the transmission paths being constituted of a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being lesistive, the other set of arms being capacitive, and the other transmission path being constituted of a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

15. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths being constituted of a ladder-type network having two sets of arms, namely, series arms and shunt arms, the terminal series arms being connected directly to an input terminal and an output terminal, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path being constituted of a resistor connected directly to the said terminal series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

16. An electric filter having a peak of high attenuation at a predetermined frequency and provided with two input terminals, two output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, the terminal series arms being respectively connected to one of the input terminals and one of the output terminals, the shunt arms being connected directly to the other input terminal and the other output terminal, and the other transmission path comprising a resistor connected directly to the said one input terminal and the said one output terminal, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

17. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two l0 transmission paths connected in parallel between the input and output terminals, one of the transmission paths being constituted of a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path 5 being constituted of a resistor having two terminals one of which is connected directly to an input terminal and the other of which is connected directly to an output terminal, the resistor and the resistive arms having resistances and the ca'0 pacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

18. An electric filter having a peak of high at5 tenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths being constituted of a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path being constituted of a resistor the resistance of which is large compared to the total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

19. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor having two terminals one of which is connected directly to an input terminal and the other of which is connected to the series arm most remote from the input terminals, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency. 20. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor having two terminals one of which is connected directly to an input terminal and 40o the other of which is connected to the series arm most remote from the input terminals, the resistance of the resistor being large compared to the total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

21. An electric filter having a peak of high attenuation at a predetermined frequency and provided with input and output terminals, and two transmission paths connected in parallel between the input and output terminals, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor having two terminals one of which is connected directly to an input terminal and the other of which is connected adjustably to the series arm most remote from the input terminals, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak 05 of high attenuation at the said frequency.

22. An electric filter having a peak of high attenuation at a predetermined frequency and provided with two circuits, namely, an input circuit and an output circuit, a condenser shunted across the input circuit, a condenser shunted across the output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having resistive series arms and capacitive shunt arms, and the other transmission path comprising a resistor having two terminals one of which is connected to one of the said two circuits and the other of which is connected adjustably to one of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

23. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

24. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by between 90 and 270 degrees plus or minus 360 degrees, the attenuation characteristic of the combined transmission paths containing the said peak of attenuation at the said frequency.

25. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by substantially 180 degrees plus or minus 360 degrees, the attenuation characteristic of the combined transmission paths containing the said peak of attenuation at the said frequency.

26. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by between 90 and 270 degrees plus or minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

27. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and havinI at the said frequency phase shifts in the samn sense differing by substantially 180 degrees pluý or minus 360 degrees, the resistors having resist. ances and the capacitors having capacitance, such that the attenuation characteristic of th( filter contains the said peak of attenuation at the said frequency.

28. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a network having substantially constant transmission over a range of frequencies including the said frequency and the other transmission path comprising a network having substantially constant phase shift greater than zero over the said range of frequencies, the attenuation characteristics of the combined transmission paths containing the said peak of attenuation at the said frequency.

29. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a network having substantially constant transmission over a range of frequencies including the said frequency and the other transmission path comprising a network comprising resistors and capacitors only and having substantially constant phase shift greater than zero over the said range of frequencies, the attenuation characteristics of the combined transmission paths containing the said peak of attenuation at the said frequency, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

30. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency similar but not necessarily identical transmission characteristics and phase . shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the attenuation characteristic of the combined transmission paths containing the said peak of attenuation at the said frequency. 31. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, the transmission 6 paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency similar but not necessarily identical transmission characteristics and phase shifts differing by substantially 180 degrees plus 6i or minus 360 degrees, the attenuation characteristic of the combined transmission paths containing the said peak of attenuation at the said frequency.

32. An electric filter having a peak of attenua- 7( tion at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only connected in parallel between the input and output circuits, the transmission paths 7Z g providing at the said frequency substantially the same degree of attenuation and having at the s said frequency similar but not necessarily identical transmission characteristics and phase S5 shifts differing by between 90 and 270 degrees i lus or minus 360 degrees, the resistors having S resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

33. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only connected in parallel between the input and cutput circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency similar but not necessarily identical transmission characteristics and phase shifts differing by substantially 180 degrees plus or minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

34. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two low-pass transmission paths connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the attenuation characteristics of the combined transmission paths containing the said peak of attenuation at the said frequency.

10 35. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two low-pass transmission paths comprising resistors and capacitors only connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or 0i minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

5 36. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, the transmission 0 paths having attenuation varying with frequency in the same sense, providing at the said frequency substantially the same degree of attenuation, and having at the said frequency phase shifts differing by between 90 and 270 degrees 5 plus or minus 360 degrees, the attenuation characteristic of the combined transmission paths containing the said peak of attenuation at the said frequency.

37. An electric filter having a peak of attenua0 tion at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, the transmission paths having attenuation varying with frequency in the same sense, providing at the said frequency substantially the same degree of attenuation, and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

38. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, the transmission paths having attenuation varying with frequency in the same sense, providing at the said frequency substantially the same degree of attenuation, and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency, and means for varying one or more of the circuit elements of the filter to vary the said frequency.

39. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths each comprising a ladder-type network having resistive series arms and capacitive arms connected in parallel between the input and output circuits, the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

40. An electric filter having a peak of substantially infinite attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths each comprising a ladder-type network having resistive series arms and capacitive shunt arms connected in parallel between the input and output circuits, the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of substantially infinite attenuation at the said frequency.

41. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths each comprising a ladder-type network having capacitive series arms and resistive shunt arms connected in parallel between the input and output circuits, the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation chracteristic of the filter contains the said peak of attenuation at the said frequency.

42. An electric filter having a peak of substantially infinite attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths each comprising a ladder-type network having capacitive series arms and resistive shunt arms connected in parallel between the input and output circuits, the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said substantially infinite peak of attenuation at the said frequency.

43. An electric filter having a peak of attenuation at a predetermined frequency and provided 7 with an input circuit, an output circuit, and two high-pass transmission paths connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the attenuation characteristics of the combined transmission paths containing the said peak of attenuation at the said frequency.

44. An electric filter having a peak of attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two 1] high-pass transmission paths comprising resistors and capacitors only connected in parallel between the input and output circuits, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts differing by between 90 and 270 degrees plus or minus 360 degrees, the resistors having resistances and the capacitors having capacitances such that the attenuation characteristic of the filter contains the said peak of attenuation at the said frequency.

45. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit and an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms be33 ing capacitive, and the other transmission path comprising a network having resistance large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

46. An electric filter having a peak of high attenuation at a predetermined frequency and .15 provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having only four resistive series arms and only three capacitive shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the resistor and the resistive arms having resistances ' and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

47. An electric filter having a peak of high at0 tenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the ;5 transmission paths comprising a ladder-type network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path comprising a 0 ladder-type network having capacitive series arms and one or more resistive shunt arms, the total resistance of the last-named series arms being large compared to the total resistance of the first-named series arms, the resistive arms 5 having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

48. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a laddertype network having two sets of arms, namely, series arms and shunt arms, one of the sets of arms being resistive, the other set of arms being capacitive, and the other transmission path comprising a ladder-type network having resistive series arms and one or more capacitive shunt arms, the total resistance of the last-named series arms being large compared to the total resistance of the first-named series arms, the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

49. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a laddertype network having capacitive shunt arms and non-capacitive series arms, and the other transmission path comprising a resistor the resistance of which is large compared to the total resistance of the series arms, the resistor and the resistive arms having resistances and the capacitive arms 3 having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

50. An electric filter having a peak of high attenuation at a predetermined frequency and 4 provided with an input circuit, an output circuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having series arms and shunt arms, and 4 the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by between 90 and 270 degrees plus or minus 360 degrees, the resistor and the resistive arms having resistances and the capacitive arms having capac- 5 itances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

r1 A u±. ni elctrinc flter naving a peak o0 hign attenuation at a predetermined frequency and yl-^/YT,(Artl n,14-^ n« :-r J.·· ^-1---JJ _ _. i- . .

cuit, and two transmission paths connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder-type network having series arms and shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by substantially 180 degrees plus or minus 360 degrees, the resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

52. An electric filter having a peak of high attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, one of the transmission paths comprising a ladder23 type network having series arms and shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the transmission paths providing at the 0 said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by between 90 and 270 degrees plus or minus 360 degrees, the resistor and the resistive arms having S5 resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

53. An electric filter having a peak of high 0 attenuation at a predetermined frequency and provided with an input circuit, an output circuit, and two transmission paths comprising resistors and capacitors only and connected in parallel between the input and output circuits, one of 5 the transmission paths comprising a ladder-type network having series arms and shunt arms, and the other transmission path comprising a resistor the resistance of which is large compared to the resistance of each of the series arms, the 0 transmission paths providing at the said frequency substantially the same degree of attenuation and having at the said frequency phase shifts in the same sense differing by substantially 180 degrees plus or minus 360 degrees, the 5 resistor and the resistive arms having resistances and the capacitive arms having capacitances such that the attenuation characteristic of the filter contains the said peak of high attenuation at the said frequency.

HERMON H. SCOTT.

pov e w an input cir r