US2185389A - Feedback amplifier filter - Google Patents

Description

Jam., 2, w40, H. A. WHEELER FEEDBACK AMPLIFIER FILTER Filed May 9, 1938 2 Sheets-Sheet l INVENTOR you) AWHEELR BY ATTORNEY j. 2, w49. H. A. WHEELER FEEDBACK AMPLIFIER 'FILTER Filed May 9, 1958 2 Sheets-Sheet 2 ATTORNEY Harold A. eeler, Grt Neck, lil.

l., imgnor to `easeltine ilorration, e corporation oi Delaware Application y t, luid, Serial No. 296,71@

, invention relates to signal-inlog vacuum-tube stares and particularly to such stares oi a. type comprisine a feedback circuit in which the ulter properties of the stage are `e utilised to incorporate the stage as one oi a series oi conduent iilter networks. Specically the invention comprises a network in which the inocuo pedance characteristics of the feedback stare are matched in the confluent series oi netiii vvorirs with the image impedance characteristics oi other 1|; z lar etapes or with the image impedance characteristics ci conventional nlter sections.

vacuo-tube stares comprising feed-bach cirii! cuits have been utilised tor various purposes.

r example, in modulated-carrier signal-translutinp systems, stages comprisinp a pair oi terminal circuits and a vacuum-tube coupling means couplinp the terminal circuits in one direction, 2d toeether with an additional coupling means coupiinn the circuits in the opposite directiomhave been utilized as hand-pass selectors in the inter mediate-frequency channel or superheierof.`

sil receivers. in prior art circuit arrangetii ments utilizing an ampliher stare with feedback,

the terminal circuits oi the stage have been indvidually loaded or damped by terminal resistai'ices to provide suitable damping for the stage. hs thus terminated, the ieedbacir stages of the prior it art have had the required damping within the ieedbact stades themselves and have been loosely coupled to adjacent similar stages or to other circuits. li such arrangements are utilized lor passinc a wide band oi irequencies, the width oi the su pass band is limited by the inherent capacitances of the tubes and the circuit elements. Also, the wr or an amplifier comprising such a stage is muterially decreased by the elements provided for individually damping the terminal circuits of the im stese.

it is an object of the invention to provide a ieedbacu vacuum-tube ampliiier and iilter having a relatively large amplification and passing a wide hand oi ireuuencies.

lt is another object of the invention to provide u, conduent filter network comprising a nlter secu tion including a vacuum-tube coupling in one direction and an additional coupling in the other cation, the stage being matched with adjacent 5@ sections oi the network on an image impedance lt is a iurthcrobiect oi. the invention to provide a confluent filter network comprising an active iiitcr section. as contrasted with a-passive ter section, at least one terminal circuit of' (ci. ira-in) l which is matched with an adjacent section of the network on an imase impedance basis.

In accordance with the invention, there is provided a filter section comprising a. vacuum-tube coupling in one direction and an additional cou- ..5 pling in the other direction, at least one terminal circuit of the stage being matched on an image impedance basis with an adjacent terminal circuit oi en adjacent lter section to which the stare is coupled in a confluent network.

In one embodiment of the invention, a hlter section comprises a vacuum-tube amplifier stage including terminal circuits, a vacuum-tube couplinu means coupling the terminal circuits in the iorward direction, and a' second vacuum-tube it coupling means coupling the terminal circuits in the backward direction. The input and output terminals of the stage are individually coupled to circuits having constant-lt image impedances. The terminal circuits of the lter section and the E relative transconductances of the vacuum tubes utilized in the stage are so proportioned that the image impedance at each pair of terminals closely matches the constant-Ic image impedance of the adjacent meer section to which a is directly couit pled. This manner oi coupling the amplier stage to adjacent nlter sections obviates the necessityoi individually loading or damping each oi the terminal circuits of the stage, since the loadine or damping of the entire networlr is adequately secured at the input and output terminals oi the system asa whole. The filter properties of the feedback stage of the invention make it possible to insert-additional filter sections between the stages for any purpose for which they are useful. Added sections may be inserted for securing more attenuation outside the pass band, for securing phase correction within the band, or for both purposes.

In a preferred embodiment of the invention, t0

the vacuum-tube stage comprises terminal circuits coupled in the forward direction by s. vacuumftube transconductance coupling means4 and .coupled in the backward direction by passive conductance or resistanceV coupling means. et i phase-shifting circuit may beassociated with. the backward coupling. means, the amount oi phase shirt being proportioned to e'ect regeneration just suillcient to compensate, at the cutoff frequency, for the losses caused by the sell-conductance or other dissipation in the terminal circuits and coupling means of the stese. The result is to maintain the sharpness of cutoi! which would be obtained in a nlter if the nlter had no inherent dissipation.

For a better lmderstandingof the invention, together with other and further objects thereof, reference is had to the following description, taken in connection with the accompanying drawings, and its scope will be pointed out iri the appended claims.

Fig. 1 of the drawings is a simplified circuit diagram of a low-pass ampliiler illter of the invention, an image impedance of the vacuum-tube feedback section of which is matched with that of an adjacent circuit to form a confluent series of sections; Figs. 2te-2e, inclusive, are graphs illustrating certain theoretical characteristics of the feed-back stage of Fig. 1; Fig. 3 is a simplified circuit diagram of a feedback lter similar to that of Fig. 1 except that a conductance feedback circuit is provided in the feedback section of the network; Fig. 4 is a circuit diagram of a band-pass amplifier ilter corresponding in type to the low-pass lter of Fig. 1; Figs. 5 and 6 are circuit diagrams of different types of conuent amplier filters of the invention, each comprisingl two feedback sections.

Referring now more particularly to Fig. 1. there is shown a vacuum-tube amplifier stage comprising one of a conuent series of iilter sections. The stage comprises input terminals 8, 8 and output terminals 1, 1 across which are coupled, respectively, condensers C1 and C2,

forming shunt arms of the stage. The terminal circuits are coupled in the forward direction by a unidirectional coupling means primarilyv transconductive, such as a vacuum tube I and are coupled with opposite polarity in the backward direction by a vacuum tube II. Sources of operating potentials (not shown) and other electrodes such as screen grids, if desired, are provided for tubes I0 and II in a conventional manner. The image impedance of the circuit between the input terminals t, 6 is indicated by Z'. Vacuum tube I I is so connected as to have eifectively a positive transconductance in contrast to the ordinary negative transconductance of a vacuum tube; that is, the output circuit of vacuum tube II is taken from ascreen circuit. This manner of utilizing a vacuum tube to procure positive transconductance is more fully explained in United States Letters Patent 1,997,865, granted .April` 16, 1985, on the application of Harold A. Wheeler. The output terminals 1, 1 of the amplifier stage are connected to `a constant-k filter section comprising series inductance arm I2 and shunt condenser arms i3 and I4. Condensers Il and Il have approximately the same value of capacitance es condenser Cn. 'I'he output terminals U, 8 of the series of networks shown may be coupled, with image impedance matching, to any other network. The image impedance at the output terminals I, 8 is indicated by Z", the image impedance termination of theoutput circuit being represented by resistor R". l

'I'he operation of the filter network described may be explained with reference to Figs. 2a'2e, inclusive, which represent certain theoretical characteristics of thel feedback ampliiier iilter section of Fig. 1,' each of the ilgures having frequency as the abscissae. Thus, Fig. 2a represents the impedance of the feedback amplifier filter section of Fig. 1 on 'either side, with the other side on short'circuit: Fig. 2b shows the' the feedback amplier illter section. The upper and lower 4dotted-line curves of Fig. 2e show the actual phase shift for a stage having, respectively, negative and positive forward transconductance. It will be understood that the characteristic curves of Figs. 2a-2c, inclusive, are equally applicable at either the input terminals 6, 6 or the output terminals 1, 1.

Thus it is seen that the feedback amplifier filter section has input and output image impedances which exactly conform to constant-Ic mid-shunt image impedances. The system may, therefore, be connected in a conuent series of networks on an image impedance basis with other similar amplifier stages or with filter sections having the constant-Ic form of image impedance. The low-pass amplifier filter stage shown has a cutoff frequency:

L :one-half the inductance of winding I2; g12=the transconductance of vacuum tube I0; gz1=the transconductance of vacuum'tube II.

Resistor R', representing the image impedance of both circuits connected at the terminals 8, 6, and resistor R", representing the image impedance of both circuits connected at the terminals 8, 8, or terminating resistors to match such image impedances, have the values:

The respective image impedances for any frequency w are:

R z Ufa/F U l R' l 5 The image impedance ratio of the network shown'is:

Ordinarily this image impedance ratio is unity in a low-pass iilter network. However, due to the fact that the amplifier filter section of the invention is an active section, the image impedance ratio of the circuit of Fig. 1 can have any desired value. -The gain of the amplifier filter section of Fig. 1, which is the voltage ratio when connected between equal impedances, is:

2-a El dal K Ordinarily the phase shift of a filter section varies over a range of 180 degrees over the pass band. It will be seen from the phase-frequency curves of Fig. 2e that the phase of the low-pass lan output circuit, as in the case of tube II in Fig. l, is one way of securing a negative transconductance. Other means for accomplishing this are two conventional tubes coupled in cascade in the normal manner, or a. phase-reversing transformer utilized with a. normal tube having a negative transconductance. Preferably the tubes utilized in the iilter networks oi the invention have a very small anode conductanceI which is a property of high-mu tubes, such as screen-grid tubes or high-mu triodes. if the ampliiier filter section is designed for operation at very high frequencies, the tubes must be shielded against internal capacitive coupling and in such cases the use of screen-grid tubes is essential.

The circuit oi Fig. 3 is, in general, similar to the circuit oi Fig. l and similar circuit elements have been given identical reference numerals. In the circuit oi Fig. 3 the coupling provided by vacuum tube ii ci Fig. l, oi opposite polarity to the couv pling oi vacuum tube it, has been replaced by a dit primarily conductive coupling. This conductive coupling is obtained by means of a resistor it connected directly between the anode and the grid oi vacuum tube it. Ii the conductance Gs oi" the feedback circuit comprising resistor it is much less than the transconductance gm ci' vacnum tube it, the operation oi the circuit ci Fig. Ii is in all respects similar to that of the circuit oi' Fig. i. vl'he ampliier nlter section of Fig. 3 has the characteristic oi a mid-shunt constant-7c image impedance across each of condensers C1 and f G2 similar to that across corresponding elements in the circuit oi? iilig. l. The following additional equations erpress the edective transconductances in the circuit oi' ilig. 3:

l dir-tdw. Gs (7) di: Ga (s) lin Fig. 'i there is shown a bandiiiter arnplifier section ci the invention connected in a titl continent network with age impedance matching. The circuit is generally similar to the circuit ci the low-pass iilter oi tig. l and similar circuit elements have been given identical reierence numerals. in addition to the circuit elements ci iiig. l, ilig. a comprises an inductance lin connected in parallel with condenser C1, and an inductance in connected in parallel with condenser Cz. The' positive transconductance in the icedbacir circuit oi Fig. d is obtained by vacuum tube Il i connected in the normal manner together with proper polarity ci the mutual inductances ci the tranciormers provided by s it and iii coupled to inductances in and Le, respectively. The inductance element it oi the constant-ic section oi' the circuit oi Fig. i has been replaced in Fig. i by inductance network it, the reactive constants oi which edectivel-y provide inductance elements for a bund-pass moi-lined constant-it niter section comprising shunt condenser-s it and iii. The operation oi the circuit of Fig. d may be understood trom the description ci the operation oi" the circuit or Fig. i given above. The following equations denne the characteristics ci the amplifier filter. section oi Fig. t:

White-JEJ- i/CxLi 1f CzLi i i ww1 m C-lj 5W,

where w24-:mean ir wir nor ot the band;

w=lower cutod irequency ci the band; m-upper cui-.od .frequency of the band. 1

- in the forward direction In Fig. there is shown a. conuent series of iilter sections coupled with image impedance matching and comprising two amplier ltersections in accordance with the invention. The rst amplier hlter section comprises a shunt reactive arm including a series-connected inductance 22 and condenser it and a second shunt reactance arm comprising a condenser 2 I. These shunt reactance arms are coupled in the forward direction by the vacuum tube 2t and are coupled in the backward direction with opposite polarity by a conductance coupling with the addition of series inductances 25 and it, resistor it being replaced by resistors it', I5". A condenser 2l is connected from the Junction between inductances 2t and it and the low-potential terminal of condenser 2t. Grid-leak resistor it is provided for vacuum tube it, while the resistance of its load circuit is represented by resistor 29. Across the input terminals of the circuit o lFig. 5 is connected a resistor it matching the image imped ance between the terminals and which is nearly constant over the pass band. Coupled to the output circuit of `Fig. 51s a constant-lc low-pass filter section comprising series inductance arm ti and shunt arms consisting of condensers t2 and 33, the value oi each of which is equal to that of condenserti. The second amplier filter section of the circuit ci Fig. 5 comprises a shunt capacitance armconsisting of a condenser it and a shunt arm including a series-connected inductance 3E and condenser it. The shunt arm comprising condenser tt and the shunt arm comprising series-connected inductance it and condenser it are coupled by vacuum tube t? and are coupled in the backward direction ywith opposite polarity by a resistor tu. A grid leal; it 'is provided for vacuum tube t?, while resistor dit represents the resistance in the output circuit ci' vacuum tube iii. Across the output terminals of the conduent network oi Fig. 5 is connected a resistor iti matching its image impedance.' @per-ating potentials are provided for the vacuum tubes in a conventional manner, while blocking oo ndensers di, it, dit, and it are provided to corinne direct currents to their proper channels.

In considering the operation of the circuit oi.v v

liig. 5, it will be seen that the conductance eleu ments it. it" provide aieedback coupling from the output circuit of vacuum tube 2li to the input circuit thereof. lnductances it, it and condenser il are proportioned to shift the phase of the feedback coupling slightly to provide regen eration in the amplicr filter section just sufiicient to compensate, at the cutod frequency, for the losses caused by the ieedbacir conductance oi resistors it', it" and the dissipation in the terminal circuits of the stage. The result is that the sharpness of cutod is maintained just as if the lter had no dissipation. Inductance element it provided in the shunt reactance `arm of the input circuit of vacuum tube 2t completes an mderlved termination having an image impedance which matches the constantresistance til. im ductance tti is provided for the same reason in series with condenser lit; that is, to complete an 11i-derived termination for the output circuit of the amplifier lter section comprising tube ti which more closely matches thel impedance ot the sections oi' the invention coupled in cascade in a confluent band-pass lter network. Thus, the

first amplifier filter section of Fig. 6 comprises a shunt reactance arm including the secondary winding of transformer 56 and a shunt reactance arm comprising the primary winding 53 of transformer 52. Winding 5| is coupled in a. forward direction to winding 53 by a vacuum tube 54 and is coupled in the backward direction with opposite polarity by a c-ircuit comprising seriesconnected resistor 55 and condenser 56. The electrode capacitances of tube 54, represented by condensers 5|' and 53', are effective to tune the transformer windings to which the electrodes-are coupled. The primary winding'i of transformer 50 is tuned by a shunt condenser 58 across which is coupled a. resistance element 59 representing the impedance of the preceding circuit to which the input circuit of Fig. 6 is coupled. The circuit of the second amplifier filter section of Fig. 6 is in all respects similar to the first amplifier filter section described above, and comprises a vacuum tube 64 coupling the secondary winding 6| of transformer 52 in the forward direction to the primary winding 63 of transformer 62, and a feedback circuit coupling windings 6I and 63 in the backward direction with opposite polarity comprising a series-connected resistor 66 and blocking condenser 61. A shunt condenser 68 is connected across the secondary winding 69 of transformer 62 to which is coupled resistance 'I0 representing the impedance of the succeeding circuit to which the output terminals of the filter network are coupled. The inherent input and output capacitances of vacuum tube Glare represented respectively by condensers 6I" and 68'. l

The operation of each amplifier filter section of Fig. 6 is similar to the operation ofthe circuit of Fig. 3, rendering a further description thereof unnecessary. The feedback circuits of Fig. 6 are tapped down on their respective transformer windings in order that a lower value of resistance may be utilized in the feedback circuits and for the purpose of reducing the capacitive coupling associated with the resistance elements. It will be seen that the circuit of Fig. 6 provides a means for coupling two vacuum-tube amplifier filter sections in cascade, there being minimum dissipation within the filter stages. The circuit of each of the amplifier filters` of Fig. 6 is similar to that of Fig. 4 in that each relates to a band-pass filter. However, the feedback coupling paths ofthe amplifier filters of Fig. 6 are similar to the conductance coupling including resistor I5 of the low-pass filter of Fig. 3. The damping necessary to..provide proper terminal impedances for the amplifier filter sections is secured mainly by resistors 59 and 10 at the ends of the confluent network.

The coefficient of coupling 1c between windings 53 and 6| of transformer 62 is much less than would be required to couple conventional vac- .uum-tube amplifier stages. If Aw is the width of the pass band and wo is the mean frequency of the pass band, the required coupling is,

where Asme. This 1s han that required without4 feedback in the adjacent stages.

While there have been described what are at afsasee aimed in the appended claims to cover all: uch changes and modifications as fall within the true spirit and scope of the invention.

What is claimed is:

1. A Wave filter network comprising a first filter section having a predetermined image impedance at one end and an active second filter section comprising input and output pairs of terminals, a reactance arm individual to and. coupled to each of said pairs of terminals, unidirective coupling means betweensaid arms primarilyitransconductive in the direction of coupling, and means coupling said arms with opposite polarity in the other direction, whereby said second filter section has a predetermined pass band and a predetermined image impedance across one of said pairs of terminals, said one of said pairs of terminals being coupled to said end of said first filter section, said coupling means being so proportioned with respect to the reactive constants of said arms that the image impedance of said second filter section matches the image impedance of said first section at their junction. A

2. A wave filter network comprising a first filter section having a predetermined image impedance at one end and an active second filter section comprising input and output pairs of terminals, a reactance arm individual to and coupled to each of said pairs of terminals, unidirective coupling means between said arms primarily transconductivein the direction of coupling, coupling means primarily conductive coupling said arms with opposite polarity in the other direction, whereby said second filter section has a predetermined pass band and a predetermined image impedance across one of said pairs of terminals, said one of said pairs of terminals being coupled to said end of said first filter section, and said coupling means beingl so proportioned with respect to the reactive constants of said arms that the image impedance of said second filter section matches the image impedance of said first section at vtheir junction.-

3. A wave filter network comprising a first filter section having a predetermined image impedance at one end and a second active filter section comprising input and output pairs of terminals, a reactance arm individual to and coupled to each of said pairs of terminals, unidirective coupling means between said arms primarily transconductive in the direction of coupling. coupling means primarily transconductive coupling said arms with opposite polarity in the other direction, whereby said second section has a predeterminedv pass band and a predetermined image impedance across one of said pairs of terminals, said one of said pairs of terminals being coupled to said end of said first filter section, and said coupling means being so proportioned with respect to the reactive constants of said arms that said image impedance of said second filter section matches said image impedance of said first filter section at their junction.

4. A low-pass filter network comprising a first filter section having a predetermined image impedance at one end and a second active filter section comprising input and output pairs of terminals, a shunt reactance arm individual to andcoupled to each of said pairs of terminals and comprising shunt capacitance, said reactance arms having coupling means between said arms primarily transconductive in the direction of'v coupling, means coupling said arms with opposite polarity in the opposite direction, whereby said iii n.so

dit

arenoso 4 sind section h a predetermined pass band and a predetened image impedance across one oi said pairs oi terminals. said one oi said pairs oi terminals being coupled to said end of said t st nlter section, and said coupling means beina so proportioned with respect to the reactive constante oi said arms that said image impedance oi said second dlter section matches the image impedance ci said ilrst filter section at their iunction.

t. n band-pass ter network comprising a first ter section having a predetermined image impedce at one end and an active second lter section comprising input and output pairs oi ternals, a parallel-resonant shunt a individual to and coupled to each oi said pairs of terminals, unidirective coupling means between said arms rimarilv transconductive in the direction of coupg, me coupling withopposite polarity said arms in the other ection, whereby said second section has a predetermined pass band and a predetermined ge impedance across one oi said pairs oi terminals, said one oi said pairs oi terals being coupled to said end of said niet nlter section, and said coupling means being so proportioned with respect to the reactive constants ci said arms that the image impedance ci said second dlter section matches the image impedance oi said nrst section at their junction.

d. it low-pms ter network comprising a first dlter section having a mld-shunt constantc image impedance at one end and an active second hiter section comprising input and output rs oi terminals, a shunt reactance arm including capacitance individual to and coupled to each ci said pairs oi terminals, unidirective coupling means in one direction between said arms primarilg transconductive in the direction of coupling, means coupling said arms with opposite polarity in the other direction, whereby said second dlter section has a predetermined pass band and constantes mid-shunt image impedance across one oi said paire oi terminals, said one titi oi said paire oi terminals. being coupled to said end oi said nist iilter section, and said coupling means being so proportioned with respect to the reactive constants oi said arms that said image impence oi cmd second nlter section matches the image impedance oi said nrst dlter section at their inaction, said second dites section having a phase shiit which varies over a range ci 9i) degrees over the pass band oi seid network.

'i'. it; wave dites network comprising a nrst ter section having a mid-shunt constant-lt impedance at one end and an active second nlter section comprising input and output pairs oi' tenais, a reactance t, i o l individual to and coupled to each oi said pairs oiteals, unidirectire coupling means between said arms primarily trconductive in the direction oi coupling, means coupling said arms with opposite polarity in the other direction. whereby said second nlter section has a predetermined pass band and a mid-shunt constant-lc image impedance across each oi said pairs of te als, one ci said pa s oi teinals being coupled to said end oi said t nlter section, said coupli means being so proportioned with respect to the reactive constants of said arms that the image impedance oi said second utter section matches the im ance oi id nrst @lier-econ attheir junction-and said image imp si ci said second section ve a constant ratio substantially dit., iereht we unity.

t. A iowss hlter network a t ter between said arms in one direction consisting primarily oi transconductance gis in the clis rection of coupling, unidirective coupling means of opposite polarity between said arms in the other direction consisting primarily of transconductance Q21, whereby said second'iilter section has a cutod frequency Y and whereby said second section has a constant-k mid-shunt image impedance across one of said pairs of terminals, said one oi said pairs of ter minals being coupled to said end of said first nlter section, and said coupling means being so proportioned with respect to the reactive constants of said arms that said image impedance of said second lter section matches the image impedance oi said first illter section at their junction.

9. in a wave lter network, an active filter section comprising input and output pairs ci terminals, a reactance arm individual to and coupled to each oi said pairs oi' terminals, unidirec-a tive coupling means between said arms in one direction primarily transconductive in the direction of` coupling, coupling means of opposite polaritts between said arms in the other direction, an mderived termination for said lter section comprising one of said arms, whereby said' lter section has a predetermined cutoil.' frequency and a predetermined constant image impedance across one of said pairs of terminals over said band, and a constant resistance circuit 'connected across said one of said pairs oi terminals.

10. In a wave filter network, an active lter section comprising input and output pairs ci terminals, a reactance arm individual to and coupled to each oi saidpairs oi terminaladirective coupling means in one direction between said arms primarily transconductive in the direction ci' coupling, and coupling means primarily conductive coupling said arms with opposite polarity in the other direction, an "in-derived termination for said lter section comprising one of said arms, whereby said Filter section has a predetermined cutoti frequency and a predetermined constant image impedance across one oi said pairs of terminals over said band, and a constant resistance circuit connected across said one of said pairs oi terminals.

11. In a low-pass filter network, an active filter section comprising input and output pairs of terminals, a reactance arm individual to and coupled to each oi said pairs of terminals, dlrective coupling means in one direction between said arms primarily transconductlve in the direction or coupling, and me coupling said arms with opposite polarity in the vother direction, one oi' said arms consisting oi a series-connected inductance and condenser, whereby' said section has a predetermined cutod frequency and a sub stantially constant resistive image impedance across the pair of terminals to which said one oi said arms is coupled, anda constant resistance circuit connected across said -ntioned pair oi terminals.

l2. An active lter section comprising input and output rs oi terminals. areactance arm dit dit

of terminals, directive coupling means in :one direction between said arms primarily transconductive in the direction of coupling, and coupling means primarily conductive coupling said arms in the other direction with opposite polarity, phase-shifting means included in said .con-

'arms with opposite polarity in the other direction,phaseshifting means comprising inductance in series with said conductive coupling means and capacitance in shunt therewith effective to provide regeneration at the cutoff frequency of said section just suiiicient to compensate for dissipation in said section, whereby said section has a predetermined cutoff frequency and a predetermined image impedance across'one of said pairs of terminals.

14. A band-pass filter comprising a plurality of coupled filter sections with image impedance matching at their junctions, each of two of said sections comprising a transformer having primary and secondary windings, transoonductive coupling means comprising a vacuum tube having inherent input and output capacitances coupling thesecondary winding of one of said transformers with the primary winding of the other of said transformersvcoupling means of opposite polarity in the other direction between said two last-mentioned windings, the coupling eect of said coupling means being proportioned with respect to the reactive constants of said transformers to provide constant-k mid-shunt image impedances across said capacitances and a predetermined pass band for said filter, said image impedances matching the image impedances of adjoining ones of said sections.

15. A band-pass filter comprising a plurality of coupled lter sections with image impedance matching at their junctions, each of two of said sections comprising a transformer having primary and secondary windings, transconductive coupling means comprising a vacuum tube having inherent input and output capacitances coupling the secondary winding of one of said transformers with the primary winding of the other of said transformers, coupling means of oppoindividualoto and coupled to each of said pairs- 'site polarity in the other' direction between said two last-mentioned windings, said couplingI` means comprising a'resistor coupled between points of said two.l lastmentioned windings, the coupling eiect of said coupling means being proportioned with respect to the reactive constants of said transformers to provide constant-1c mid-shunt image impedances across said capacitances 'and a predetermined pass band for said filter, said image impedances matching the image impedances of adjoining ones of said sections.

16. A band-pass lter comprising a plurality of coupled filter sections with image impedance matching at their junctions and including two similar sections, two shunt reactance arms for each of said sections, a transformer having primary and secondary windings individually comprising one of said arms in each of said sections, transconductive coupling means comprising a vacuum tube inl each of said sections coupling its respective arms,- coupling means between said arms in each of said sections coupling said arms with' opposite polarity in the other direction, the coupling eiect of-said coupling means being proportioned with respect to the reactive constants iov of said similar sections to provide constant-k mid-shunt image impedances and a predetermined pass band for said similar sections, said image impedances matching the image impedances of adjoining ones of said sections, said transformer having a coemcient of coupling k=Aw/2w0, where Aw is the width of the pass band of said similar sections and wo is the mean frequency of said similar sections, Aw being substantially less than so.

17. A wide band iilter network comprising a first filter section having a predetermined image impedance at one end and an active lter section comprising input and output pairs of terminals, two capacitive shunt arms coupled to said terminals and having unidirective coupling means between said arms primarily transconductive in the direction of coupling, said coupling means comprising a vacuum tube having input and output capacitances, one of said capacitances of said tube comprising the capacitance of a full-shunt element of said iilter network, and means coupling said arms with opposite polarity in the other direction, whereby said section has a predetermined pass band and a predetermined image impedance across said one of said arms, said one of said pairs of terminals being coupled to said end of said first iter section, and said coupling means being so proportioned with respect to the reactive constants ot said arms that the image impedance of said second filter section matches the image impedance of said first iilter section at their junction.

HAROLD A. WHEELER.

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