US2149356A

US2149356A - Wave transmission network

Info

Publication number: US2149356A
Application number: US100400A
Authority: US
Inventors: Warren P Mason
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1936-09-12
Filing date: 1936-09-12
Publication date: 1939-03-07
Anticipated expiration: 1956-03-07
Also published as: GB498332A; FR826617A; BE423379A; NL49003C; CH202644A

Description

March 7 1939.

WAVE TRANSMISSION NETWORK W. P. MASON Filed Sept. 12,1936

2 Sheets-Sheet l ATTORNE V Marh 7, 1939. W. l MASON 2,149,356

WAVEl TRANSMISSION NETWORK @ya .27W

ATTORNEY Patented Mar. 7, 1939 UNITED` STATES PATENT OFFICE 2,149,356 WAVE TRANSMISSION NETWORK Application September 12, 1936, Serial No. 100,400

13 Claims.

, 'Ihis invention relates to wave transmission networks and more particularly to networks adapted to couple loads having different impedances.

An object of the invention is to provide an impedance transforming network suitable for use Yat high frequencies and capable of transmitting a wide band with uniform ratio of transformation.

Other objects are to reduce the cost of such networks, decrease the loss in the transmission band, and increase the power carrying capacity.

A further object is to provide a network of this type whichk may be very effectively shielded.

15 `A featurewof the invention is the use of short lengths of transmission line, or transmission lines in, combination with one or more condensers, as component elements in impedance transforming networks of the type set forth above.

Atthe higher radio frequencies, transmission networks using coils and condensers as reactance elements are diicult to construct and unsatisfactory in operation on account of the small sizes of the elements required and the large effects of the interconnecting windings. Also, if

coils are used in networks designed for highfrequency application the loss in the transmission band will be excessive due tothe low Qfof the coils, defined as the ratio of reactance to ei'ective f resistance.

In accordance with the present invention these objections-are overcome by providing impedance transforming networks for high frequency use which employ as component elements only short lengths of transmission line, or lengths of line in conjunction with` condensers. The networks are capable of transmitting comparatively widel bands withy asubstantially uniform ratio of impedance transformation. Such transformers have 40 the advantages of low cost due to the cheapness` of the component elements, low loss in the transmission band because of the high values of Q obtainable in transmission lines and condensers,

impedances dependent upon the input and output impedances of the transformer and the ratio of transformation. Each section of line is preferably uniform throughout its length and should be substantially dissipationless. The line may consist 5 of a balanced pair of parallel wires or rods, or

it may be of the concentric conductor type in which the outer conductor surrounds the inner one and is coaxial therewith. The former type is preferable for use in balanced structures, and l0 the latter in unbalanced structures. The concentric line has the advantage that it is inherently well shielded.

In one embodiment, one of the line sections is connected in series with the direction of wave l5 propagation and used as a four-terminal network, with transmission therethrough, and another line section is used as a two-terminal impedance connected either in series or in shunt with the rst-mentioned section. In another 20 form of the network, two line sections are used 'as shunt impedances, and in still another embodiment the sections of line are connected in tandem. In some cases an L, T or 1r network of condensers is used in combination with the transmission 25 lines. As a modication, shunt condensers are provided at the ends of the network to absorb distributed capacity associated with the terminal loads.

The impedance transforming networks described herein may be used to couple together any two loads having impedances, preferably pure resistances, which differ in magnitude. The networks are especiallyy adapted for use at high 35 frequencies where it is desired to transmit a wide band with a uniform ratio of impedance transformation for the entire band. Examples of such applications are the connection of a transmission line to an antenna, or to a thermi- 4o onic tube, and the coupling of two therrnionic tubes. l

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying draw- 4.5 ings of which: l, I

Fig. 1 represents a` section of uniform transmission line taken from an innite sequence of such sections;

Fig. 2 is a diagrammatic representation of one 50 entitled form of the impedance transforming network in accordance with the invention;

Figs. 3 and 4 represent respectively unbalanced and balanced physical structures for the network of Fig. 2;

Fig. 5 shows the equivalent electrical circuit of the network of Fig. 2 and is used in explaining the invention;

Fig. 6 shows another embodiment of the invention;

Fig. 7 represents a possible physical structure for the network of Fig. 6;

Fig. 8 represents the physical structure of another embodiment of the invention;

Fig. 9 shows the network of Fig. 8 used as an interstage coupler between two thermionic tubes;

Figs. 10 and 12 show alternative circuits for another embodiment of the invention;

Figs. l1 and 13 represent possible physical structures for the networks shown respectively in Figs. 10 and 12;

Figs. 14 and 15 show respectively the electrical circuit and the physical structure for another embodiment of the invention;

Figs. 16 and 17 are schematic representations of two other embodiments of the invention; and

Fig. 18 is a perspective View, partly in section, showing the central portion of Fig. 11 on a larger scale.

In order to be able to employ the equations of transmission lines in working out the designs of the networks hereinafter described, a brief review of them will first be given. The equations of propagation for a section of uniform transmission line, such as l of Fig. 1, having a propagation constant P, a characteristic impedance Zo and a length l can be expressed in terms of the input voltage e1, the input current i1, the output voltage e2 and the output current i2 by the relations 112:1', cosh lezsinh P1 In terms of the distributed resistance R, the distributed inductance L, the distributed conductance G and the distributed capacitance C, all per unit length ofline, P and Zo are given by the expressions R=41.6 10-91/ ohms per centimeter L=2 log., XIO-9 henries per centimeter fai-ads per centimeter 2 loge -awhere l1 is the inside radius of the outer conductor and a the outside radius of the inner conductor. In this connection reference is made to the article by E. J. Sterba and C. B. Feldman Transmission Ylines for short wave radio systems appearing in the Bell system Technical Journal, Vol. XI, No. 3, July 1932, page 411, especially at pages 414, 415 and 417. The Q of a concentric conductor, defined as the ratio of the series inductive reactance to the series resistance, is given by where For a balanced transmission line the values of R, L and C are given by the equations ohms per centimeter L=4 log, 1E) X 10g henries per centimeter C fai-ads per centimeter 4 loge E where D is the spacing between wires, and a the radius of one of the pair of wires. With these values, the expressions for Q and Zu become A balanced and shielded transmission line may be obtained by placing two coaxial lines side by side and using the inner conductors. In this case the values of R. and L will be double, and the value of C will be half, those given by Equations (3).

Turning to specic embodiments of the invention, Fig. 2 is a diagrammatic representation of a network comprising only transmission lines and capable of transforming from one impedance to another over a wide range of frequencies. The network consists of two transmission lines each a quarter wave-length long at the mid-frequency of the band to be transformed. The line 2, of length Z1, and characteristic impedance Zul, is connected in series between input terminals 3, 4 and output terminals 5, 6. The line l, having a length Z2 and a characteristic impedance Zu2, is short-circuited at one end and at the other end is connected in shunt with the line 2. An input load impedance R1 in series with an electromotive force E is shown connected to the input terminals of the network, and an output load impedance Ro is connected to the output terminals.

'Ihe physicalstructure of the network of Fig. 2 when coaxial transmission lines are used is indicated by Fig. 3, in which 8 and 9 are respectively the inner and outer conductors of line 2 and l0 and Il are respectively the inner and outer conductors of line l. The inner conductor may be separated from the outer conductor in a well-known manner by means of rings or spiders, made of suitable insulating material, not shown G are small.

in Fig. 3. Fig. 4 shows the physical structure when a balanced pair of parallel wires is used for each transmission line.

The design equations for the network of Figs. 2, 3 and 4 will now be considered. In determining the transmission band of Va. network it is convenient to neglect the dissipation occurring in the elements, that is, to assume that the distributed resistance vR and the distributed conducance G are zero. This procedure is justified in the present case because the transmission lines have a high Q and therefore the values of R and Neglecting R and G Equations (1) become w 1 I 12-11 COS v 1Z0 Slfl where v the velocity of propagation and Zo the characteristic impedance have the values and since the impedance of the short-circuited line 1 is the current i2 is and therefore the current in is given by 1 1 i=11 cos Sil-1% s1niV1\-j e0 w1 01 Z132 tan -V-2 which, after substituting for eu its value given by Equation` (10), may be written in the form In order to interpret. Equations (10) and (11) in terms of transformer theory, it will be shown that they are identical in form to the equations applying to a perfect transformer in combination with a symmetrical filter. Fig. 5 shows the equivalent circuit consisting of, two

half sections

8, 9 vof a symmetrical lter coupled by a perfect transformer lhaving an impedance step-down 412 to l. The propagation constantof each half section is. and the characteristic impedance K1 of the mst i-sa2 times the characteristic impedance K2 of theJ second. Using the notation for currents and voltages given in Fig. 5, the equations for the first half section, the transformer and the last half section are respectively Combining these equations on the assumption that In order to provide a network which will have a constant transformation ratio over a wide transmission band the length of the line 2 of Fig. 2 is made equal to' the length of the line 1, that is Z1=I2=L For this case, from VEquations (10), (11), (12) and (13) the following identities are found.

The mid-band frequency occurs whenv cosh I`= cos =0 This condition is satisfied when l isI equal to onequarter wave-length at the mid-band frequency, andtherefore the lines 2 and 1 are made of this length.

At the mid-band frequency the characteristic impedance K10 of the network on the high impedance side is and therefore the input load impedance R1 should be of this magnitude. The characteristic impedance Kzo at mid-band frequency on the low impedance side is which determines the proper magnitude for the output load impedance Re.

The width of the pass band is determined by The cut-off frequencies f1 and f2 of the filter transformer are given by the formula V d, 18) For relatively narrow bands, the ratio of the band width to the mean frequency fm is given by the simple formula tion (19).

as can readily be shown from Equation (18) by using the approximation formula for the cosine in the neighborhood of the angle 1r/2.r

Hence the structure shown on Fig. 2 is equivalent to a perfect transformer whose ratio is and a filter whose band width is given by Equa- Such a lter will have a flat attenuation loss over about per cent of its theoretical band when it is terminated on each side by re-` where R1 and Ro are respectively the input and the output resistances that the transformer works between. Y

Another example of a transforming network comprising only transmission lines is the one shown diagrammatically in Fig. 6 which is the inverse of the network of Fig. 2. A possible physical structure is shown in Fig. 7. The network consists of a section of transmission line Il of length l and characteristic impedance Zo1 in series with an open-circuited line of length Z and characteristic impedance Zo. Using the same notation as above, it can be shown that Y kThe band width of the filter for narrow bands is given approximately by y The first transformer discussed is a step-down transformer while the one considered here has a step-up from the input of the line to the output. The rst filter had a mid-shunt impedance characteristic on each end, that is, the impedance of the band is infinity at the two edges whereas the transformer with the series open-circuited iine has a mid-series impedance, since the impedance given by the last expression in Equation (23) goes to zero at the two cut-0H frequencies. The range of transformation is about the same for each and hence one type has. no particular advantage over the other.

Fig. 8 shows another impedance transforming network made up only of sections of transmission line which is useful where only a moderate ratio of transformation is required. The network consists of two portions of line I3, I4 having characteristic impedances Zo1 and Zn3 respectively,

1 0g cotz 3 1 (21) and each of length l1, shunted at their junction Zal y v point by a short-circuited line l5 of length l2 I l y and characteristic impedance 202.v The expres- 10=11 COS ji sin (22)` sions for the output current in and the output V 01 V voltage en are I- Z Z sin w-Il cos (5y-I1 Z Z cos w11 w11 01 w11 01 V V 01 02xY w11 w11 T 1=11 cos2 sin2 -JeI -f-{vsin cos (26) Z v Z I Z Z I. V o 02 tan (E 01 03 V V 202 tan E@ Y w11 w11 w11 Z l Zo sm-cos- ZZ smi- 2 I1 3'2 l 3 V Q l 0 11 0103 V eo el cos V Zolsm V -l-Zol t w12 J11 (Zoli-Zas) Sm V COS V "i" ZOB w12 (27) an tan T For this case the image transfer'constant and the impedance ratio of the transforming filter are given by the equations .i all o M1 2 2w11 Zufl-Zoa n V c S v 2 2w11 ZUiZUs Y (Z01"`Z03)2 cosh I- cos -V--l-V 22o E ---Sm X T-T 2 4 gztan Y 01 3' 1 0 11 (I0-11g 01 2 1 Zl Sln COS V V VY Zoz tan (JJ-12- 2: V (28) i L11 11 2 w11 Y 03 2 w11 Z03 Sln V COS V s V V y Z0,V ta w12 rWhen we solve the expression for cosh I for the cut-off frequencies, we nd that one of them is given by the expression and the other by at the middle of the pass band is given by the expression K i mi l (34,

1 -711' (f2-i1)V Zolzoi Zo,

If we consider the special case Equation (30) reduces to the simple form 4 `or for narrow bands and f1: Y V.

A t the two cut-off frequencies, it can be shown that and for narrow band filters does not differ much from this value throughout the band.

Hence the structure of Fig. 8 acts asa narrow band coupling unit which introduces a transformation from input to output. For narrow bands it is easily shown that the image impedance The design equations for this transforming filter are Y The network of Fig. 8 is useful as an interstage coupler between the plate of one screen grid or pentode tube and the grid of the next one. Such an application is illustrated by Fig. 9 where the v network 25 is used to couple the plate of tube I6 to the kgrid of tube The output impedance of,

. a high'frequency pentode, such as |6, at 100 to work .between 30,000'ohms at its input and r'20,000 ohms at its output.

y scale used in the latter figure. is that between the discs 3| and 34, and C3 is the The shunt line I5 is effectively short-circuited at high frequencies by means of the condenser 30 of large capacitance connected between the inner and outer conductors near the outer end of the line. A dire'ct metallic connection cannot be made here because the B-battery 3| would thereby be short-circuited. The condenser 32 also has a large capacitance and is used to keep the voltage of the battery 3| off of the grid of the tube This method of coupling together two stages of vacuum tubes has an advantage over using a concentric conductor or a coil and condenser as a tuned circuitl on several lcounts. In the first place the width of the band passed can be accurately controlled and a atter gain characteristic is obtained. As will be shown later, distributed capacity in the plate and grid of the vacuum tube can be absorbed in the iilter by making the line length Z1 shorter. Since only half of the total distributed capacity has to be absorbed on each end of the filter, a higher impedance can be built up in the filter for the same band width, and hence more gain per section can be obtained than with a tuned circuit.

Next will be considered networks which employ bothy transmission lines and condensers as component elements. Condensers can'be constructed which have little dissipation at radio frequencies and therefore may be used in the networksiwithout unduly increasing' the'los's in the transmission band. Combinations of lines with condensers have the advantages that much more isolatedbands can be obtained, in general narrower pass bands can vbe obtained, and at the lower frequencies shortersectons of lines can be -employed if they are4 resonated vby capacities.

Also when such structures are used as interstage coupling units working between vacuum tubes,

Athey usually will be able to incorporate the grid to iilament and plate to filament capacities as part of the coupling circuit.

Fig. shows one type of network using transmission lines and condensers. The network consists of a transmission line I8 of length Z and characteristic impedance Zul and a second line I9 of length l and characteristic impedance Zon connected in tandem, with a vT network made up of condensers C1, C2 and C3 interposed between the two line sections. The physical construction of the network of Fig. 10 is shown in the perspective view of Fig. 11, and the central portion is shown in more detail in Fig. 18, which is a Aperspective View partly in section. The inner conductor 30 terminates in a metallic disc 3| which is soldered to its end, and the inner conductor 32 terminates in a similar disc 33. Between these two discs but separated therefrom is the flanged disc 34, the flange 35 of which is separated from the outer conductor 36 by the insulating ring 4|. The ring 4| is shown in Fig. 18, but is not shown in Fig. 11 due to the small The capacity C1 capacity betweenthe discs 33 and 34. The capacity between the flange 35 and the outer conductor 36 constitutes C2.

In the network of Fig. 10 the expressions for the output voltage e@ and the output current i@ arrived at by the same method used above, are

In order that the structure shall transform uniformly over a band of frequencies We must have Z 152: C1C2)(C23C3)=Z-:1= impedance transforma With this substitution, Equations (36) and (37) simplify to sin -il v Cri-Cz-l-Ca Comparing these equations With Equations (12) and (13) We have for the image parameters tion ratio (38) These equations give the image parameters for a general transforming band pass filter. The two uses to Which such a structure will ordinarily be put ar-e either to obtain a transformer with as Wide a pass band as possible for a given impedance transformation or else to obtain a lter Without transformation ratio. For the trans- The mid-band frequency occurs when cosh 1=0. Uponk substituting the relation Solvingy for the frequencies for which cosh CB, as shown'in Fig. 12.

I=i1, it is easily shownv that the ratio of the band width tothe mean frequency is given by the expression .K n i y The image impedance K1 at the mid-frequency of the band is from Equation (41) the design equations of the transformer are found to be f 33.31. C-* in upf where R1 is the input impedance from which the transformer must work.

For narrow transmission bands it is necessary for the condenser C3 to have a iinite value. Also, for. this case, the formulas give afairly large value for the shunt condenser C2. A more practical arrangement is to replace the two series condensers C1 and C3 and the shunt condenser Cz by a 1r network consisting of two shunt condensers CA and Cc separated by a series condenser These condensers will s between the partition and the disc 40. The capacity CB is that effective between the two discs 39 and 40, through the hole 2|. By adjusting the size of this hole, this capacity can be made as small as desired. Y

The transformer just discussed is suitable for transforming from line impedances down to very low impedances, but cannot be used to transform from line impedances up to very high impedances such as the impedance of a vacuum tube. This generally requires a shunt type of termination rather than the series type discussed above. One such transformer is shown in Fig. 14 and the physical structure in Fig. 15. It consists of two short-circuited

shunt lines

23 and 24 of length Z and having characteristic impedances Z01 and Zo2 respectively, connected together by av T or 1r network of capacities. In Fig. I5 the capacities C1' C2 and C3 are furnished by a physical structure similar to that shown in Figs. 11 and 18, described above. For the condition of maximum transformation for a given band width, which occurs when C3 and for eighth wave-length conductors on each end, the design equations for this transformer are found to be The theoretical band Width for this type of transformer is given approximately by the expression Such a transformer is also suitable for connecting together vacuum tubes of high impedance.

Another type of transformer of some interest is one which will transform from very high impedances to very low impedances. Such a transformer is shown on Fig. 16. It has a short-circuited shunt line 26 of length Z1 and characteristic impedance Zo1 on the high impedance end and a series line 21 of length Z2 and characteristic impedance Zo2 on the low impedance end. Such a transformer does not have a constant transformation ratioy over the whole band but for about per cent of the theoretical band with the transformation ratio is approximately constant. The design equations for this transformer are 'I'he transformer is especially useful since it will give the widest transmission band for a given transformation ratio of any of the transformers discussed. Also, the capacitance of the condenser C'z can be adjusted to compensate for the reactive component of the input load impedance.

Fig. 1'7` shows a modification of the network of Fig. 2 in which a shunt condenser appears at each end of the network. Such a structure is useful where it is desired to absorb capacity associated with one or both of the load impedances. This may be done by adjusting the values of the condensers C1 and C2. On the assumptions that the two sections of

line

28 and 29 are of equal length l and that je Z01 c0200 Z01 s V Comparing these with the equations for a perfect transformer and a filter we have pedances disposed at respective ends of said network and means interposed between said sections and cooperating therewith to interconnect said sections without impedance mismatch, the length of said sections being not substantially greater than a quarter of the wave-length corresponding Ato the mean frequency of said band, and the ratio of the characteristic impedances of said sections being equal to the ratio of the impedances of said loads.

2. A network in accordance with claim 1 in which said two sections of line are connected in tandem between the loads.

3. A network in accordance with claim 1 in which said two sections of line are short-circuited at their distant ends and at their other ends are connected in shunt at the ends of said network.

4. A network in accordance with claim 1 in which said interposed connecting means comprise a third section of uniform transmission line connected in shunt between said two sections of line.

5 A network in accordance with claim 1 in K1 Zul co1 v2 vC? V Ca upon replacing z0l by its value where C0 is the total distributed capacity of the line 28 having a characteristic impedance The mid-band frequency fm occurs when cosh I=0 and can be obtained from the equation wml V At the mid-frequency of the band the characteristicimpedance of the filter is Ca V met Il Co 2 V2 w/lfmm from Equation (56). Solving for the band width of the transformer, we find wml 'where is the distributed capacity per centimeter length for the line 28.

What is claimed is:

1. A four-terminal wave transmission network adapted to transmit freely a selected band of frequencies with a substantially uniform ratio of impedance transformation for coupling two loads having unequal impedances comprising two sections of uniform transmission line having equal lengths but different characteristic imwhich said interposed connecting means comprise a series-shunt arrangement of, condensers.

6. A network in accordance with claim 1 in which said interposed connecting means comprise a network of condensers having an impedance transformation ratio equal to the ratio of the characteristic impedances of said sections of line.

7. A four-terminal wave transmission network adapted to transmit freely a selected band of frequencies with a substantially uniform ratio of impedance transformation for coupling two loads having unequal impedances, said network comprising two sections of uniform transmission line and a series-shunt arrangement of condensers interconnecting said sections, the lengths of said sections being equal and each being not substantially greater than a quarter of the wavelength corresponding to the mean frequency of said band, the ratio of the characteristic impedances of said sections being equal to the ratiov of the impedances of said loads, and the capacitances of said condensers being proportional so that said arrangement of condensers provides an impedance transformation equal to the ratio of the impedances of said sections of line.

8. A network in accordance with claim 7 in which said two sections of line are connected in tandem between the loads.

9. A network in accordance with claim '7 in which said two sections of line are short-circuited at their distant ends and at their other ends are connected in shunt at the two ends respectively of said arrangement of condensers.

10. A network in accordance with claim 7 in which said condensers are arranged in the form of a T-network. Y

11. A network for transmitting with a substantially uniform ratio of impedance transformation a selected band of frequencies between two loads having unequal impedances., said network comprising two sections of uniform transmission line connected in tandem between said loads, and a third section of uniform line shortcircuited at one end and at its other end connected in shunt between said two sections, the length of each of said first-mentioned two sections being substantially equal to a. quarter of the wave-length corresponding to the upper cutoi frequency of said band, and the ratio of the characteristic impedances of said two sections being equal to the ratio of the impedances of said loads.

12. A network for transmitting with la substantially uniformratio of impedance transformation a selected band of frequencies between two loads having unequal impedances,rsaid network comprising two sections of uniform transmission line connected in tandem between said loads, and a series-shunt arrangement of condensers interposed between said two sections, the length of eachy of said sections beingknot substantially greater than a quarter of the wavelength corresponding to the mean frequency of said band, the ratio of the characteristic impedances of said sections being equal to the ratio of the impedances of said loads, and the capacitances of said condensers being so proportional that said sections of line are connected without impedance mismatch.

13. A network for transmitting with a substantially uniform ratio of impedance transformation a selected band of frequencies between two loads having unequal impedances, said network comprising a series-shunt arrangement of condensers and two sections of uniform transmission line, said sections being short-circuited at their distant ends and connected at their other ends in shunt at the two ends respectively of said arrangement of condensers, the length of each of said sections being not substantially greater than a quarter of the wave-length corresponding to the mean frequency of said band, the ratio of the characteristic impedances of said sections being equal to the ratio of the impedances of said loads, and the capacitances of said condensers being so proportional that said arrangement of condensers has an impedance transformation ratio equal to the ratio of the characteristic impedances of said sections of line.

WARREN P. MASON.