US2058210A

US2058210A - Wave transmission networks

Info

Publication number: US2058210A
Application number: US752420A
Authority: US
Inventors: Hendrik W Bode
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1933-04-28
Filing date: 1934-11-10
Publication date: 1936-10-20
Anticipated expiration: 1953-10-20

Description

Oct. 20, 19346. H. w. 5cm:

Y WAVE TRANSMISSION NETWORKS Original Filed April 28, 1953 INVENTOR H. W 8005 BY rrow/5r Patented Oct. 20, 1936 UNITED STATES WAVE TRANSMISSION NETWORKS Hendrik W. Bode, New York, N. Y., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Original application April 28, 1933, Serial No.

668,312. Divided and this application November 10, 1934, Serial No. 752,420

13 Claims.

This invention relates to wave transmission networks and more particularly to reactive networks, such as wave filters, of the unbalanced type in which one side of the circuit may be grounded. This application is a division of my copending application, Serial No. 668,312, filed April 28, 1933 which has matured into Patent 2,029,698, Feb. 4, 1936.

An object of the invention is the reduction of the number of elements required in a symmetrical network.

Another object is the elimination of the requirement of mutual inductance in building unbalanced networks.

A further object is to improve the transmission and impedance characteristics obtainable in unbalanced networks.

A feature of the invention is a bridged type network comprising a plurality of pairs of series arms and a plurality of shunt branches.

As a matter of convenience, transmission networks are often designed in the form of symmetrical lattice structures because the mathematical expressions applying thereto are partic- "ularly simple and because this configuration gives the widest possible range of transmission and impedance characteristics obtainable from a symmetrical network. In many instances, however, the lattice is an unsatisfactory form in which tobuild the network since it frequently requires a large number of elements and, moreover, can not be used in unbalanced systems.

A well-known unbalanced equivalent of the symmetrical lattice is a bridged-T network com- "prising a bridging impedance and a shunt impedance coupled by a unity ratio transformer. However, for complete equivalence it is necessary that this coupling transformer be a perfect one, that is, one having infinitely great Winding inductances and unity coupling.

In accordance with the present invention the coupling transformer is eliminated entirely and no mutual inductance is required between the componentv reactance elements. The network may be made the equivalent of the lattice in its transmission properties but is unbalanced in form, with a consequent saving in the number of elements required. The network of the invention is of the bridged type, comprising a plurality of pairs of series arms and a plurality of shunt branches forming a plurality of T-networks which are connected in parallel, with a single common bridging branch.

The nature of the invention will be more fully "understood from the following detailed description and by reference to the accompanying drawing of which:

Fig; 1 is a diagrammatic representation of a network embodying the invention;

Fig. 2 shows diagrammatically the lattice network of which the network of Fig. l is theelectrical equivalent;

Fig. 3 represents a Wave filter designed inaccordance with the invention; and.

Fig. 4 shows the lattice structure of which the network of Fig. 3 is the unbalanced equivalent.=

The network of the invention, as shown diagrammatically in Fig. 1, is of the'bridged type comprising a bridging branch Z1 and a plurality of T-networks connected in parallel at their ends.

The network shown in Fig. .1 has three such T-networks, one comprising a pair ,of equal series arms, Z2, Z2 and a shuntv branch Z3, another consisting of series arms Z4, Z4 and a shunt branch Z5 and the third made up of the series arms Z6, Z6 and the shunt branch Z1. Although the network shown in the figure comprises only three component T-networks, the invention is not limited to this number. Any number of partial networks of the T-type maybe employed, the

number required depending in generalv upon the complexity of the lattice structure of which the bridged-type network is the electrical equivalent.

The network shown in Fig. 1 is the unbalanced equivalent of the lattice network shown in Fig. 2,

which comprises two equal line impedances Zx and two equal impedances Zy connected diagonally between the input and output. terminals.

The impedances Zx and Z may haveany degree of complexity and any of a wide variety of schematic forms. For a detailed explanationof how to design a lattice network which will have any I desired transmission characteristics reference is made to my prior Patent 1,828,454, issued October 29, 1931.

Proof of the equivalence of the bridged-type network of Fig. 1 to the symmetrical lattice-net! work having the line and diagonal branches shown in Fig. 2 rests upon the conversion of simple lattice structures to their equivalent T-networks.

The lattice shown in Fig. 2 may be consideredtobe a combination of four simple lattices connected in parallel at both ends, terminal for terminal. In one of these simple lattices each line impedance is Z2 and each diagonal branch consists of Z2 in series with 2Z3. The second lattice has a line impedance Z4 and a diagonal impedance-comprising Z4 in series with 225. The third lattice has Z6 for the line branch and-Z6 in series with 2Z1 for the diagonal branch, and the fourth lattice has a line impedance. i

with an infinite impedance for "its diagonal impedances A, A as line branchesand impedances B, B as diagonal branches is the equivalent of a T-network having two series arms A, A and an intervening shunt arm equal to In this connection reference is made to Equation (24) of the paper by O. J. Zobel entitled, Theory and Design of Uniform and Composite Electric Wave-Filters published in the Bell System Technical Journal for January 1923. The same equivalence is shown in Figs. 24A and 24B appearing in Appendix B, page 281 of K. S. Johnsons Transmission Circuits for Telephonic Communicationf published by D. Van Nostrand Company.

Applying the process outlined above to the networks under consideration, the simple lattice having Z6 for the line branch and Z6 in series with 2Z7 for the diagonal branch may be converted into the simple T-network in Fig. 1 having Zs for each series arm and 5 for the shunt arm. The other two simple T-networks of Fig. 1 are obtained in a similar manner. The bridging branch Z1 may be considered to be a T-network having two series arms each equal to with an interposed shunt branch infinite in impedance.

' It will be observed that the conversion from a lattice tothe bridged type network shown in Fig. 1 will be possible provided the branches of the lattice can be arranged as combinations of paral- .;.-lel impedances such that each parallel arm of one can be subtracted from one of the arms of the other without leaving a negative remainder. For example,one of the parallel arms of the impedance branch Z; of Fig. 2 consists of an ,impedance Z6 and therefore the other branch impedance Zy is required to have an arm comprising an impedance Z6 in series with a positive, that is, a physical, impedance 2Z7 which latter impedance may, of course, be zero. The specific application of the network of Fig. 50 1 is ilustrated in the low-pass wave filter of Fig. 3,

which is the unbalanced equivalent of the symmetrical lattice shown in Fig. 4 and requires no mutual inductance in its construction. Each line branch of the lattice network of Fig. 4 consists of three parallel arms in one of which are the inductance L1 and the capacitance C1 in series, in another is the capacitance C2, and in the third the inductance L2. Each diagonal branch of the lattice is composed of two arms, one made up of 60 the inductance L3 and the capacitance C3 in series, and the other consisting of the capacitance C4. In the bridged type network of Fig. 3 the bridging arm is constituted by the inductance 65. 2L1 andthe capacitance 0204- Ga -C 75 and the other pair of series arms consist of the inductances L2, L2, the associated shunt branch being made up of an inductance equal to in series with a capacitance equal to 203. The designations employed in Figs. 3 and 4 clearly indicate the relationship between the component elements comprising the two networks. The only restrictions imposed upon the values of the elements are that the inductance L3 must be equal to or larger in magnitude than L2, and the capacitance C2 must be equal to or larger than C4, so that all of the elements of the bridged type network will be physically realizable without using mutual inductance.

The equivalence of the bridged type network shown in Fig. 3 to the lattice of Fig. 4 becomes readily apparent when the relationship of the component impedances to those of Figs. 1 and 2 is pointed out. The impedance Z1 of Figs. 1 and 2 corresponds to the inductance 2L1 connected in series with the capacitance in Fig. 3, Z2 corresponds to C2, Z3 to the capacitance of value c c 2 2 to L and Z corresponds to 2C3 in series with an inductance equal to is seen to be the unbalanced equivalent of the simple lattice in Fig. 4 having C2 for each line branch and C4 for each diagonal branch. Likewise, the T-network in Fig. 3 having L2, L2 as series arms and having a shunt arm consisting of 203 in series with is the equivalent of the simple lattice in Fig. 4

comprising L2 as the line impedances and L3 in series with C2 as the diagonal branches.

As an illustrative example, a low-pass filter has been designed which employs elements having the following values:

L1=0.67 henry L2=0.50 henry L3=1.33 henries C1=O.60 microfarad C2=1.00 microfarad C3=0.75 microfarad 04:0.50 microfarad It is to be noted that the network of Fig. 3 may be built without using mutual inductance, but if a simple bridged-T structure were employed, mutual inductance would be required.

What is claimed is:

1. A bridged type wave transmission network comprising a bridging branch and a plurality of symmetrical T-networks connected in parallel, said network being the equivalent of a lattice type structure.

2. A Wave transmission network comprising four impedance branches arranged in the form of a bridged-T network, and three additional impedance branches arranged in the form of a T-network, said T-network being connected in parallel with said bridged-T network, terminal for terminal.

3. A wave transmission network of the bridged type comprising a bridging branch and a plurality of T-networks connected in parallel, the component impedance branches of said network having such values that said network is the equivalent of a lattice type network.

4. A bridged type wave transmission network comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, the outer terminals of each of said pairs of series arms being connected to the outer terminals of said bridging branch, and said shunt branches being connected, respectively, to the mid-points of said pairs of series arms to form a plurality of symmetrical T-networks.

5. An unbalanced bridged type wave transmission network comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, the outer terminals of each of said pairs of series arms being connected to the outer terminals of said bridging branch, and said shunt branches being connected, respectively, to the mid-points of said pairs of series arms to. form a plurality of symmetrical T-networks.

6. A selective wave transmission network of the bridged type comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, said network being the equivalent of a lattice type network.

'7. An unbalanced wave transmission network of the bridged type comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, said network being the unbalanced equivalent of a lattice type network.

8. A bridged type wave transmission network comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, the component impedance elements comprising said network being primarily reactances, and said network being the equivalent of a lattice type network.

9. A wave filter of the bridged type comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, said network being the equivalent of a lattice type wave filter.

10. An unbalanced wave filter of the bridged type comprising a bridging branch, a plurality of pairs of series arms and a plurality of shunt branches, said network being the equivalent of a lattice type wave filter.

11. A wave transmission network of the bridged-T type comprising a bridging branch, a plurality of pairs of series arms, and a plurality of shunt branches, the number of shunt branches being equal to the number of pairs of series arms, and each of said shunt branches being associated with one pair of said series arms, one terminal of each of said shunt branches being connected, respectively, to the junction point formed by a pair of said series arms.

12. A wave transmission network having a pair of input terminals and a pair of output terminals, said network comprising an impedance path connected directly between an input terminal and a corresponding output terminal, a plurality of additional impedance paths connected in parallel with said first path, each of said additional paths comprising a. pair of equal impedances serially connected, and a number of shunt impedance paths, said number being equal to the number of additional impedance paths connected in parallel with said first path, each of ,said shunt impedance paths having one terminal separately connected to the common terminal of said pair of equal impedances in one of said additional paths, and having connections from the other terminal of each of said shunt impedance paths to the remaining input and output terminals of said network.

13. A wave transmission network having a pair of input terminals and a pair of output terminals comprising a pair of equal impedances connected in series between an input terminal and an associated output terminal, a shunt branch connected to the common terminal of said pair of impedances, a second pair of equal impedances connected in series with each other and in parallel with said first mentioned pair of impedances between the aforesaid input terminal and output terminal, a second shunt branch connected to the common terminal of said second pair of impedances, and a bridging branch connected between the aforesaid input terminal and output terminal.

HENDRIK W. BODE.