Reactive power combiners and dividers including nested coaxial conductors

Abstract

A power divider/combiner includes a main conductor defining an axis and having an outer surface; an input connector, at a front end, having a center conductor, electrically coupled to the main conductor and having an axis aligned with the main conductor axis; a first hollow cylindrical conductor having an open end facing rearwardly, having an inner cylindrical surface, the main conductor being received in and spaced apart from the inner cylindrical surface, the first hollow cylindrical conductor being electrically coupled to the second conductor of the input connector; a second hollow cylindrical conductor having an open end facing forwardly, the first cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the second cylindrical conductor; a third hollow cylindrical conductor having an open back end facing rearwardly, the second cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the third cylindrical conductor; and a plurality of output connectors, the output connectors being angularly spaced apart relative to each other, the output connectors having center conductors electrically coupled to the third cylindrical conductor. Methods are also provided.

Claims

1. A power divider/combiner having a front end and a rear end and comprising: a main conductor defining an axis and having an outer surface; an input connector, at the front end, having a center conductor, adapted to be coupled to a signal source, electrically coupled to the main conductor and having an axis aligned with the main conductor axis, and having a second conductor; a first hollow cylindrical conductor having an open end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface, the main conductor being received in and spaced apart from the inner cylindrical surface, the first hollow cylindrical conductor being electrically coupled to the second conductor of the input connector; a second hollow cylindrical conductor having an open end facing forwardly, having an inner cylindrical surface, and having outer cylindrical surface, the first cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the second cylindrical conductor; a third hollow cylindrical conductor having an open back end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface, the second cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the third cylindrical conductor; and a plurality of output connectors, the output connectors being angularly spaced apart relative to each other, the output connectors having center conductors electrically coupled to the third cylindrical conductor.

2. A power divider/combiner in accordance with claim 1 wherein the outer surface of the main conductor and the inner surface of first cylindrical conductor, the outer surface of the first cylindrical conductor and the inner surface of the second cylindrical conductor, and the outer surface of the second cylindrical conductor and the inner surface of the third cylindrical conductor define respective unit element coaxial transmission lines.

3. A power divider/combiner in accordance with claim 2, and further comprising a ground conductor having an inner cylindrical surface, the third cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the ground conductor, and comprising a unit element shorted shunt stub including the inner surface of the ground conductor and the outer surface of the third cylindrical conductor.

4. A power divider/combiner in accordance with claim 1 wherein the inner cylindrical surfaces of the first, second, and third cylindrical conductors have respective cylinder axes coincident with the axis of the main conductor.

5. A power divider/combiner in accordance with claim 1, and further comprising a ground conductor having an inner cylindrical surface, the third cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the ground conductor, wherein the output conductors have respective second conductors electrically coupled to the ground conductor proximate the back end of the third cylindrical conductor.

6. A power divider/combiner in accordance with claim 5 and further comprising a rear flange, at the rear end, supporting the second cylindrical conductor relative to the main conductor, and spaced apart from the open ends of the first and third cylindrical conductors by respective gaps.

7. A power divider/combiner in accordance with claim 6 wherein the rear flange is secured to the main conductor.

8. A power divider/combiner in accordance with claim 1 and further comprising means for selectively receiving and retaining a gas.

9. A power divider/combiner having a front end and a rear end and comprising: a main conductor defining an axis and having an outer surface; an input connector, at the front end, having a center conductor, adapted to be coupled to a signal source, electrically coupled to the main conductor and having an axis aligned with the main conductor axis, and having a second conductor; a first hollow cylindrical conductor having an open end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface, the main conductor being received in and spaced apart from the inner cylindrical surface, the first hollow cylindrical conductor being electrically coupled to the second conductor of the input connector; a second hollow cylindrical conductor having an open end facing forwardly, having an inner cylindrical surface, and having outer cylindrical surface, the first cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the second cylindrical conductor; a third hollow cylindrical conductor having an open back end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface, the second cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the third cylindrical conductor, the outer surface of the main conductor and the inner surface of first cylindrical conductor, the outer surface of the first cylindrical conductor and the inner surface of the second cylindrical conductor, and the outer surface diameter of second cylindrical conductor and the inner surface of the third cylindrical conductor define respective unit element coaxial transmission lines, and the first, second and third hollow cylindrical conductors having respective cylinder axes that are coincident with the axis of the main conductor; and a plurality of output connectors spaced apart relative to each other, the output connectors having center conductors electrically coupled to the third cylindrical conductor.

10. A power divider/combiner in accordance with claim 9, and further comprising a ground conductor having an inner cylindrical surface, the third cylindrical conductor being received in and spaced apart from the inner cylindrical surface of the ground conductor, wherein the output conductors have respective second conductors electrically coupled to the ground conductor proximate the back end of the third cylindrical conductor.

11. A power divider/combiner in accordance with claim 10, and comprising a unit element shorted shunt stub including the inner surface of the ground conductor and the outer surface of the third cylindrical conductor.

12. A power divider/combiner in accordance with claim 9 and further comprising a rear flange, at the rear end, supporting the second cylindrical conductor relative to the main conductor, and spaced apart from the open ends of the first and third cylindrical conductors by respective gaps.

13. A power divider/combiner in accordance with claim 12 and further comprising a screw securing the rear flange to the main conductor.

14. A power divider/combiner in accordance with claim 9 and further comprising means for selectively receiving and retaining a gas.

15. A method of manufacturing a power divider/combiner having a front end and a rear end, the method comprising: providing a first hollow cylindrical conductor having an open end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface, and providing an input port flange forward of the first cylindrical conductor, electrically coupled to and secured to the first cylindrical conductor; providing a main conductor defining an axis and having an outer surface inside the inner cylindrical surface, spaced apart from the inner cylindrical surface; securing an input connector to the input port flange, the input connector having a center conductor and being adapted to be coupled to a signal source, electrically coupling the center conductor of the input connector to the main conductor, coupling a second conductor of the input connector to the input port flange; providing a second hollow cylindrical conductor having an open end facing forwardly, having an inner cylindrical surface, and having outer cylindrical surface, and providing a rear flange rearward of the second cylindrical conductor, electrically coupled to and secured to the second cylindrical conductor; providing a third hollow cylindrical conductor having an open back end facing rearwardly, having an inner cylindrical surface, and having outer cylindrical surface; receiving the first cylindrical conductor and main conductor in the third cylindrical conductor; providing a plurality of output connectors, the output connectors being spaced apart relative to each other, the output connectors having center conductors electrically coupled to the third cylindrical conductor; and inserting the second cylindrical conductor between the first and third cylindrical conductors, spaced apart from the inner surface of the third conductor and the outer surface of the first conductor.

16. A method in accordance with claim 15 wherein the output connectors have respective second connectors, the method further comprising providing a ground conductor having an inner cylindrical surface, receiving the third cylindrical conductor in the ground conductor, and securing the output connectors to the ground conductor with the second conductors of the output connectors electrically coupled to the ground conductor.

17. A method in accordance with claim 16 wherein a fluid chamber is defined in the power divider/combiner, and the method further comprising providing a threaded bore in fluid communication with the fluid chamber, and providing a threaded plug, complementary to the threaded bore, plugging the threaded bore.

18. A method in accordance with claim 15 and further comprising securing the rear flange to the main conductor.

19. A method in accordance with claim 15 and further comprising configuring the divider/combiner using o-ring seals, to be able to retain a gas introduced via the threaded bore.

20. A method of manufacturing a power divider/combiner in accordance with claim 19 and further comprising removing the threaded plug and replacing the threaded plug with a pressure valve configured to be used to introduce a gas into the power divider/combiner.

Description

BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWINGS

(1) FIG. 1 is a side view of a power divider/combiner in accordance with various embodiments, partly in section.

(2) FIG. 2 is the power divider/combiner shown in FIG. 1 with coaxial cables attached and with both plugs replaced with pressure valves to allow the introduction of a gas.

(3) FIG. 3 is a sectional view taken along line 3-3 of FIG. 1 or FIG. 2.

(4) FIG. 4 is a partial cut-away view of the divider-combiner of FIG. 3.

(5) FIG. 5 is a partial cut-away view of the divider/combiner of FIG. 1 or FIG. 2 showing a connection point.

(6) FIG. 6 is a partial cut-away view of the divider/combiner of FIG. 1 or FIG. 2 in accordance with alternative embodiments.

(7) FIG. 7 is a partial cut-away view of the divider/combiner of FIG. 1 or FIG. 2 showing a connection point.

(8) FIG. 8 is a partial cut-away view of the divider/combiner of FIG. 1 or FIG. 2 in accordance with alternative embodiments.

(9) FIG. 9 is a sectional view taken along 9-9 of FIG. 5 or FIG. 6.

(10) FIG. 10 is an end view of the divider/combiner of FIG. 1.

(11) FIG. 11 is a sectional view taken along line 11-11 of FIG. 10.

(12) FIG. 12 is a partial cut-away view of embodiments of the divider/combiner of FIG. 11 including a cap screw O-ring seal.

(13) FIG. 13 is a partial cutaway view of embodiments of the divider/combiner of FIG. 11 including a cap screw O-ring seal.

(14) FIG. 14 is a perspective view of a conductor included in the divider/combiner of FIG. 1, partly in section.

(15) FIG. 15 is a perspective view of a conductor included in the divider/combiner of FIG. 1.

(16) FIG. 16 is a perspective view of a conductor included in the divider/combiner of FIG. 1, partly in section.

(17) FIG. 17 is a perspective view of the divider-combiner of FIG. 1.

(18) FIG. 18 is an equivalent circuit diagram for the divider/combiner shown in FIG. 1 or FIG. 2, when it is operated as a power divider.

(19) FIG. 19 is a graph showing typical input port return loss and output port insertion loss vs. frequency for embodiments of the divider-combiner of FIG. 1 or FIG. 2 that have one input port and ten output ports (when being used as a power divider).

(20) FIG. 20 is a graph showing typical input port return loss and output port insertion loss vs. frequency for embodiments of the divider-combiner of FIG. 1 or FIG. 2 that have one input port and ten output ports (when being used as a power divider).

(21) FIG. 21 is an exploded perspective view of the power divider/combiner as shown in FIG. 1.

(22) FIG. 22 is a partial cutaway view of embodiments of the divider/combiner of FIG. 11 including a cap screw O-ring seal.

(23) FIG. 23 is a section of nested coaxial line that defines mode amplitude reflection coefficients.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

(24) Attention is directed to U.S. patent application Ser. No. 15/493,074, invented by the inventor hereof, filed Apr. 20, 2017, and incorporated herein by reference. Attention is also directed to U.S. patent application Ser. No. 15/493,591, invented by the inventor hereof, filed Apr. 21, 2017, and incorporated herein by reference. FIG. 1 shows a microwave power divider 100, which can alternatively be used as a power combiner, in accordance with various embodiments. It will hereinafter be referred to as a power divider-combiner 100.

(25) Hereinafter described as if for use as a power divider, the power divider-combiner 100 has (see FIGS. 1 and 17) a single main input port flange 112, and a quantity N of output port connectors 101. It is to be understood that, for convenience, the terms “input” and “output”, when used herein and in the claims, assume that the divider-combiner is being used as a power divider. The roles of the inputs and outputs are reversed when the divider-combiner is being used as a power combiner.

(26) In the illustrated embodiments, the power divider-combiner 100 (see FIG. 1) has, at a forward end, an input RF connector 209 which is Type N female. Other connector types, such as Type N male, SC (male or female), LC (male or female), TNC (male or female), or SMA (male or female), for example, could be employed. In the illustrated embodiments, the divider-combiner 100 of FIG. 1 includes a center conductor 110.

(27) The power divider-combiner 100-has (see FIG. 1, 2, 3, or 17), in the illustrated embodiments, ten Type N (female) connectors for the output ports 101. Other types of output and input RF connectors are possible.

(28) The power divider-combiner 100 includes a cylindrical conductor 103 defining, in some embodiments, the shape of or the general shape of a hollow cylinder (see FIGS. 4, 9, 14, and 21). Each output RF connector 101 has a center conductor 102 electrically connected with an outer end of the conductor 103.

(29) The conductor 103 has a rear end including bores 122 (FIG. 14) extending from the outer cylindrical surface of the center conductor 103 to the inner cylindrical surface of the conductor 103. FIG. 5 shows center conductor 102 with a slotted end 121 distal from the output port 101 (see FIG. 3) and compression fit into one of the receiving bores 122. FIG. 6 shows an alternative connection. In the embodiments of FIG. 6, the center conductor 102 is attached with solder or braze alloy 123 into the bore 122 to form the electrical and thermal connection to the conductor 103.

(30) The power divider-combiner 100 includes (see FIG. 1, 2, 4, 5 or 6, 7 or 8, 9, 11, and 21) a main center conductor 108 which is cylindrical in the illustrated embodiments; however, other shapes are possible. FIG. 7 shows an embodiment in which the forward end of the main center conductor 108 includes a receiving bore 111. The input center conductor 110 has a slotted end 128 distal from the input port 209 (FIG. 1, 11) and compression fit into the receiving bore 111, in the illustrated embodiments. FIG. 8 shows an alternative connection. In the embodiments of FIG. 8, the center conductor 110 is attached with solder or braze alloy 129 into bore 111 to form the electrical and thermal connection to main center conductor 108. Also embodied in FIG. 8 is a bore 130 in the sidewall of center conductor 108 which allows pressure relief out of bore 111 during soldering or brazing. A customer's coax cables 222 are shown in FIG. 2 making connection to the input port RF connector 209 and to each output port RF connector 101.

(31) The power divider-combiner 100 includes a cylindrical conductor 106 defining, in some embodiments, the shape of or the general shape of a hollow cylinder (see FIGS. 4, 9, 16, and 21) and having an inner cylindrical surface 106b with a cylinder axis, an outer cylindrical surface, and a forward facing opening. The power divider-combiner 100 further includes a cylindrical conductor 109 defining, in some embodiments, the shape of or the general shape of a hollow cylinder (see FIGS. 4, 9, 15, and 21) and having an inner cylindrical surface 109b with a cylinder axis, an outer cylindrical surface 109a, and a rearward facing opening. At least a portion of the conductor 109 is received in the conductor 106, via its forward facing opening, with a gap between inner surface 106b and outer surface 109a

(32) The power divider-combiner 100 further includes, at a rearward end, an electrically and thermally conducting rear flange 107 to which the rearward end of main center conductor 108 electrically and mechanically connects, and to which the rearward end of conducting cylinder 106 also connects. In the embodiments shown in FIGS. 1, 2, 5, 6, 11, and 16 the cylinder conductor 106 and rear flange 107 are shown as one piece, hereafter referred to as cylinder-flange 400 (see FIG. 16). Other embodiments are possible, such as a soldered or brazed connection. The flange 107 includes an alignment hub outer surface 107b and a radial line conducting surfaces 107a and 107c.

(33) In the illustrated embodiments, there is a gap between the inner surface 109b and the outer surface of the main conductor 108.

(34) The forward end of the cylinder conductor 109 electrically and mechanically connects to the input port flange 112, hereafter referred to as cylinder-flange 300 (see FIG. 1 or 2, and 15). In the embodiments shown in FIGS. 1, 2, 7, 8, 11, and 15 the cylinder conductor 109 and conducting flange 112 are shown as one piece. Other embodiments are possible, such as a soldered or brazed connection. Input port flange 112 includes an alignment hub outer surface 112b and a radial line conducting surface 112a.

(35) In the illustrated embodiments, the power divider-combiner 100 further includes a sidewall or exterior ground conductor 105 that has a central aperture receiving conductor 103, with a gap between the ground conductor 105 and the conductor 103. The output RF connectors 101 are angularly spaced apart relative to each other, mounted to the sidewall 105, and their center conductors 102 pass through the sidewall 105. Further, the RF connector center conductors 102 define respective axes that are all perpendicular to coincident cylinder axes defined by the conductors 106 and 109, in some embodiments.

(36) The power divider-combiner 100 further includes a forward flange 104 that is electrically and thermally conducting, in the illustrated embodiment. The cylindrical conductor 103 has a forward end that is electrically and thermally connected to the forward flange 104, hereafter referred to as cylinder-flange 200 (see FIG. 14), and has an inner surface 103b spaced apart from cylinder conductor 106 (see FIG. 1 or 2, 6, 7 or 8, and 9).

(37) In various embodiments, the outer surface of main center conductor 108 and the inner surface of cylindrical conductor 109, the outer surface of conductor 109 and the inner surface of cylindrical conductor 106, the outer surface of conductor 106 and the inner surface of cylindrical conductor 103 define three unit element (quarter-wave) coaxial transmission lines. The outer surface of the conductor 103 and the inner surface of the ground conductor 105 and their connection to the flange 104 define a unit element (quarter-wave at mid-band) transmission line shorted shunt stub 132 (see FIG. 18).

(38) In the illustrated embodiments, FIG. 1 shows the power divider-combiner 100 further includes a circular O-ring groove 113a in a forward surface of input port flange 112, and an O-ring 114a in the groove 113a, so the O-ring 114a sits between and engages the input port flange 112 and the input RF connector 209. Instead of a groove, in the illustrated embodiments, the input flange 112 has a circular 45 degree chamfer 115 in a rearward facing radially exterior cylindrical surface, and the power divider-combiner 100 further includes an O-ring 114b residing within the chamfer 115, so the O-ring 114b sits between and engages input flange 112 and a forward facing surface 104c (FIG. 14) within flange 104. In the illustrated embodiments, the power divider-combiner 100 further includes a circular O-ring groove 113b in a forward surface of ground conductor 105, and an O-ring 114c in the groove 113b, so the O-ring 114c sits between and engages the ground conductor 105 and the flange 104. In the illustrated embodiments, the power divider-combiner 100 further includes angularly spaced-apart circular O-ring grooves 113c in an outer surface of the sidewall 105, and O-rings 114d in the grooves 113c, so the O-rings 114d sit between and engage the sidewall 105 and the output port connectors 101. The grooves 113c and O-rings 114d are also shown in FIG. 3. Instead of a groove, in the illustrated embodiments, the outer back plate 107 has a circular 45 degree chamfer 116 in a forward facing radially exterior cylindrical surface, and the power divider-combiner 100 further includes an O-ring 114e in the chamfer 116, so the O-ring 114e sits between and engages the outer back plate 107 and a rearward facing surface of the sidewall 105. In the illustrated embodiments, O-ring 114f engages a circular O-ring groove 113d located within the head of cap screw SC5 (see FIGS. 11, 12, and 21) and sits between the rear back plate 107 and the head of cap screw SC5. In the illustrated embodiments, O-ring 114g engages a circular O-ring groove 113e located within the head of cap screw SC3 (see FIGS. 11, 13, and 21) and sits between input flange 112 and the head of cap screw SC3. In the illustrated embodiments, O-ring 114h engages a circular O-ring groove 113f located within the head of cap screw SC4 (see FIGS. 11, 22, and 21) and sits between rear flange 107 and the head of cap screw SC4.

(39) It should be apparent that when an O-ring is provided in a groove of one component that faces another component, the groove could instead be provided in the other component. For example, the groove 114c could be provided in the rearward face of flange 104 instead of in the forward face of ground conductor 105. Also, an O-ring groove containing an O-ring may be included within the flange of input RF connector 209, thereby eliminating the need for O-ring groove 113a and O-ring 114a. Additionally, an O-ring groove containing an O-ring may be included within the flange of output RF connector 101, thereby eliminating the need for O-ring groove 113c and O-ring 114d.

(40) In the illustrated embodiments, the power divider-combiner 100 further includes threaded bores or apertures 118 extending inwardly from the radially exterior cylindrical surface of the sidewall 105. In the illustrated embodiments, the divider-combiner 100 further includes smaller diameter bores or apertures 119, aligned with the bores 118, and extending from the bores 118 to a gap between the sidewall 105 and the cylindrical conductor 103. In the illustrated embodiments, there are two bores 118 and they are ⅛ NPT threaded bores. In the illustrated embodiments, the power divider-combiner 100 further includes threaded sealing plugs 117 threadedly received in the bores 118. One or both of the plugs 117 may be removed and replaced with a pressure valve such as, for example, a Schrader (e.g., bicycle tube) pressure valves so that dry Nitrogen or arc suppression gas mixture may be introduced into the interior of the divider-combiner 100 via the bores 119. Other types of pressure valves may be used, such as Presta or Dunlop valves, for example.

(41) There are several reasons why the O-rings 114a-h, threaded bores 118, bores 119, and plugs 117 are advantageous. In FIG. 1, with both plugs 117 replaced with Schrader valves by the customer, dry Nitrogen can be introduced through one Schrader valve and allowed to exit the other Schrader valve so as to purge moisture-laden air from the sealed divider/combiner interior.

(42) Higher-pressure gas, introduced by means of the Schrader valves and an external gas source connection 221 (FIG. 2), increases the air dielectric breakdown strength within the divider-combiner 100. The entire system including cables may then withstand higher microwave power transmission.

(43) In some microwave radar and countermeasure systems used in fighter aircraft, the microwave waveguide and cable system components are pressurized at ground level. For example, in FIG. 2 the Type N input connector O-ring 114a and the cable 222 which connects to it completely seals the forward end of the divider-combiner. Both plugs 117 may be replaced with Schrader valves 120 and the divider-combiner interior then purged with moisture-free pressurized nitrogen or other pressurized gas mixture. Then the gas feed connection 221 is removed, the Schrader valves 120 are capped, and the divider/combiner 100 is expected to hold pressure for the duration of the flight mission. The O-rings 114a-h help maintain this interior pressure.

(44) The O-rings 114a-h provide containment of high-breakdown strength gas, such as sulfur hexafluoride. The O-rings 114a-h keep this expensive (and possibly toxic) gas contained in the divider-combiner 100. The divider-combiner 100 with O-rings 114a-h and built with a Type N or Type SC input connector 209 is sealed, in some embodiments. There are no ventilation holes in the connector dielectric. The divider-combiner 100 then must use two Schrader valves 120 mounted so that the divider-combiner's interior may be successfully filled with the arc-protection gas compound.

(45) Referring to FIG. 1, the electrical short 104a is located at reference plane a-a, and the shorted shunt stub 132 (see FIG. 18) makes connection to the output connector center conductors 102 at reference plane b-b.

(46) Collectively, the three unit element transmission lines with characteristic impedances Z.sub.1, Z.sub.2, and Z.sub.3 and the shorted shunt stub section with characteristic impedance Z.sub.SH are electrically modeled, in a generalized form, as a passband filter equivalent circuit shown in FIG. 18. A passband is a portion of the frequency spectrum that allows transmission of a signal with a desired minimum insertion loss by means of some filtering device. In other words, a passband filter passes a band of frequencies to a defined passband insertion loss vs. frequency profile. Desired filter passband performance is achieved by a four-step process:

(47) 1) Given a source impedance quantity Z.sub.S, divider quantity (number of outputs) N, load impedance quantity Z.sub.L/N and desired passband a) bandwidth, and b) input port return loss peaks within the passband, calculate the unit element transmission line characteristic impedances Z.sub.1, Z.sub.2, Z.sub.3 and unit element shorted shunt stub characteristic impedance value Z.sub.SH (see FIG. 18). This may be accomplished, as one approach, using the design theory as described in M. C. Horton and R. J. Wenzel, “General theory and design of quarter-wave TEM filters,” IEEE Trans. on Microwave Theory and Techniques, May 1965, pp. 316-327.

(48) 2) After determining the above desired electrical transmission line characteristic impedances, then find corresponding diameters for the conductor 108, inner and outer diameters of cylindrical conductors 109, and 106, and the inner diameter of conductor 103 which define unit element characteristic impedances Z.sub.1, Z.sub.2, and Z.sub.3. In addition, the outer diameter of the conductor 103 and the inner diameter of ground conductor 105 define the shorted shunt stub unit element characteristic impedance Z.sub.SH. For example (referring to Section 9-9 FIG. 9), the characteristic impedance Z.sub.1 is defined according to the formula Z.sub.1=60*log.sub.e(R.sub.b/R.sub.a) where quantity R.sub.b is the radius of the inner surface 109b of the conductor 109, and where quantity R.sub.a is the radius of the outer surface of the main center conductor 108. The characteristic impedance Z.sub.2 is defined according to the formula Z.sub.2.sup.=60*log.sub.e(R.sub.d/R.sub.c) where quantity R.sub.d is the radius of the inner surface 106b of the conductor 106, and where quantity R.sub.e is the radius of the outer surface 109a of conductor 109. The characteristic impedance Z.sub.3 is defined according to the formula Z.sub.3=60*log.sub.e(R.sub.f/R.sub.e) where quantity R.sub.f is the radius of the inner surface 103b of the conductor 103, and where quantity R.sub.e is the radius of the outer surface 106a of conductor 106. Similarly, the characteristic impedance Z.sub.SH is defined according to the formula Z.sub.SH=60*log.sub.e(Rh/R.sub.g) where quantity Rh is the radius of the inner surface of the ground conductor 105, and quantity R.sub.g is the radius of the outer surface 103a of conductor 103. The above expressions for impedances Z.sub.1, Z.sub.2, Z.sub.3 and Z.sub.SH assume air or vacuum-dielectric, but other dielectric materials may be used along the lengths of unit element transmission lines corresponding to Z.sub.1, Z.sub.2, Z.sub.3, and Z.sub.SH, such as (but not limited to) Teflon, boron nitride, beryllium oxide, or diamond, for example.

(49) 3) Referring to FIG. 5 or 6, 15 and the equivalent circuit FIG. 18, the radial transmission line gap 125 formed between conductor surfaces 109c and the forward facing surface 107c of back plate 107 is adjusted so that the magnitude of the complex reflection coefficient at this junction is made as close as possible to the quantity (Z.sub.1/Z.sub.2−1)/(Z.sub.1/Z.sub.2+1) over the passband frequency range F.sub.1 to F.sub.2. Referring to FIG. 7 or 8 and 16, the radial transmission line gap 126 formed between conductor surfaces 106c and the rearward facing surface 112a of input flange 112 is adjusted so that the magnitude of the complex reflection coefficient at this junction is made as close as possible to the quantity (Z.sub.2/Z.sub.3−1)/(Z.sub.2/Z.sub.3+1) over the passband frequency range F1 to F2. Referring to FIG. 5 or 6 and 14, the radial transmission line gap 124 formed between conductor surfaces 103c and the forward facing surface 107a of back plate 107 is adjusted so that the magnitude of the complex reflection coefficient at this junction is made as close as possible to the quantity (Z.sub.SH/Z.sub.3−1)/(Z.sub.SH/Z.sub.3+1) over the passband frequency range F1 to F2. FIG. 23 shows two nested coaxial transmission lines 1 (inner line) and 2 (outer line) with a third shorted coaxial line. All three coaxial lines are each modeled using a combination of propagating TEM and evanescent TM modes. Complex reflection coefficients ρ.sub.1 and ρ.sub.2 at a nested coax junction (see FIG. 23) may be modeled, as one approach, by first using a field analysis formalism as presented by J. R. Whinnery, H. W. Jamieson, and T. E. Robbins, “Coaxial line discontinuities,” Proceedings of the I. R. E., November 1944, pp. 695-710, and then creating a mode-matching amplitude matrix M (FIG. 23) using the formalism as presented by H. Patzelt, and F. Arndt, “Double-plane steps in rectangular waveguides and their application for transformers, irises, and filters,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 771-776, May 1982.

(50) 4) Determining at each coax line junction the complex reflection coefficients ρ.sub.1 and ρ.sub.2 in the manner described above, the phases pi and p at each successive nested junction are used to adjust the physical length of each coax transmission line (with respective characteristic impedances Z.sub.1, Z.sub.2, Z.sub.3, and Z.sub.SH) to preserve unit element phase length for each section. This may be accomplished, as one approach, using the technique outlined in FIGS. 6.08-1 “Length corrections for discontinuity capacitances,” from G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-matching Networks, and Coupling Structures, Artech House Books, Dedham, M A, 1980.

(51) As an example, given: N=10, Z.sub.S=Z.sub.L=50 ohms, 23 dB return loss peaks are desired for a bandwidth F.sub.2/F.sub.1=2.91, where F.sub.1, F.sub.2 represent the lower and upper edges of the passband, respectively. Using the Horton & Wenzel technique, unit element characteristic impedances Z.sub.1, Z.sub.2, Z.sub.3 and the shorted shunt stub unit element characteristic impedance value Z.sub.SH were found. FIG. 19 shows calculated response using the derived characteristic impedances of the equivalent circuit in FIG. 18. Cross-section dimensions throughout the filter device were then determined so as to achieve these unit element characteristic impedances. The radial line gaps 124, 125, and 126 (FIG. 4 or 5, and 6 or 7) were optimized to give as closely as possible the correct magnitude (as stated earlier) of the complex reflection coefficients calculated for each unit element junction, and the physical lengths of each unit element were adjusted to achieve quarter-wave phase length at mid-band. For example, a quarter-wave length at, for example, a mid-band frequency of 1.75 GHz is equal to 1.686 inches. The length between reference plane b-b and the forward-looking face of main center conductor 108 is 1.450″ for the divider-combiner 100 (FIG. 1). In comparison, for a non-nested design, the length would be at least 4.7 inches. The calculated scattering parameters S.sub.11, . . . , S.sub.n1 plotted in FIG. 19 characterize a Chebyshev filter response throughout the passband F.sub.1 through F.sub.2. The Horton & Wenzel technique can also be used to find different values for Z.sub.1, Z.sub.2, Z.sub.3, and Z.sub.SH to achieve other types of filter response such as, for example, maximally flat filter response.

(52) FIG. 20 shows measured RF performance of the divider-combiner of FIG. 1. Tested as a power divider, measured RF performance shows good correlation with predicted main port return loss −20*log.sub.10(|S.sub.11|) (dB) and typical output port insertion loss −20*log.sub.10(|S.sub.n1|) (dB) vs. frequency.

(53) Various conductive materials could be employed for the conductive components of the power divider-combiner 100. For example, in some embodiments, the parts (other than those parts for which materials have been already described) are fabricated from 6061 alloy aluminum. For corrosion resistance, some of these parts may be a) alodine coated, or b) electroless nickel flash-coated and MlLspec gold plated. In other embodiments, parts are made of brass or magnesium alloy, also MlLspec gold plated. Another possibility is MILspec silver plated, with rhodium flash coating to improve corrosion resistance.

(54) To better enable one of ordinary skill in the art to make and use various embodiments, FIG. 21 is an exploded view of the power divider-combiner 100 of FIG. 1. In the illustrated embodiments (see FIGS. 10, 11, and 21), the flange-cylinder assembly 200 is mounted with four 8-32×0.625″ socket head screws SC1 to the forward face of outer ground conductor 105. In the illustrated embodiments (see FIGS. 10, 21), the Type N female RF connector 209 is mounted with four 4-40×0.25″ socket head cap screws SC2 to the input connector flange 112. Referring to FIGS. 11, 12, and 21, five 6-32×0.625″ socket head screws SC5 each include an O-ring 114f contained in a groove 113d machined into the head of the cap screw (FIG. 12). Referring to FIGS. 11, 13, and 21, four 4-40×0.50″ socket head screws SC3 each include an O-ring 114g contained in a groove 113e machined into the head of the cap screw (FIG. 13). Referring to FIGS. 11, 22, and 21, a single 2-56×0.625″ socket head screw SC4 includes an O-ring 114h contained in a groove 113f machined into the head of the cap screw (FIG. 22). In some embodiments, the screws SC3, SC4, and SC5 that are employed are obtained from ZAGO Manufacturing. In some embodiments, other types of screw fasteners can be used such as, for example, button head cap screws. Other fastener thread sizes, lengths, and materials or attachment methods can be employed.

(55) The main center conductor 108 is bolted to surface 107c of the rear flange 107 using a single 2-56×¾″ stainless steel cap screw SC4 (FIG. 1 or 2, 11, 16, and 21). Other size screws or other methods of attachment can be employed. Additionally, conductor 108 and rear flange 107, both which may be plated for soldering, are shown in FIG. 5 or 6 with solder fillet 127 after soldering, so as to improve thermal and electrical contact at this connection.

(56) FIG. 14 shows a perspective view of a flange-cylinder assembly 200 in accordance with various embodiments. In the illustrated embodiments, the flange cylinder assembly 200 includes the conducting flange 104 and the conductor 103. In the illustrated embodiments, the flange 104 and the conductor 103 are machined from a common piece. In alternative embodiments, the flange 104 and conductor 103 are separate pieces that are thermally and electrically connected together. The conductor 103 is bolted, soldered, or brazed, or press fit onto conducting flange 104 in alternative embodiments. The conductor 103 includes an outer conductive surface 103a that is cylindrical or generally cylindrical in the illustrated embodiments. The conductor 103 further includes an inner conductive surface 103b that is cylindrical or generally cylindrical in the illustrated embodiments. The flange cylinder assembly 200 includes a first end defined by the flange 104 and a second end 103c, defined by the conductor 103. The end 103c defines a radial line conductor surface. The flange 104 includes an alignment hub outer surface 104b and a short circuit conducting surface 104a. The outer surface 104b has an outer cylindrical surface having a diameter that is larger than the diameter of the outer cylindrical surface 103a of the conductor 103. The flange 104 also has an outer cylindrical surface having a diameter greater than the diameter of the surface 104b. Previously described apertures 122 for receiving center conductors 102 are shown.

(57) FIG. 17 shows a perspective view of the power divider-combiner 100 of FIG. 21 after assembly.

(58) In the filter circuit synthesis technique as presented in the Horton & Wenzel reference, a desired circuit response (return loss over a passband as shown in FIG. 16, for example) results from the synthesis of transmission line characteristic impedances for a sequence of one or more unit element (substantially quarter-wave at the mid-band frequency f.sub.O) transmission lines followed by a unit element shorted shunt stub transmission line connected in parallel with circuit load Z.sub.L/N, as shown in FIG. 18 for this example.

(59) Referring to FIG. 1 or 2, 3, 4, and 5 and the equivalent circuit shown in FIG. 18, the inner conductor 108 and the inner surface 109b of conductor 109 form a unit element (substantially quarter-wave) transmission line with characteristic impedance Z.sub.1. The outer surface 109a of conductor 109 and the inner surface 106b of conductor 106 form a unit element transmission line with characteristic impedance Z.sub.2. The outer surface 106a of conductor 106 and the inner surface 103b of the conductor 103 form a unit element transmission line with characteristic impedance Z.sub.3, which has a unit element mid-band frequency phase length θ=θ′+θ.sub.R where θ.sub.R is the phase length of the radial transmission line 124 (FIG. 5 or 6) formed by the end 103c of the conductor 103 and the forward facing surface 107a of the rear flange 107. 1) Electrical reference plane a-a (FIG. 18) corresponds to the physical reference plane a-a shown in FIG. 1, where the flange 104 conducting surface 104a in FIG. 14 serves as the short circuit for a unit element shorted shunt stub 132 (FIG. 18). 2) Electrical reference plane b-b (FIG. 18) corresponds to the physical reference plane b-b shown in FIG. 1, where the shorted shunt stub 132 (FIG. 18) connects in parallel with output termination impedance quantity Z.sub.L/N. 3) Between reference planes a-a and b-b (FIG. 18) is a unit element with characteristic impedance Z.sub.SH. The above described unit elements are substantially one-quarter wavelength long at the passband mid-band frequency f.sub.O. One way of interpreting a quarter-wavelength transmission line (at the mid-band frequency f.sub.O) is that it ‘transforms’ the wave admittance on a Smith Chart along a circle about the origin (where the reflection coefficient magnitude is zero) exactly 180 degrees.

(60) In the illustrated embodiments, the quantity N of output RF connectors equals ten, and the corresponding quantity N of receiving bores 122 (FIG. 5 or 6, 14, and 21) in the conductor 103 equals ten. Other values of N=2, 3, . . . , 12 or more are possible. For example, a two-way divider-combiner has quantity N=2 equally spaced receiving bores 122 (and therefore N=2 output RF connectors).

(61) In the illustrated embodiments, the overall structure may alternatively be constructed (excluding the input connector 209 and its center conductor 110, and the ten output connectors 101 and their respective center conductors 102) using 3D printing using plastic or metal material, followed by plating with an electrically conducting material.

(62) Divider output connectors 101 (FIGS. 1, 2, 3, 17, and 21) are shown as flange mounted Type N (female) connectors. Each output connector (only one of ten connectors 101 is shown in FIG. 21) mounts to outer conductor 105 using two 4-40× 3/16″ cap screws SC6 (FIG. 21). Other Type N (female, or male) mounting types and other fastener sizes and types, or mechanical attachments can be employed. Other kinds of output RF connectors, such as TNC, SMA, SC, 7-16 DIN, 4.3-10 DIN male or female, and other EIA-type flanges can be employed. Press-fit, brazed or soldered non-flanged RF connectors may also be employed.

(63) In the illustrated embodiments, the center conductor 108 plus flange-cylinder 400 assembly is bolted to the end interior of ground conductor 105 by means of five 6-32×⅝″ stainless steel O-ring-sealed cap screws SC5 (FIGS. 11, 12, 21). Other fastener sizes and types, or other mechanical attachment methods can be employed.

(64) In various embodiments, the conductive cylinders 109, 106, and 103 are solid conducting cylinders connected thermally and electrically to respective 112, 107, and 104 thermally and electrically conductive flanges. This provides a superior thermal, electrical, and easier-to-fabricate design. Main port return loss, in some embodiments, measures approximately 23 dB or better over the frequency range 1.0 to 2.5 GHz, and divided power measures approximately −10 dB at one of the ten output ports.

(65) In compliance with the patent statutes, the subject matter disclosed herein has been described in language more or less specific as to structural and methodical features. However, the scope of protection sought is to be limited only by the following claims, given their broadest possible interpretations. Such claims are not to be limited by the specific features shown and described above, as the description above only discloses example embodiments.