Patent Publication Number: US-11043725-B1

Title: Reactive power combiners and dividers including nested coaxial conductors

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This is a continuation of U.S. patent application Ser. No. 16/295,804 filed Mar. 7, 2019, which is a continuation of U.S. patent application Ser. No. 16/016,457 filed Jun. 22, 2018 (now U.S. Pat. No. 10,276,906), which is a continuation of U.S. patent application Ser. No. 15/923,515 filed Mar. 16, 2018, naming David B. Aster as inventor (now U.S. Pat. No. 10,312,565), which in turn is a continuation-in-part of U.S. patent application Ser. No. 15/582,533, filed Apr. 28, 2017 (now U.S. Pat. No. 9,947,986), which is a continuation-in-part of U.S. patent application Ser. No. 15/043,570, filed Feb. 14, 2016 (now U.S. Pat. No. 9,673,503) and a continuation-in-part of U.S. patent application Ser. No. 15/078,086, filed Mar. 23, 2016 (now U.S. Pat. No. 9,793,591), both of which (Ser. No. 15/043,570 and Ser. No. 15/078,086) in turn claim priority to U.S. Provisional Patent Application Ser. No. 62/140,390, filed Mar. 30, 2015, all of which were invented by the inventor hereof and all of which are incorporated herein by reference. 
     U.S. patent application Ser. No. 15/923,515 is also a continuation in part of U.S. patent application Ser. No. 15/614,572, filed Jun. 5, 2017, (now U.S. Pat. No. 9,960,469), which is a continuation-in-part of U.S. patent application Ser. No. 15/043,570, filed Feb. 14, 2016 (now U.S. Pat. No. 9,673,503), and a continuation-in-part of U.S. patent application Ser. No. 15/078,086, filed Mar. 23, 2016 (now U.S. Pat. No. 9,793,591), both of which (Ser. No. 15/043,570 and Ser. No. 15/078,086) in turn claim priority to U.S. Provisional Patent Application Ser. No. 62/140,390, filed Mar. 30, 2015, all of which were invented by the inventor hereof and all of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The technical field includes methods and apparatus for summing (or combining) the signals from a microwave antenna array or for combining a number of isolator-protected power sources or for dividing power into a number of separate divided output signals. 
     BACKGROUND 
     The communications and radar industries have interest in reactive-type broadband microwave dividers and combiners. Even though not all ports are RF matched, as compared to the Wilkinson power divider/combiner (see Ernest J. Wilkinson, “An N-way hybrid power divider,” IRE Trans. on Microwave Theory and Techniques, January, 1960, pp. 116-118), the reactive-type mechanical and electrical ruggedness is an advantage for high-power combiner applications. This assumes that the sources to be combined are isolator-protected and of equal frequency, amplitude and phase. Another combiner application is improving the signal-to-noise ratio of faint microwave communication signals using an antenna dish array connected to the reactive power combiner using phase length-matched cables. The signal from each dish antenna sees an excellent “hot RF match” into each of the N combining ports of the reactive power combiner and is therefore efficiently power combined with the other N−1 antenna signals having equal frequency, amplitude, and phase. However, the cable- and antenna-generated thermal noise signal into each port of the N-way power combiner (with uncorrelated phase, frequency and amplitude) sees an effective “cold RF match” and is thus poorly power combined. The signal-to-noise ratio improves for large values of the number of combiner ports N. Still another application is for one of two reactive N-way power dividers to provide a quantity N signals of equal phase, amplitude and frequency as inputs to a set of N broadband amplifiers each with a noise figure X db/MHz. A second high-power N-way reactive power combiner is used to combine the N amplified signals with the benefit of improving the overall total noise figure by several dB.  
     An example of a reactive combiner/divider is described in U.S. Pat. No. 8,508,313 to Aster, incorporated herein by reference. Broadband operation is achieved using two or more stages of multiconductor transmission line (MTL) power divider modules. An 8-way reactive power divider/combiner 200 of this type is shown in FIGS. 4 and 5 of application Ser. No. 15/043,570. Described as a power divider, microwave input power enters coax port 201, which feeds a two-way MTL divider 202. Input power on the main center conductor 206 (FIG. 6a, Section a1-a1) is equally divided onto two satellite conductors 207 which in turn each feed  quarter-wave transmission lines housed in module 203 (FIG. 4). Each of these quarter-wave lines feeds a center conductor 208 (FIG. 6b, Section a2-a2) in its respective four-way MTL divider module 204, power being equally divided onto satellite conductors 209 which in turn feed output coax connectors 205. This may  also be described as a two-stage MTL power divider where the first stage two-way divider (Stage B, FIG. 7) feeds a second stage (Stage A, FIG. 7) consisting of two 4-way MTL power dividers, for a total of eight outputs 205 of equally divided power. This two-stage divider network is described electrically in FIG. 7 as a shorted shunt  stub ladder filter circuit with a source admittance Y S   (B)  and a load admittance N S   (B) N S   (A) Y L   (A) . The first-stage (Stage B) quarter-wave shorted shunt stub transmission line characteristic admittances have values Y 10   (B)  and N S   (B) Y 20   (B) , respectively, which are separated by a quarter-wave main line with characteristic admittance value N S   (B) Y 12   (B) . Here the number of satellite conductors N S   (B) =2, N S   (A) =4 and Y 12   (B)  is the value of the row 1, column 2 element of the 3×3 characteristic admittance matrix Y (B)  for the two-way MTL divider (Section a1-a1, FIG. 6). Also, Y 10   (B) =Y 11   (B) +N S   (B) Y 12   (B)  and Y 20   (B) =Y 22   (B) +Y 12   (B) +Y 23   (B) . Each quarter-wave transmission line within housing 203 (FIG. 4) has characteristic admittance Y T  and  is represented in the equivalent circuit FIG. 7 as a quarter-wave main transmission line with characteristic admittance N S   (B) Y T . The second stage (Stage A) quarter-wave shorted shunt stub transmission line characteristic admittances have values N S   (B) Y 10   (A)  and N S   (B) N S   (A) Y 20   (A) , respectively, which are separated by a quarter-wave main line with characteristic admittance N S   (B) N S   (A) Y 12   (A) . Here Y 12   (A)  is the value of the row 1, column 2 element of the 5×5 characteristic admittance matrix Y (A)  for one of the two identical four-way MTL divider modules 204 (FIG. 4) with cross-section a2-a2 in FIG. 6b. A plot of scattering parameters for an octave bandwidth two-stage eight-way divider is shown in FIG. 4c of U.S. Pat. No. 8,508,313. Due to its complexity, the two-stage, three MTL module power divider/combiner as shown in FIGS. 4 and 5 is expensive to fabricate.            
     SUMMARY 
     Some embodiments provide a power divider/combiner having an input, a plurality of outputs, and nested unit element conductors, having approximately a 2.7:1 bandwidth, and having a shorter length than non-nested power divider/combiners. For example, some embodiments have a bandwidth of about 0.95 GHz to 2.55 GHz. Other embodiments have a bandwidth of about 0.47 GHz to 1.27 GHz. Still other embodiments have a bandwidth of about 0.40 GHz to 1.08 GHz. Some embodiments provide a reactive 10-way divider/combiner. 
     Some embodiments provide a power divider/combiner having a front end and a rear end and including 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. 
     Other embodiments provide a power divider/combiner having a front end and a rear end and including 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 center 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, the output connectors being angularly spaced apart relative to each other, the output connectors having center conductors electrically coupled to the third cylindrical conductor. 
     Still other embodiments provide a method of manufacturing a power divider/combiner having a front end and a rear end, the method including 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 front 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 center conductor in the third cylindrical conductor; providing 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 and having respective second conductors electrically coupled to the ground conductor proximate the back end of 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. 
    
    
     
       BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWINGS 
         FIG. 1  is a side view of a power divider/combiner in accordance with various embodiments, partly in section. 
         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. 
         FIG. 3  is a sectional view taken along line 3-3 of  FIG. 1  or  FIG. 2 . 
         FIG. 4  is a partial cut-away view of the divider-combiner of  FIG. 3 . 
         FIG. 5  is a partial cut-away view of the divider/combiner of  FIG. 1  or  FIG. 2  showing a connection point. 
         FIG. 6  is a partial cut-away view of the divider/combiner of  FIG. 1  or  FIG. 2  in accordance with alternative embodiments. 
         FIG. 7  is a partial cut-away view of the divider/combiner of  FIG. 1  or  FIG. 2  showing a connection point. 
         FIG. 8  is a partial cut-away view of the divider/combiner of  FIG. 1  or  FIG. 2  in accordance with alternative embodiments. 
         FIG. 9  is a sectional view taken along 9-9 of  FIG. 5  or  FIG. 6 . 
         FIG. 10  is an end view of the divider/combiner of  FIG. 1 . 
         FIG. 11  is a sectional view taken along line 11-11 of  FIG. 10 . 
         FIG. 12  is a partial cut-away view of embodiments of the divider/combiner of  FIG. 11  including a cap screw O-ring seal. 
         FIG. 13  is a partial cutaway view of embodiments of the divider/combiner of  FIG. 11  including a cap screw O-ring seal. 
         FIG. 14  is a perspective view of a conductor included in the divider/combiner of  FIG. 1 , partly in section. 
         FIG. 15  is a perspective view of a conductor included in the divider/combiner of  FIG. 1 . 
         FIG. 16  is a perspective view of a conductor included in the divider/combiner of  FIG. 1 , partly in section. 
         FIG. 17  is a perspective view of the divider-combiner of  FIG. 1 . 
         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. 
         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). 
         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). 
         FIG. 21  is an exploded perspective view of the power divider/combiner as shown in  FIG. 1 . 
         FIG. 22  is a partial cutaway view of embodiments of the divider/combiner of  FIG. 11  including a cap screw O-ring seal. 
         FIG. 23  is a section of nested coaxial line that defines mode amplitude reflection coefficients. 
     
    
    
     DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS 
     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 . 
     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. 
     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 . 
     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. 
     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 . 
     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 . 
     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&#39;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 . 
     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  106   b  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  109   b  with a cylinder axis, an outer cylindrical surface  109   a , 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  106   b  and outer surface  109   a    
     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  107   b  and a radial line conducting surfaces  107   a  and  107   c.    
     In the illustrated embodiments, there is a gap between the inner surface  109   b  and the outer surface of the main conductor  108 . 
     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  112   b  and a radial line conducting surface  112   a.    
     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. 
     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  103   b  spaced apart from cylinder conductor  106  (see  FIG. 1 or 2, 6, 7 or 8, and 9 ). 
     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 ). 
     In the illustrated embodiments,  FIG. 1  shows the power divider-combiner  100  further includes a circular O-ring groove  113   a  in a forward surface of input port flange  112 , and an O-ring  114   a  in the groove  113   a , so the O-ring  114   a  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  114   b  residing within the chamfer  115 , so the O-ring  114   b  sits between and engages input flange  112  and a forward facing surface  104   c  ( FIG. 14 ) within flange  104 . In the illustrated embodiments, the power divider-combiner  100  further includes a circular O-ring groove  113   b  in a forward surface of ground conductor  105 , and an O-ring  114   c  in the groove  113   b , so the O-ring  114   c  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  113   c  in an outer surface of the sidewall  105 , and O-rings  114   d  in the grooves  113   c , so the O-rings  114   d  sit between and engage the sidewall  105  and the output port connectors  101 . The grooves  113   c  and O-rings  114   d  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  114   e  in the chamfer  116 , so the O-ring  114   e  sits between and engages the outer back plate  107  and a rearward facing surface of the sidewall  105 . In the illustrated embodiments, O-ring  114   f  engages a circular O-ring groove  113   d  located within the head of cap screw SC 5  (see  FIGS. 11, 12, and 21 ) and sits between the rear back plate  107  and the head of cap screw SC 5 . In the illustrated embodiments, O-ring  114   g  engages a circular O-ring groove  113   e  located within the head of cap screw SC 3  (see  FIGS. 11, 13, and 21 ) and sits between input flange  112  and the head of cap screw SC 3 . In the illustrated embodiments, O-ring  114   h  engages a circular O-ring groove  113   f  located within the head of cap screw SC 4  (see  FIGS. 11, 22, and 21 ) and sits between rear flange  107  and the head of cap screw SC 4 . 
     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  114   c  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  113   a  and O-ring  114   a . 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  113   c  and O-ring  114   d.    
     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. 
     There are several reasons why the O-rings  114   a - 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. 
     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. 
     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  114   a  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  114   a - h  help maintain this interior pressure. 
     The O-rings  114   a - h  provide containment of high-breakdown strength gas, such as sulfur hexafluoride. The O-rings  114   a - h  keep this expensive (and possibly toxic) gas contained in the divider-combiner  100 . The divider-combiner  100  with O-rings  114   a - 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&#39;s interior may be successfully filled with the arc-protection gas compound. 
     Referring to  FIG. 1 , the electrical short  104   a  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. 
     Collectively, the three unit element transmission lines with characteristic impedances Z 1 , Z 2 , and Z 3  and the shorted shunt stub section with characteristic impedance Z 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: 
     1) Given a source impedance quantity Z S , divider quantity (number of outputs) N, load impedance quantity Z 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 1 , Z 2 , Z 3  and unit element shorted shunt stub characteristic impedance value Z 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. 
     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 1 , Z 2 , and Z 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 SH . For example (referring to Section 9-9  FIG. 9 ), the characteristic impedance Z 1  is defined according to the formula Z 1 =60*log e (R b /R a ) where quantity R b  is the radius of the inner surface  109   b  of the conductor  109 , and where quantity R a  is the radius of the outer surface of the main center conductor  108 . The characteristic impedance Z 2  is defined according to the formula Z 2   = 60*log e (R d /R c ) where quantity R d  is the radius of the inner surface  106   b  of the conductor  106 , and where quantity R e  is the radius of the outer surface  109   a  of conductor  109 . The characteristic impedance Z 3  is defined according to the formula Z 3 =60*log e (R f /R e ) where quantity R f  is the radius of the inner surface  103   b  of the conductor  103 , and where quantity R e  is the radius of the outer surface  106   a  of conductor  106 . Similarly, the characteristic impedance Z SH  is defined according to the formula Z SH =60*log e (Rh/R g ) where quantity Rh is the radius of the inner surface of the ground conductor  105 , and quantity R g  is the radius of the outer surface  103   a  of conductor  103 . The above expressions for impedances Z 1 , Z 2 , Z 3  and Z SH  assume air or vacuum-dielectric, but other dielectric materials may be used along the lengths of unit element transmission lines corresponding to Z 1 , Z 2 , Z 3 , and Z SH , such as (but not limited to) Teflon, boron nitride, beryllium oxide, or diamond, for example. 
     3) Referring to  FIG. 5 or 6, 15  and the equivalent circuit  FIG. 18 , the radial transmission line gap  125  formed between conductor surfaces  109   c  and the forward facing surface  107   c  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 1 /Z 2 −1)/(Z 1 /Z 2 +1) over the passband frequency range F 1  to F 2 . Referring to  FIG. 7 or 8 and 16 , the radial transmission line gap  126  formed between conductor surfaces  106   c  and the rearward facing surface  112   a  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 2 /Z 3 −1)/(Z 2 /Z 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  103   c  and the forward facing surface  107   a  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 SH /Z 3 −1)/(Z SH /Z 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 1  and ρ 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. 
     4) Determining at each coax line junction the complex reflection coefficients ρ 1  and ρ 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 1 , Z 2 , Z 3 , and Z 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. 
     As an example, given: N=10, Z S =Z L =50 ohms, 23 dB return loss peaks are desired for a bandwidth F 2 /F 1 =2.91, where F 1 , F 2  represent the lower and upper edges of the passband, respectively. Using the Horton &amp; Wenzel technique, unit element characteristic impedances Z 1 , Z 2 , Z 3  and the shorted shunt stub unit element characteristic impedance value Z 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 11 , . . . , S n1  plotted in  FIG. 19  characterize a Chebyshev filter response throughout the passband F 1  through F 2 . The Horton &amp; Wenzel technique can also be used to find different values for Z 1 , Z 2 , Z 3 , and Z SH  to achieve other types of filter response such as, for example, maximally flat filter response. 
       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 10 (|S 11 |) (dB) and typical output port insertion loss −20*log 10 (|S n1 |) (dB) vs. frequency. 
     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. 
     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 SC 1  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 SC 2  to the input connector flange  112 . Referring to  FIGS. 11, 12, and 21 , five 6-32×0.625″ socket head screws SC 5  each include an O-ring  114   f  contained in a groove  113   d  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 SC 3  each include an O-ring  114   g  contained in a groove  113   e  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 SC 4  includes an O-ring  114   h  contained in a groove  113   f  machined into the head of the cap screw ( FIG. 22 ). In some embodiments, the screws SC 3 , SC 4 , and SC 5  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. 
     The main center conductor  108  is bolted to surface  107   c  of the rear flange  107  using a single 2-56×¾″ stainless steel cap screw SC 4  ( 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. 
       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  103   a  that is cylindrical or generally cylindrical in the illustrated embodiments. The conductor  103  further includes an inner conductive surface  103   b  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  103   c , defined by the conductor  103 . The end  103   c  defines a radial line conductor surface. The flange  104  includes an alignment hub outer surface  104   b  and a short circuit conducting surface  104   a . The outer surface  104   b  has an outer cylindrical surface having a diameter that is larger than the diameter of the outer cylindrical surface  103   a  of the conductor  103 . The flange  104  also has an outer cylindrical surface having a diameter greater than the diameter of the surface  104   b . Previously described apertures  122  for receiving center conductors  102  are shown. 
       FIG. 17  shows a perspective view of the power divider-combiner  100  of  FIG. 21  after assembly. 
     In the filter circuit synthesis technique as presented in the Horton &amp; 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 O ) transmission lines followed by a unit element shorted shunt stub transmission line connected in parallel with circuit load Z L /N, as shown in  FIG. 18  for this example. 
     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  109   b  of conductor  109  form a unit element (substantially quarter-wave) transmission line with characteristic impedance Z 1 . The outer surface  109   a  of conductor  109  and the inner surface  106   b  of conductor  106  form a unit element transmission line with characteristic impedance Z 2 . The outer surface  106   a  of conductor  106  and the inner surface  103   b  of the conductor  103  form a unit element transmission line with characteristic impedance Z 3 , which has a unit element mid-band frequency phase length θ=θ′+θ R  where θ R  is the phase length of the radial transmission line  124  ( FIG. 5 or 6 ) formed by the end  103   c  of the conductor  103  and the forward facing surface  107   a  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  104   a  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 L /N. 3) Between reference planes a-a and b-b ( FIG. 18 ) is a unit element with characteristic impedance Z SH . The above described unit elements are substantially one-quarter wavelength long at the passband mid-band frequency f O . One way of interpreting a quarter-wavelength transmission line (at the mid-band frequency f 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. 
     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). 
     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. 
     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 SC 6  ( 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. 
     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 SC 5  ( FIGS. 11, 12, 21 ). Other fastener sizes and types, or other mechanical attachment methods can be employed. 
     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. 
     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.