Abstract:
Devices are described that combine or divide electromagnetic signal power using short-circuited parallel-coupled multiconductor transmission lines. Such devices include single-stage, multi-stage ‘traveling wave’, and multi-stage broadband filter structures. Electrically shorting each coupled conductor simultaneously provides thermal cooling from heat generated by RF dissipative loss. These features may provide a compact, thermally robust power combiner/divider covering 3:1 bandwidth or greater. The devices may be applicable to radar, electronic countermeasures (ECM), and communications transmitters.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims benefit of, and priority under 35 USC §119(e) from U.S. provisional application No. 61/152,191, entitled “Multiconductor Transmission Line Power Combiner/Divider” filed Feb. 12, 2009, which is incorporated by reference herein in its entirety. 
    
    
     FIELD 
     The present invention relates generally to devices for summing (or combining) the power of a number of electromagnetic power sources or dividing power into a number of separate divided output signals, and more particularly, to devices using a multiconductor transmission line corporate ‘tree’ for summing or dividing signal power. 
     BACKGROUND 
     The communications and radar industries have had considerable interest in microwave amplifier power combiners featuring non-overmoded compactness, thermal robustness, high combining efficiency, and the ability to perform over a large bandwidth. 
     One power combining method uses a corporate ‘tree’ structure (see  FIG. 1 ; see also Kenneth J. Russell, “Microwave power combining techniques,”  IEEE Trans. on Microwave Theory and Techniques , May 1979, pp. 472-478). For example,  FIG. 1  is a block diagram of an 8-input, three-stage conventional corporate ‘tree’ structure that comprises eight isolator-protected source modules  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 , and  8  of equal frequency, magnitude, and relative phase delivering combined power to a load  16  through seven 2-input combiner subunits  9 ,  10 ,  11 ,  12 ,  13 ,  14  and  15 . Each of the 2-input combiner subunits  9 - 15  may be a three-port structure (two inputs, one output) for which not all ports can be impedance-matched. Alternatively, each of the 2-input combiner subunits  9 - 15  may have a source isolation port in addition to its output port, thus making it a four-port structure with all ports impedance-matched. The three combining stages include stage ‘A’ formed of the combiner subunit  15 , stage ‘B’ formed of the combiner subunits  13  and  14 , and stage ‘C’ formed of the combiner subunits  9 - 12 . Transmission lines  17 ,  18 ,  19 ,  20 ,  21 , and  22  separate each stage. Typically, each transmission line  17 - 22  has a uniform impedance, impedance-matched to its mating port on each end, and has a length compatible with convenient separation of the 2-input combiner subunits  9 - 15 . The large number of separate components for this prior art approach, and the physical space used for the overall structure, is often problematic, especially for low-frequency applications. 
     Another restriction is its useful bandwidth, which is limited to that of the individual combiner subunits. This bandwidth is further compromised due to adverse summing of the individual stage vector reflection coefficients within the corporate combiner structure. 
     An additional disadvantage of this prior art approach is that the combining efficiency of the corporate structure is compromised. This is due to the large number of separate components which contribute RF losses and also due to stage-to-stage reflection coefficient scattering which exacerbates the overall combiner loss. 
     The corporate ‘tree’ approach typically uses 2-input combiner subunits. This limits application to 2 N  input sources, where N is the number of combining stages. Therefore it is not possible to power combine, say, twelve input sources using the prior art corporate structure approach. 
     SUMMARY 
     The N-stage power combiner/divider is summarized for clarity as a power divider with N=2. A two-stage power combiner/divider comprises a first power divider stage, a plurality of transmission lines, and a second stage comprising a plurality of second power dividers. The first power divider stage comprises a first main conductor that includes a first terminal for electrical connection to a signal source and includes a second terminal electrically connected to a short circuit. A plurality of first satellite conductors is disposed symmetrically spaced apart from and substantially parallel to the first main conductor. Each of the first satellite conductors includes a first terminal electrically connected to a short circuit. Each transmission line includes a first terminal electrically connected to a second terminal of a respective first satellite conductor. Each second power divider belonging to the second stage comprises a second main conductor and a plurality of second satellite conductors. The second main conductor includes a first terminal electrically connected to a second terminal of a corresponding transmission line and includes a second terminal electrically connected to a short circuit. Each second satellite conductor is disposed symmetrically spaced apart from and substantially parallel to the second main conductor. Each second satellite conductor includes a first terminal electrically connected to a short circuit and includes a second terminal electrically connected to a respective termination admittance. There are a total of (N S1 ·N S2 ) such termination admittances, where there are N S1  number of first stage satellite conductors and an N S2  number of second stage satellite conductors. Each of these termination admittances receives substantially 1/(N S1 ·N S2 ) of the incident signal power incident to the first terminal of the first main conductor of the first power divider stage—assuming, for purposes of descriptive summary, a perfectly matched and lossless structure. 
     A first aspect of the present invention is summarized as a single-stage multiconductor transmission line combiner/divider, where the stage cross-section geometry may be designed for optimum scattering parameter performance at an operating frequency f 0 . 
     A second aspect of the present invention is summarized as two or more stages, where the cross-section geometry for each stage may be designed individually and independently for optimum scattering parameter performance at the operating frequency f 0 . This is defined as a ‘traveling wave’ design for optimum scattering parameter performance at frequency f 0 . 
     A third aspect of the present invention is summarized as incorporating a passband filter design for two or more combiner/divider stages, where the stage multiconductor transmission line cross-section geometries are interdependently designed for passband filter scattering parameter performance over a frequency range f LOW ≦f≦f HIGH . This aspect of the present invention may be demonstrated as a two-stage coax multiconductor combiner/divider structure with the ratio f HIGH /f LOW  approximately equal to 2. 
     Each of the summarized aspects of the present invention may include thermal robustness due to the electrical short circuit connection of one end of each main and satellite conductor to ‘ground’. Any heat created from RF dissipative loss on the main or satellite conductors may be thermally conducted to the short-circuit ground connection. Thus, every conductor within a combiner stage may serve as a thermal heat pipe, serving to cool the overall combiner structure. This constitutes another feature of the present invention, making possible the power combining/dividing of high-average-power RF signal amplifiers. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a conventional three-stage corporate ‘tree’ structure for combining eight power amplifiers or for dividing a power source into eight equal-amplitude output signals. 
         FIGS. 2   a  and  2   b  are an orthographic cutaway view and a cross-sectional view along a line  2 - 2  of  FIG. 2   a , respectively, of a single-stage 4-way divider/combiner according to the first aspect of the present invention. 
         FIG. 2   c  is a generalized electrical schematic of the single-stage 4-way combiner/divider of  FIGS. 2   a  and  2   b.    
         FIGS. 3   a  and  3   b  are orthographic views of one embodiment of the two-stage 1:8 divider/combiner according to either the second or third aspects of the present invention. 
         FIG. 3   c  is a cross-sectional view (section  3 - 3 ) of the two-stage 1:8 divider/combiner of  FIG. 3   a.    
         FIG. 3   d  is a generalized schematic of a two-stage corporate ‘tree’ combiner/divider of  FIGS. 3   a ,  3   b  and  3   c.    
         FIG. 4   a  is a graph illustrating a calculated scattering matrix response of a single-stage 4-way divider  400  of  FIGS. 2   a  and  2   b  according to the first aspect of the present invention. 
         FIG. 4   b  is a graph illustrating a calculated scattering matrix response of the two-stage 1:8 divider  500  of  FIGS. 3   a ,  3   b , as designed for ‘traveling wave’ operation according to the first and second aspects of the present invention. 
         FIG. 4   c  is a graph illustrating a calculated scattering matrix response of the two-stage 1:8 divider  500  of  FIGS. 3   a ,  3   b , as designed for approximately octave bandwidth operation according to the third aspect of the present invention. 
         FIG. 4   d  is a graph illustrating the calculated scattering matrix response of a three-stage 1:8 divider, as designed for 3:1 bandwidth operation according to the third aspect of the present invention where N SA =N SB =N SC =2. 
         FIG. 5   a  shows orthographic and cross-sectional views along lines a 1 -a 1  and a 2 -a 2  of an 8 input two stage combiner. 
         FIG. 5   b  shows orthographic and cross-sectional views along lines b 1 -b 1  and b 2 -b 2  of an 9 input two stage combiner. 
         FIG. 5   c  shows orthographic and cross-sectional views along lines c 1 -c 1  and c 2 -c 2  of a 12 input two stage combiner. 
         FIG. 5   d  shows orthographic and cross-sectional views along lines d 1 -d 1 , d 2 -d 2  and d 3 -d 3  of a 24 input three-stage combiner. 
         FIG. 6   a  is a schematic diagram illustrating an extracted filter circuit corresponding to  FIG. 2   c.    
         FIG. 6   b  is a schematic diagram illustrating an extracted filter circuit corresponding to  FIG. 3   d    
         FIG. 6   c  is a schematic diagram illustrating a filter circuit model for a three-stage combiner/divider using quarter-wave separation transmission lines between each stage. 
     
    
    
     DETAILED DESCRIPTION 
     Various embodiments of the present invention are now described with reference to the figures where like reference numbers indicate identical or functionally similar elements. Reference in the specification to “one embodiment” or to “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiments is included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
     In one aspect, the present invention combines the corporate ‘tree’ with an N-way non-resonant combiner using successive stages of coupled multiconductor transmission lines (see Clayton R. Paul, Analysis of Multiconductor Transmission Lines, John Wiley &amp; Sons, New York, N.Y., 1994 for description and modeling of multiconductor transmission lines). Although one-stage and two-stage power combiner/dividers are described, the power combiner/dividers of the present invention are not so limited, but may include any number of stages. For the sake of simplicity and convenience, the embodiments of the present invention are presented as power dividers as described next, but may be used as power combiners. 
       FIGS. 2   a  and  2   b  are an orthographic cutaway view and a cross-sectional view along a line  2 - 2  of  FIG. 2   a , of a single-stage N S -way divider  400 , respectively, according to the first aspect of the present invention, where the quantity N S =4.  FIG. 2   c  is a generalized electrical schematic of the single-stage 4-way combiner/divider  400  of  FIGS. 2   a  and  2   b . The cross-sectional view of  FIG. 2   b  depicts a multiconductor transmission line comprising a conducting shield  412 , a plurality of satellite conductors  405 , and a main conductor  407 . The 4-way single-stage divider  400  comprises an input coaxial connector  409  and four output coaxial connectors  401 . The center conductors  402  of each of the four output connectors  401 , and the inner diameter of the bores  414  constitute simple coaxial transmission lines with characteristic impedance identical to that of their respective output connectors  401 . Each transmission line is fed at the end of each of four satellite transmission lines  405 . The four satellite conductors  405  symmetrically surround the main conductor  407 . In one embodiment, the perimeter of each of the satellite conductors  405  is symmetric about the axis of the main conductor  407  with respect to each other. The main conductor  407  is shorted to ground where it mates to the conductive base  403 . Each of the satellite conductors  405  is electrically shorted to ground at the location where they join an electrically conductive plate  406 , which may be formed of a thermally conductive material. The slotted ends of the four output feed center conductors  402  are received by a bore  415  in the end of each satellite conductor  405 . Alternatively, this connection may be soldered or brazed. The main conductor  407  may be thermally and electrically mounted to the conducting base  403  by a threaded fastener  408 , or alternatively by soldering or brazing joining methods. The main conductor  407  may also comprise a thermally conductive material, and may be plated to form a suitable electrically conductive outer surface. Although the four satellite conductors  405  and the conductive plate  406  are shown in  FIG. 2   a  as one integral piece part, they may be formed separately and assembled. Each of the four output connector flanges  418  are shown mounted (mounting screws not shown in  FIGS. 2   a  and  2   b ) on a base  403 , which may be formed of an electrical conductor, or which has all surfaces plated with an electrically conductive material. In one embodiment, the base  403  is thermally conductive. The base  403  is contoured  417  to aid in minimizing power reflection due to junction reactances. The inner diameter  419  of the plate  406  is also the inner diameter of the satellite conductors  405 . The inner diameter  419  also serves as the outer conductor of the input coaxial transmission line which has an inner conductor  410 . The input connector  409  has a slotted center conductor which is received by a bore  416  on the end of the input transmission line center conductor  410 ; this connection alternatively may be soldered or brazed. The input connector dielectric  413  is received by a counterbore in the conductive plate  406 . The counterbore axis is aligned with the main conductor axis. Although the divider  400  is shown in  FIG. 2   a  to include a coaxial input connector  409 , the input transmission line center conductor  410  instead, 1) may be fed by a transmission line centering bullet assembly (comprised of a centering dielectric bead  504 , and slotted-end center conductor  505  shown in  FIG. 3   a , for example) connected to a previous combiner stage separation transmission line, or 2) may be fed by a waveguide-to-coax transition, where the input is a waveguide instead of the coaxial connector  409 . In one embodiment, the output center conductors  402  may be connected to coax-to-waveguide transitions, where four waveguides replace the coaxial connectors  401 . 
     In one embodiment of the present invention, described as a power divider: 1) the multiconductor transmission line (MTL), with a substantially uniform cross-section as shown in  FIG. 2   b , is designed to have an effective phase length equal to one quarter-wavelength at the operating midband frequency f 0 ; 2) the admittance matrix for this multiconductor cross-section is designed such that near-perfect power division to the four output connectors  401  and near-zero reflection at the input connector  409  is achieved at the operating midband frequency f 0 . Referring to  FIG. 2   c , this scattering matrix performance at f 0  may be achieved where the cross-section dimensions of the multiconductor transmission line of  FIG. 2   b  are such that the associated admittance matrix element values Y (1)(2) , . . . , Y (1)(NS+1)  are substantially equal to √{square root over (Y (105) Y (108) /(N S) )}{square root over (Y (105) Y (108) /(N S) )}{square root over (Y (105) Y (108) /(N S) )}, where the number Y (105)  represents the source input characteristic admittance  105 , the number Y (108)  represents the termination admittance  108  for each satellite conductor  405 - 1  through  405 -N S , and N S  is the number of satellite conductors. In the above notation for the admittance matrix element value Y (1)(x) , the first subscript index is associated with the main conductor  407 , and the second subscript represents the column index number associated with its respective satellite conductor  405 - 1  through  405 -N S . An example of an N S =4 power divider designed in this manner gives the ‘divider operation’ scattering parameter performance as shown in  FIG. 4   a . The |S 11 | trace shows near-perfect match at f/f 0 =1.0 with one quarter (6.02 dB) of the power input to the divider being coupled onto each of the four satellite line output connectors—traces |S 21 | through |S 51 |. 
     Referring to  FIG. 2   c , the single-stage N-way combiner/divider  400  is shown schematically. A signal source  104  with source admittance  105  feeds the main conductor  407  at a reference plane a. The main conductor  407  terminates in a short circuit  106  at a reference plane b. The satellite lines  405  terminate in corresponding short circuits  107  at the reference plane a, and are coupled to corresponding finite-magnitude termination admittances  108  at the reference plane b. At the operating frequency f 0 , the phase length θ separation between the reference planes a and b is one quarter-wavelength. 
     If operating the single-stage device  400  as a combiner, a quantity N S =4 isolator-protected sources of the same frequency, relative phase and magnitude feeding the input connectors  401  sum along the multiconductor transmission line (of cross-section as shown in  FIG. 2   b  as designed according to the first aspect of the present invention) delivering the combined power to the output connector  409  at the operating midband frequency f 0 . 
     The number N S  of satellite conductors  405  is equal to 4 for the divider/combiner  400  shown in  FIGS. 2   a ,  2   b . Not limited to N S =4 satellite conductors, this aspect of the present invention N S -way divider/combiner may be designed and built with any number N S  satellite conductors  405 . Consistent with the first aspect of the present invention, the multiconductor cross-section geometry dimension admittance matrix for a selected value of N S  is designed such that near-perfect power division from the main conductor input to the N S  satellite output connectors and near-zero reflection at the input connector  409  is achieved at the operating midband frequency f 0 . 
     Although the satellite conductors  405  are described as being arranged spaced apart symmetrically about the main conductor  407  (in  FIGS. 2   a ,  2   b  for N S =4, for example), the divider/combiner of this first aspect of the present invention may include other spatial configurations of the satellite conductors  405  about the main conductor  407 . Although the satellite conductors  405  are described in  FIG. 2   b  with the quasi-rectangular individual cross-sections as shown, the combiner/divider  400  satellite conductors may be formed with other dimensions, shapes (such as circular or elliptical) and placement configurations. Similarly, the main conductor  407  and conductive shield  412  are shown in  FIG. 2   b  with circular cross-sections, but may be formed with other dimensions, shapes (such as, but not limited to, rectangular or hexagonal) and placement configurations. 
       FIGS. 3   a  and  3   b  are orthographic views of a two-stage 1:8 corporate ‘tree’ divider/combiner  500 , according to a second embodiment of the present invention.  FIG. 3   d  is a generalized schematic of a two-stage corporate ‘tree’ combiner/divider  500 . Describing the two-stage 1:8 corporate ‘tree’ divider/combiner  500  as a power divider for convenience, input signal power entering coaxial connector  521  feeds a coaxial input transmission line with an outer conductor housing  520  and a center conductor  519 . The center conductor  519  is connected by a threaded fastener  522  to a conical transmission line center conductor  516  (with a conical outer conductor shield  517 ) to a coaxial transmission line with a center conductor  528 . The characteristic impedance of the input connector  521  is maintained throughout the transmission lines so described. Signal power on the center conductor  528  in turn feeds the main conductor  529  of an N SA -way divider multiconductor transmission line which extends over a physical length designated as stage ‘A’ in  FIG. 3   a , and has an effective phase length equal to one-quarter-wavelength at the midband operating frequency f 0 . The stage ‘A’ multiconductor transmission line cross-sectional view along line  3 - 3  ( FIG. 3   a ) is shown in  FIG. 3   c . The transmission line comprises an outer conductor shield  523 , a main conductor  529 , and a plurality of satellite conductors  511  symmetrically spaced apart from and parallel to the main conductor  529 . In one embodiment, each of the plurality of satellite conductors  511  has a substantially identical cross-section with the other conductors  511 . Perimeters of each of the satellite conductors  511  are symmetric about the axis of the main conductor  529  with respect to each other. 
     The stage ‘A’ main conductor  529  is electrically, mechanically and thermally connected using a threaded fastener  524  to a conductive block  526  which is press-fit or soldered to a thermally and electrically conductive base  503 . The number N SA  of satellite conductors equals two in the illustrative embodiment depicted in  FIGS. 3   a  and  3   c . Each satellite conductor  511  is connected to a thermally and electrically conductive ground plate  527 .  FIG. 3   a  shows that both satellite conductors  511  and the plate  527  are one single piece part, but may be formed as separate pieces. Each of the quantity N SA  satellite conductors is electrically and mechanically connected by a respective threaded fastener  513  to a center conductor  506  which is part of a respective stage separation transmission line with a conductive shield  525 . In lieu of a threaded fastener  513 , this connection may be soldered or brazed. Both input center conductors  506  comprise thermally conductive material, and have corresponding exteriors plated with an electrically conductive and corrosion-resistant outer surface layer. The center conductor  506  is shown in  FIG. 3   a  with a counterbore  507  which receives a slotted-end center conductor  505  of a centering bullet assembly including a dielectric centering bead  504 . Each of the quantity N SA  centering bullet assembly transmission line center conductors  505  feeds a main conductor  510  of a respective second stage  T N SB -way divider  502 . The number N SB  satellite conductors  405  ( FIG. 3   d ) for each of the quantity N SA  stage ‘B’ dividers  502  equals four in the illustrative embodiment shown in  FIGS. 3   a ,  3   b . Each of the two stage  T dividers  502  is the same divider embodiment  400  shown in  FIGS. 2   a  and  2   b , except where the input connector  409  with slotted center conductor  411  is replaced with the input centering bullet assembly comprising the dielectric centering bead  504  and the slotted-end center conductor  505  shown in  FIG. 3   a . Each stage  T divider  502  input center conductor  510  shown in  FIG. 3   a  is also labeled as  410  in  FIG. 2   a.    
     Combining the first and second aspects of the present invention, a ‘traveling wave’ combiner/divider is formed by first optimizing the scattering parameter performance at the frequency f 0  for each of the two 4-input combiner subunits  502 , second by choosing conductor diameters of the transmission lines  506 ,  525  such that these two separation transmission lines  506 ,  525  have the same characteristic admittance as that for: a) the output transmission line of each 4-input combiner subunit  502 , and b) the input design impedance of the 2-input combiner unit, and third by optimizing the scattering parameter performance at the frequency f 0  for the 2-input combiner subunit. In other words, each of the three combiner subunits is designed for optimum scattering parameter performance at the frequency f 0  independently from each other. In this second aspect of the present invention, the two separation transmission lines comprised of inner and outer conductors  506  and  525 , respectively, may have a length that is different from one quarter-wavelength at f 0 . 
     In the third aspect of the present invention, a ‘broadband’ combiner/divider is formed by 1) making the length of the separation transmission lines (referring to  FIG. 3   a , comprised of inner and outer conductors  506  and  525 , respectively) equal to one quarter-wavelength at the mid-band frequency f 0 , and 2) designing the stage ‘A’ and ‘B’ multiconductor transmission line admittance matrices and separation transmission line admittances together in such a way as to form a passband filter. 
     A passband filter circuit model for the present multi-stage combiner/divider invention is arrived at by first finding the wave admittance function for the single-stage combiner/divider circuit shown in  FIG. 2   c  (see Clayton R. Paul,  Analysis of Multiconductor Transmission Lines , John Wiley &amp; Sons, New York, N.Y., 1994). At reference plane ‘a’ in  FIG. 2   c , the main conductor  407  wave admittance is found to be 
     
       
         
           
             
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     In the above notation, the frequency of operation is f, the mid-band frequency is f 0 , the number of satellite conductors  405 - 1  through  405 -N S  symmetrically surrounding the main center conductor  407  is N S , and Y mn  is the mth row and nth column component of the admittance matrix for this multiconductor transmission line. Each satellite conductor  405 - 1  through  405 -N S  terminates in an admittance  108  of value Y L , referring again to  FIG. 2   c.    
     Using Richard&#39;s Theorem, the extracted filter circuit (see G. C. Temes and S. K. Mitra,  Modern Filter Theory and Design , John Wiley &amp; Sons, New York, N.Y., 1973) is shown in  FIG. 6   a . Operating as a divider, this equivalent ‘ladder circuit’ is composed of simple shorted stub transmission lines which are ‘unit elements’ (quarter-wavelength at the mid-band frequency f 0 ), each separated by a unit element transmission line. The filter circuit transmission line characteristic admittances are shown, as well as a source admittance of value Y S   (B)  (corresponding to  105  in  FIG. 2   c ) and a circuit termination admittance N S   (B) Y L   (B) , where Y L   (B)  corresponds to a stage ‘B’ termination admittance  108  in  FIG. 2   c.    
     The extension of this procedure for a two-stage combiner/divider is shown in  FIG. 6   b . The number of shorted stub transmission lines is equal to twice the number of stages, each shorted stub separated by transmission lines that are also ‘unit elements’, that is, a quarter-wave at the mid-band frequency f 0 . The characteristic admittance for each transmission line is shown in  FIG. 6   b , as well as the termination admittance for the ladder circuit. This termination admittance N S   (A) N S   (B) Y L   (B)  is, in general, not equal to the ladder circuit stage ‘A’ source admittance Y S   (A) . In this notation, Y L   (B)  corresponds to the value of each load admittance  211  shown in  FIG. 3   d , and Y S   (A)  corresponds to the value of the stage ‘A’ main conductor  529  source admittance  202  in  FIG. 3   d . The separation transmission line characteristic admittance Y T  shown in  FIG. 6   b  corresponds to the characteristic admittance of each separation transmission line  207 - 1  through  207 -N S   (A)  shown in  FIG. 3   d . Ladder circuit admittances ( FIG. 6   b ) yielding a bandpass filter response substantially analagous to the scattering parameter vs. frequency response shown in  FIG. 4   c  are chosen using many possible methods. One approach is to use modern filter analysis techniques (see G. C. Temes and S. K. Mitra,  Modern Filter Theory and Design , John Wiley &amp; Sons, New York, N.Y., 1973). They may also be determined by an extension of the bandpass filter design theory presented in section 10.03 of  Microwave Filters, Impedance - Matching Networks, and Coupling Structures , by G. Matthaei, L. Young, and E. M. T. Jones, Artech House, Dedham, Mass., 1980 edition, the contents of these sources which are incorporated herein by reference in their entirety. Whatever bandpass filter design method is used, and not limited to those techniques cited here, a feature of this aspect of the invention is that all admittances of the two-stage ‘corporate tree’ function together interdependently to form a bandpass filter. 
     The filter circuit model for a three-stage combiner/divider using quarter-wave separation transmission lines between each stage is shown in  FIG. 6   c . Depicted is a divider ladder circuit with stage ‘A’ main conductor source admittance Y S   (A)  and a circuit termination admittance equal to N S   (A) N S   (B) N S   (C) Y L   (C) . For the sake of brevity, the shunt stub ladder admittances are labeled Y 1  through Y 6 , and the intervening unit element transmission line characteristic admittances are labeled Y 12  through Y 56 . Using any of the passband filter design methods cited above, the ladder circuit admittances shown in  FIG. 6   c  can be found giving scattering parameter performance substantially analogous to that shown in  FIG. 4   d . Again, a feature of this aspect of the invention is that all admittances of the three-stage ‘corporate tree’ function together interdependently to form a bandpass filter. 
     Referring now to  FIG. 3   d , a signal source  201  with a source admittance  202  feeds a main conductor  529  at the reference plane a. A quantity N SA  satellite conductors  511 - 1  through  511 -N SA  are arranged spaced apart symmetrically, in an orthogonal cross sectional view, about the main conductor  529 . The main conductor  529  terminates in a short circuit  204  at a reference plane c. The satellite conductors  511 - 1  through  511 -N SA  terminate in corresponding short circuits  206  at the reference plane a, and are coupled to corresponding transmission lines (T)  207 - 1  through  207 -N SA  at the reference plane c. This constitutes a stage ‘A’. At the operating frequency f 0 , the phase length θ separation between the reference planes a and c is one quarter-wavelength. Each of the quantity N SA  transmission lines  207 - 1  through  207 -N SA , having a phase length φ, delivers its share of the stage ‘A’ subdivided power to a corresponding main conductor  407 - 1  through  407 -N SA  of a stage ‘B’ at a reference plane d. In one embodiment, there is a quantity N SA  such stage ‘B’ dividers. In one embodiment, the transmission lines  207 - 1  through  207 -N SA  each comprise a simple transmission line with a single center conductor and outer conductor. 
     In the stage ‘B’, each of the quantity N SA  groups of quantity N SB  satellite conductors  405 - x− 1, . . . ,  405 - x -N SB  (x=1, . . . , N SA ) are arranged spaced apart symmetrically, in an orthogonal cross sectional view, about each of the respective main conductors  407 - 1  through  407 -N SA . Each main conductor  407 - 1  through  407 -N SA  terminates in a short circuit  209  at the reference plane b. Each set of satellite lines  405 - 1 - 1  through  405 -N SA·N   SB  terminates in corresponding short circuits  214  at the reference plane d, and each set is coupled to corresponding finite-magnitude admittance terminations  211  at the reference plane b. In this illustrative example, there is a total of N SA ·N SB  such termination admittances  211 , each receiving 1/(N SA ·N SB ) of the input power from the source  201 , minus any loss due to RF dissipation and internal reflections. At the midband operating frequency f 0 , the phase length θ separation between the reference planes d and b is one quarter-wavelength. 
     The combiner/divider invention in  FIGS. 3   a ,  3   b  shows a coaxial output connector  521 , but the output transmission line center conductor  519  may instead  1 ) feed an additional combiner stage, or 2) be part of a coax-to-waveguide transition, where a waveguide is the output rather than a coaxial connector  521 . Also, referring to  FIG. 2   a , in one embodiment, the input center conductors  402  may be coupled to waveguide-to-coax transitions, where four waveguides replace the coaxial connectors  401  as inputs. 
       FIG. 5   a  shows orthographic and cross-sectional views along lines a 1 -a 1  and a 2 -a 2  of an 8 input two stage combiner. The 8-input two-stage combiner with coaxial output connector is similar to  FIGS. 3   a  and  3   b , but with each of the 4-input stage ‘B’ combiners rotated 45 degrees for reduced overall thickness (compared to that of  FIG. 3   b ). 
       FIG. 5   b  shows orthographic and cross-sectional views along lines b 1 -b 1  and b 2 -b 2  of an 9 input two stage combiner. The 9-input two-stage combiner with coaxial output connector includes one 3-input combiner comprising stage ‘A’ and three 3-input combiners comprising stage ‘B’. 
       FIG. 5   c  shows orthographic and cross-sectional views along lines c 1 -c 1  and c 2 -c 2  of a 12 input two stage combiner. The 12-input two-stage combiner with an output transition to rectangular waveguide includes: one 3-input combiner comprising stage ‘A’, and three 4-input combiners comprising stage ‘B’. 
       FIG. 5   d  shows orthographic and cross-sectional views along lines d 1 -d 1 , d 2 -d 2  and d 3 -d 3  of a 24 input three-stage combiner. The 24-input three-stage combiner includes one 2-input comprising stage ‘A’, two 3-input combiners comprising stage ‘B’, and six 4-input combiners comprising stage ‘C’. The output is an end-launch coax transition to rectangular waveguide. 
     Having described the power combiner/dividers  400 ,  500  and other power combiner/dividers, various features of various embodiments of the present invention are next described. The combiner/divider of the present invention may use a smaller number of stages than the conventional combiner/divider of  FIG. 1  to achieve an N-input combiner. For example, the conventional combiner/divider of  FIG. 1  has three stages and seven 2-input combiner subunits for an 8-input combiner system. However, the combiner/divider of the present invention may include only two stages where, for example, a design with N SA =2 and N SB =4 uses only three combiner subunits instead of seven, as shown in  FIG. 3   a . Combining this advantage with each stage length being only one-quarter of a wavelength at the midband operating frequency f 0 , the overall size of the structure may be greatly reduced compared to the conventional combiner/divider of  FIG. 1 . RF losses and internal reflection problems also may be greatly reduced because of the reduced size and number of subcomponents. 
     The combiner/dividers  400 ,  500  and other power combiner/dividers of the present invention have more flexibility than the conventional combiner/divider of  FIG. 1  over the number of sources that may be combined in, say for example, a two-stage combiner. The corporate tree structure of the conventional combiner/divider of  FIG. 1  cannot combine twelve sources, but must use eight (three-stage) or sixteen (four-stage) sources because of the 2-input combiner subunit restriction. In contrast, the combiner/divider  500  ( FIGS. 3   a ,  3   b ), may combine twelve sources (for example) using only two stages with N SA =3 and N SB =4, where there are three satellite conductors  511  surrounding the stage ‘A’ main conductor  529  ( FIGS. 3   a  and  3   d ), and four satellite conductors  405  ( FIGS. 2   a ,  2   b ,  3   d ) surrounding each of the three stage ‘B’ main transmission lines  407 . 
     In the conventional power combiner/divider of  FIG. 1 , each of the seven 2-input combiner subunits  9 - 15  are identical and function independently from the each other. This restricts the bandwidth performance to that of the 2-input combiner subunits  9 - 15 , minus adverse interaction effects due to the large separation between each of the seven 2-input combiner subunits  9 - 15 . However, the power combiner/dividers  500  treats the entire corporate ‘tree’ as a passband filter device, according to the third aspect of the present invention, with quarter-wavelength elements throughout (defined at the mid-band frequency f 0 ). Each stage may be designed interdependently and together with the other stage(s) along with the connecting transmission lines between the stages. Accordingly, 2:1 bandwidth power combining performance for two-stage combiners (see  FIGS. 4   c ), and 3:1 bandwidth performance for a three-stage combiner (see  FIG. 4   d ) may be achieved, where N SA =N SB =N SC =2. 
     The power combiner/dividers  400 ,  500  and other power combiner/dividers have thermal robustness due to the thermal as well as electrical connection of one end of each main and satellite conductor to ground as shown in  FIGS. 2   a  and  3   a . Any heat created due to RF dissipation loss on the main conductors  407  and  529  or the satellite conductors  405  and  511  may be thermally conducted to the ground connection. Thus every conductor within a combiner stage may serve as a thermal heat pipe to cool the overall structure. This feature allows the combiner/dividers  400 ,  500  to be used for power combining of high-average-power RF signal amplifiers. 
     Although the quarter wave length described above for the combiner/dividers  400 ,  500  and other power combiner/dividers are described for a midband frequency f 0 , the quarter wave length may be based on other frequencies in the operating band. The main conductors and the satellite conductors are described above as being parallel, but may be implemented to be substantially parallel. 
     Although the operation of the combiners  400 ,  500  and other power combiner/dividers has been described as being operational with isolator-protected sources of the same frequency, relative phase and magnitude, different frequencies, relative phases and magnitudes may be used with the combiners  400 ,  500 , depending on the applied use. 
     In some embodiments, the multiconductor transmission lines for the combiners  400 ,  500  and other power combiner/dividers may be formed using various cross-sectional shapes of the outer shield, main conductors, and/or satellite conductors, such as, but not limited to, circular, elliptical, rectangular, and hexagonal. 
     The terms “couple” and “connect” and their derivatives are used herein. Both terms may be used to describe embodiments in which two or more elements are in direct physical or electrical contact with each other, or two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other. The embodiments are not limited in this context. 
     In the foregoing description, various methods and apparatus, and specific embodiments are described. However, it should be understood that various alternatives, modifications, and changes may be possible without departing from the spirit and the scope of the present invention.