as shown in the drawings for purposes of illustration , the present invention is concerned with radial structures for combining or dividing microwave power signals . a radial divider / combiner comprises a pair of parallel circular plates , a center input or output port , and multiple peripheral ports . in the past it has proved very difficult to obtain a desired wide bandwidth response from such a device , especially at higher frequencies . design has typically been accomplished by matching the center port of the device to the radial waveguide mode , and then adjusting the peripheral port configuration for best results . the resulting complex impedance presented at the center port restricts the operating bandwidth and limits the performance of the device . in accordance with the invention , a radial power divider / combiner is configured as a number of adjoining annular waveguide sections , each of which provides an impedance approximately equivalent to that of a lumped circuit parameter of a filter designed to yield the desired frequency response . in effect , the radial waveguide of the invention is synthesized to provide a desired response characteristic . the starting point in the design is the desired frequency response characteristic , and the first step in achieving the desired result is to employ a conventional filter synthesis program to formulate the design of a lumped - parameter filter having the desired response . one example of such a filter is shown in fig1 . the synthesized filter with the desired broadband response includes an input circuit , indicated by reference numeral 10 and an output circuit indicated by a reference in numeral 12 . the desired characteristic input impedance is 50 ohms and desired characteristic output impedance is 3 . 125 ohms , or one - sixteenth of the input impedance . this relationship arises because the power divider is to have sixteen output ports , which will be connected in parallel . the filter shown in fig1 is derived from the exact solution of a sixth - order 0 . 1 db ripple chebyshev filter . the circuit includes a shunt capacitance 14 and a series inductance 16 connected to the input circuit 10 , a second shunt capacitance 18 and a second series inductance 20 , a shunt inductance 22 , a series capacitance 24 , and a third series inductance 26 is connected to the output circuit 12 , shown by its characteristic impedance 28 . this circuit can be derived using any of a number of available filter synthesis computer programs for the computer - aided design of filters . for example , filsyn is such a program available from comsat general integrated systems inc ., of palo alto , calif . 94303 . if all of the lumped circuit parameters of fig1 could be realized in the form of a radial waveguide , the design could be completed by merely synthesizing such a device and including elements in the waveguide that are the equivalent of corresponding elements in fig1 . however , a series capacitance has no direct equivalent in a radial waveguide . a short length of low - impedance microwave transmission line is equivalent to a shunt capacitance , and a short length of high - impedance transmission line is equivalent to a series inductance . a shunt inductance can take the form of a shorted transmission line stub . because a series capacitance has no direct microwave transmission line equivalent , the circuit of fig1 cannot be used without modification . the modification arrived at is shown in fig2 b . basically , the series capacitance 24 is eliminated , and the other impedances are modified , as indicated by primed reference numerals . the shunt inductance 22 &# 39 ;, series inductances 16 &# 39 ;, 20 &# 39 ; and 26 &# 39 ; and shunt capacitances 14 &# 39 ; and 18 &# 39 ; in general have different values from those of the corresponding components of fig1 . the transformation from the fig1 circuit to the fig2 b circuit may be derived empirically . by way of example , the transformation may be made using a program package known as compact , also available from comsat general integration systems inc . the circuit of fig2 b still represents a lumped - parameter filter , and not a radial waveguide . the final transformation to radial waveguide components is complicated by the geometry of the waveguide . as the radius increases , so does the area between the two plates of the waveguide , with a resulting decrease in characteristic impedance . an approximation of a lumped circuit parameter may be made by means of a waveguide section in which the spacing between the plates increases with increasing radius . this would mean that at least one of the plates would have to have a part - conical shape . however , fabrication of a waveguide with tapered sections presents some practical problems . from a manufacturing standpoint , a radial waveguide should have parallel plates , and this is one of the goals of the invention . in the structure of the invention , each circuit parameter in fig2 b is represented in a radial waveguide by an annular waveguide section , as shown in fig2 a . a central input port 40 provides for the input of microwave energy to the waveguide , and the first shunt capacitance 14 &# 39 ; is represented by a first waveguide section 42 at the center of the device . the first series inductance 16 &# 39 ; is represented by a second waveguide section 44 adjoining the first and having a larger plate spacing . then the second shunt capacitance 18 &# 39 ; is represented by a third waveguide section 46 , having a reduced spacing and much shorter length than the first two sections . the second series inductance 20 &# 39 ; is represented by a fourth waveguide section 48 , extending to a plurality of peripheral output ports 50 , only one of which is shown in the drawings . the shunt inductance 26 &# 39 ; is represented by the inductance of a probe 51 associated with each peripheral port 50 . finally , the shunt inductor 22 &# 39 ; is represented by a further radial extension of the waveguide , indicated by the peripheral waveguide section 52 , which functions as a backshort section . as a first approximation , each section of the waveguide is selected to have a fixed spacing or height dimension that is the average spacing of the approximately optimum &# 34 ; conical &# 34 ; waveguide section , and the same radial length as the conical waveguide section . this approximation provides a reasonably good response characteristic , but further improvement is still highly desirable . using conventional optimization techniques , the length and spacing , or height of each waveguide section can be optimized to yield much more desirable characteristics . by way of example , an optimization program for this purpose is provided as appendix a to this specification . using the dimensions of conical waveguide sections as a starting point in the optimization process is not an essential element of the invention . with an appropriate optimization program , consideration of the conical waveguide solution could be completely omitted from the procedure . fig3 shows the detailed design of a radial waveguide in accordance with the invention . the device shown was configured to provide a passband of 800 - 1600 megahertz ( mhz ). the following table gives the inner radius and height of each waveguide section : ______________________________________waveguide inner radius heightsection ( inches ) ( inches ) ______________________________________42 0 . 060 . 10044 0 . 550 . 62546 3 . 860 . 41548 4 . 500 . 41552 5 . 750 . 415outer radius = 7 . 900______________________________________ note that the heights of waveguide sections 46 and 48 have been made the same . for this illustrative design , the optimized height dimensions of these two sections were so nearly identical that it was expedient to force them to be identical to permit further savings in manufacturing costs . one measure of the passband performance of a device is the power loss in decibels ( db ) over the passband . another , more sensitive measure is the voltage standing wave ration ( vswr ). for the ideal passband , the vswr has a value of unity . a reasonable goal in the range 1 . 3 - 1 . 5 has been achieved with the invention as described . this corresponds to a loss of about 0 . 1 db . reaching this performance goal may require post - construction &# 34 ; tweaking &# 34 ; in one significant respect . the inductance of the probe 51 depends largely on its diameter , length , and spacing between adjacent probes . selection of these dimensions may not always afford sufficient control over the inductance 26 &# 39 ;, and some impedance matching adjustments may have to be made at the output ports 50 , to attain the desired performance goal . prior to optimization of the waveguide section dimensions , a vswr of about 2 . 0 is achievable , corresponding to a loss of about 0 . 5 db . although the latter figure represents a good performance by some standards , it is unacceptable for use as a high - power combiner or divider . it will be appreciated from the foregoing that the present invention represents a significant advance in the field of microwave divider / combiners for use at high powers and high frequencies . in particular , the invention provides a divider / combiner with a desired broad bandwidth for use at high powers and frequencies . the resulting waveguide hardware has a simple geometry and is therefore convenient to manufacture at relatively low cost . it will also be appreciated that , although an embodiment of the invention has been described in detail for purposes of illustration , various modifications may be made without departing from the spirit and scope of the invention . accordingly , the invention is not to be limited except as by the appended claims .