Patent Publication Number: US-6714097-B2

Title: Impedance matching/power splitting network for a multi-element antenna array

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to impedance matching networks and, more particularly, to an impedance matching and RF power splitter device for substantially matching the characteristic impedance from a transmitter to a load impedance of a multi-element directional antenna array of an RF transmission network. 
     2. Description of the Related Art 
     A generator, such as a transmitter, for example, is typically designed to operate into a specific impedance of a network. However, a load (e.g., an antenna) that is coupled to the generator usually does not provide the specific impedance in which the generator is designed to operate. 
     When the impedance of the load and the impedance as seen by the generator are equal, maximum power is transferred from the generator to the load over a transmission line coupling the generator to the load. If a mismatch between the impedances of the load and generator occurs, however, the power that is not transferred to the load will be returned towards the generator through the transmission line. These rearward-traveling waves combine with their respective forward-traveling waves along the transmission line, and because of the phase differences along various positions within the line, causes standing waves in the transmission line by the alternate cancellation and reinforcement of the voltage and current distributed along the transmission line. The larger the standing waves that occur along the transmission line, the greater the mismatch of the impedance of the load that is coupled to the generator. 
     The present invention is directed to overcoming, or at least reducing the effects of, one or more of the problems set forth above. 
     SUMMARY OF THE INVENTION 
     One aspect of the present invention is seen in an apparatus for impedance matching a signal generator to a plurality of elements of a multi-element load. The apparatus comprises an outer conductor having an inner surface and an inner conductor positioned within the outer conductor, and having an outer surface. The apparatus further includes a first set of transformation sections for impedance matching a first impedance of the signal generator to a second impedance, and a second set of transformation sections for matching the second impedance to a third impedance of the plurality of elements of the multi-element load. Each of the first and second sets of transformation sections provides a particular separation distance between the inner surface of the outer conductor and the outer surface of the inner conductor to yield a particular characteristic impedance for each of the first and second sets of transformation sections, thereby substantially matching the first impedance to the third impedance. 
     Another aspect of the present invention is seen in a method for impedance matching a signal generator to a plurality of antenna elements of a multi-element load. The method includes providing an outer conductor having an inner surface and an inner conductor positioned within the outer conductor, and having an outer surface. The method further includes providing a first set of transformation sections for impedance matching a first impedance of the signal generator to a second impedance, and providing a second set of transformation sections for matching the second impedance to a third impedance of the plurality of elements of the multi-element load. The first and second transformation sections provide a particular separation distance between the inner surface of the outer conductor and the outer surface of the inner conductor to yield a particular characteristic impedance for each of the plurality of transformation sections. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention may be understood by reference to the following description taken in conjunction with the accompanying drawings, in which like reference numerals identify like elements, and in which: 
     FIG. 1 shows a simplified block diagram of a wireless transmission network, including and impedance matching and RF power splitter device, in accordance with one embodiment of the present invention; 
     FIGS. 2A and B illustrate a more detailed representation of the impedance matching and RF power splitter device of FIG. 1; 
     FIG. 3A provides a side-view perspective of the impedance matching and RF power splitter device of FIG. 2B according to one embodiment of the present invention; 
     FIG. 3B shows a cross-sectional view for each transformation section of the impedance matching and RF power splitter device of FIG. 3A; 
     FIG. 4 illustrates tables that provide normalized “step-down” and “step-up” ratio design criteria for a set of transformation sections of the impedance matching and RF power splitter device of FIG. 2B; 
     FIG. 5 provides a side-view perspective of the impedance matching and RF power splitter device of FIG. 2B in accordance with another embodiment of the present invention; and 
     FIG. 6 illustrates a process for designing the impedance matching and RF power splitter device according to one embodiment of the present invention. 
    
    
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims. 
     DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS 
     Illustrative embodiments of the invention are described below. In the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. 
     Turning now to the drawings, and specifically referring to FIG. 1, a simplified block diagram of a transmission network  100  that incorporates impedance matching and power splitting for a multi-element antenna array is shown in accordance with one embodiment of the present invention. In the illustrated embodiment, the transmission network  100  may be used for a variety of wireless applications including, but not necessarily limited to, AM, FM, SSB, TV, paging, satellite, cellular, and PCS communications. In addition to the aforementioned examples, it will be appreciated that the transmission network  100  may operate in accordance with various other wireless transmission protocols without departing from the spirit and scope of the present invention. In one embodiment, the transmission network  100  resides in a land-based station, such as a base station in a paging network, for example. It will also be appreciated that the transmission network  100  may alternatively take the form of a receiving network for receiving signals either in addition to or in lieu of transmitting signals without departing from the spirit and scope of the present invention. 
     The transmission network  100  comprises a transmitter  105  for generating signals, a transmission line  110  for carrying the signals generated by the transmitter  105 , an impedance matching device  115 , an RF power splitter  120 , and a multi-element antenna array  130  for sending the signals generated by the transmitter  105  via a wireless communication medium to a receiver station (not shown). It will be appreciated that the transmission network  100 , shown in one of its simplest forms, may include various other components (in addition to those components shown in FIG. 1) to facilitate the transmission of wireless signals. Additionally, although the network  100  of FIG. 1 is provided in the form of a wireless transmission network, its application is not so limited. It will be appreciated that the transmitter  105  may take the form of any type of signal generator and the antenna array  130  may take the form of any type of multiple load. Accordingly, the transmission network  100  illustrated in FIG. 1 need not necessarily be limited to a wireless transmission network, but may take on a variety of other forms where the need for impedance matching and power splitting capabilities from a signal generator to a load is desirable. 
     According to the illustrated embodiment, the antenna array  130  comprises a multi-element antenna with a twelve-degree electrical downtilt for substantially directing RF energy off of the earth&#39;s horizon. It will be appreciated, however, that the antenna array  130  may include various other types of antenna systems without departing from the spirit and scope of the present invention. In the illustrated embodiment, the antenna array  130  comprises a total of eight antenna elements (not shown), and the feed point location for each of these antenna elements is adjustable so as to provide each antenna element with a substantially equivalent impedance. That is, the location of the element feeds of the antenna array  130  may be adjusted from the center of the element until substantially equal impedance values are attained for each antenna element. The impedance for each antenna element is desirably as close to the input impedance as seen by the transmitter  105  such that the disparity between the impedance of the transmitter  105  and the load impedance of each antenna element of the antenna array  130  is minimized. Although the antenna array  130  comprises eight antenna elements in the illustrated embodiment, it will be appreciated that the number of antenna elements may vary. The impedance matching device  115  and RF power splitter  120  collectively form an impedance matching/power splitter device  125 , which serves to substantially match the impedance as seen by the transmitter  105  to the load impedance of each antenna element of the antenna array  130  and to divide the power equally between each antenna element of the antenna array  130 . 
     Turning now to FIG. 2A, a more detailed representation of the impedance matching/power splitter device  125  of the transmission network  100  is shown according to one embodiment of the present invention. An input impedance (i.e., the impedance as seen by the transmitter  105 ) is shown at  205  as an input to the impedance matching device  115 . In the illustrated embodiment, the input impedance is 50-ohms; however, it will be appreciated that the input impedance  205  need not necessarily be limited to 50-ohms. In the illustrated embodiment, the impedance matching device  115  comprises a thirty-degree (i.e., one-twelfth wavelength) impedance matching transformer that includes two sections  210 ,  215 . The first section  210  is eighteen-degrees in length and provides a characteristic impedance of 10-ohms and the second section  215  is twelve-degrees in length and provides a characteristic impedance of 100-ohms. It will be appreciated that the order of the first and second sections  210 ,  215  of the impedance matching device  115  may be reversed. That is, the twelve-degree section  215  may alternatively precede the eighteen-degree section  210  without departing from the spirit and scope of the present invention. 
     In one embodiment of the present invention, the output impedance of the impedance matching device  115  (and, thus, the input to the RF power splitter  120 ) is set to the impedance of each antenna element of the antenna array  130  divided by the number of antenna elements. As previously mentioned, the antenna array  130  of the illustrated embodiment includes eight antenna elements, and each antenna element has an output impedance of approximately 117.3-ohms (i.e., the load impedance at which the feeds of the elements were adjusted such that the load impedances of all the antenna elements substantially match). Accordingly, the desired output impedance of the impedance matching device  115  is approximately 14.67-ohms (i.e., the output load impedance of 117.3-ohms for each antenna element divided by the eight antenna elements of the antenna array  130 ). 
     The output of the impedance matching device  115  is fed into the input of the RF power splitter  120 , which includes three stages in accordance with the illustrated embodiment. A first stage  230  of the power splitter  120  includes two 90-degree, quarter-wavelength sections that divide the power from the output of the impedance matching device  115 , and, as a result, doubles the impedance of the output of the impedance matching device  115  from 14.67-ohms to approximately 29.33-ohms. That is, when the output power is halved, the impedance is doubled. A second stage  235  of the power splitter  120  includes four 90-degree, quarter-wavelength sections that divide the power from the first stage  230  and doubles the impedance from 29.33-ohms to approximately 58.65-ohms. A third stage  240  of the power splitter  120  includes eight 90-degree, quarter-wavelength sections that divides the power from the second stage  235  and doubles the impedance from 58.65-ohms to approximately 117.3-ohms, which is the desired output load impedance for each of the eight antenna elements of the antenna array  130  in the illustrated embodiment. Accordingly, the input impedance  205  of 50-ohms (as seen by the transmitter  105 ) is “stepped-down” to 14.67-ohms by the impedance matching device  115 , and the RF power splitter  120  then doubles this impedance through each of the three stages  230 ,  235 , and  240 . Accordingly, the impedance matching/power splitter device  125  provides the desired output load impedance of 117.3 ohms for each antenna element of the antenna array  130 , and, thus substantially matches the load impedances of each antenna element to the input impedance  205 . 
     Referring now to FIG. 2B, a simplified representation of the impedance matching device  115  and RF power splitter  120  for one output port of an antenna element of the antenna array  130 , is shown. As illustrated, the impedance matching device  115  includes the first eighteen-degree section  210  and second twelve-degree section  215 , thereby forming a thirty-degree impedance matching transformer, to step-down the 50-ohm input impedance as seen from the transmitter  105  to approximately 14.67-ohms. As previously mentioned, the ordering of the eighteen and twelve degree sections  210 ,  215  may be reversed. It will be appreciated that the output impedance of the impedance matching device  115  may differ depending on the number of antenna elements of the antenna array  130  and the desired load impedance of each antenna element. 
     The RF power splitter  120  includes the third, fourth, and fifth sections  230 ,  235 , and  240  that correspond to the three stages of the power splitter  120 . The sections  230 ,  235 , and  240  of the power splitter  120  “step-up” the output impedance of approximately 14.67-ohms from the impedance matching device  115  to the desired output impedance of 117.3-ohms for each of the antenna elements of the antenna array  130 . Of course, the number of stages in the power splitter  120  may vary depending on the number of antenna elements of the antenna array  130 . Accordingly, if there are more than three power splitting stages, then additional sections may be needed to transform the input impedance to the RF power splitter  120  to the desired load impedance of each antenna element of the antenna array  130 . 
     An impedance matching/power splitter device  125  is formed by the combination of the impedance matching device  115  and the power splitter  120  and comprises five transformation sections  210 - 240 , which in combination, act to substantially match the input impedance  205  (as seen from the transmitter  105 ) to the load impedance of each antenna element of the antenna array  130 . In one embodiment of the present invention, the impedance matching/power splitter device  125  comprises five coaxial cables having various characteristic impedances that are connected end-to-end. It will be appreciated, however, that waveguides, striplines, eccentric coaxial, twin wire, microstrip, trough line, slab line, equal-gap rectangular, or various other techniques for producing differing characteristic impedances with distributed reactances may be used in lieu of coaxial cables without departing from the spirit and scope of the present invention. The impedance matching/power splitter device  125  of the present invention enables matching almost any impedance between the transmitter  105  and each antenna element of the antenna array  130 , while maintaining a relatively small physical size. 
     Turning now to FIG. 3A, a side-view perspective of the impedance matching/power splitter device  125  is shown in accordance with one embodiment of the present invention. The device  125  of FIG. 3A is shown for one antenna element of the antenna array  130  for simplification purposes. It will be appreciated, however, that the device  125  illustrated in FIG. 3A actually takes the form of the impedance matching/power splitter device  125  illustrated in FIG. 2A for all eight antenna elements. In the illustrated embodiment, the impedance matching/power splitter device  125  of FIG. 3A comprises an outer conductor  305  and an inner conductor  310  that is disposed lengthwise within the outer conductor  305 , such that the outer conductor  305  surrounds the inner conductor  310 . In one embodiment, the outer conductor  305  may take the form of a copper tube. It will be appreciated, however, that the outer conductor  305  may be constructed out of other suitable conductive materials, as opposed to copper, without departing from the spirit and scope of the present invention. 
     In one embodiment, the outer conductor  305  includes five transformation sections  210 - 240 , which include the two transformation sections  210 ,  215  of the impedance matching device  115  and the three transformation sections  230 ,  240  and  250  of the RF power splitter  120 . In accordance with one embodiment of the present invention, each transformation section  210 - 240  may take the form of a shim  321 - 325  that is disposed along the inner surface of the outer conductor  305  so that the shim  321 - 325  encircles the inner conductor  310 . The shims  321 - 325 , as illustrated in FIG. 3A, are viewed as if one could see through the outer conductor  305 ; although in reality, the shims  321 - 325  reside on the inner surface of the outer conductor  305 , and are not viewable from the outside surface of the outer conductor  305 . 
     Each shim  321 - 325  located at the transformation sections  210 - 240  of the outer conductor  305  may have a different thickness, thereby essentially varying the distance between the inner surface of the outer conductor  305  and the outer surface of the inner conductor  310 . A particular thickness of the shim  321 - 325  will yield a specific characteristic impedance (i.e., impedances z 1 -z 6 ) for its corresponding transformation section  210 - 240  of the outer conductor  305 . In the illustrated embodiment, the five shims  321 - 325  are adjoined together, side-by-side, along the inner surface of the outer conductor  305  such that there are no spaces or gaps between the five adjoining shims  321 - 325 . 
     In one embodiment, the shims  321 - 325  may be serially connected to one another, and affixed to the inner surface of the outer conductor  305  to prevent any movement between the adjoining shims  321 - 325 . In an alternative embodiment of the present invention, the shims  321 - 325  may be configured with mating teeth (not shown) on each mating edge of the shims  321 - 325  such that the shims  321 - 325  may be joined in a “locking” relationship so as to form a single unit along the inner surface of the outer conductor  305 . The “mating edge” is the edge of one shim  321 - 325  that is adjacent the edge of the adjoining shim  321 - 325 . The mating of the shims  321 - 325  may reduce the likelihood that the shims  321 - 325  will shift their positioning along the inner surface of the outer conductor  305 , thereby decreasing the probability of gaps or spaces from forming between the shims  321 - 325 . It will further be appreciated that the shims  321 - 325  may be joined using other types of mating mechanisms, as opposed to the use of mating teeth, as herein described, without departing from the spirit and scope of the present invention. 
     As mentioned shims  321  and  322  disposed within the outer conductor  305  form the impedance matching device  115 . Shim  321  specifically forms the eighteen-degree section  210  of the impedance matching device  115 , and has a specific thickness to yield a desired characteristic impedance z 1 , which is 10-ohms in the illustrated embodiment. Shim  322  specifically forms the twelve-degree section  215  of the impedance matching device  115 , and has a specific thickness to yield a desired characteristic impedance z 2 , which is 100-ohms in the illustrated embodiment. The two shims  321  and  322  transform the input impedance  205  to an output impedance of the impedance matching device  115  that equals the desired load impedance for each antenna element divided by the number of elements of the antenna array  130 , which is 14.67-ohms in the illustrated embodiment. It will be appreciated that shim  321  may alternatively form the twelve-degree section  215  and shim  322  may alternatively form the eighteen-degree section  210  without departing from the spirit and scope of the present invention. 
     Shims  323 ,  324 , and  325  disposed within the outer conductor  305  form the RF power splitter  120 , and each shim  323 ,  324 , and  325  corresponds to each of the three power splitting stages  230 ,  235 , and  240 , respectively, of FIG.  2 A. In the illustrated embodiment, each shim  323 ,  324 , and  325  yields a transformation between two characteristic impedances. Section “A” of shims  323 ,  324 , and  325  (as denoted in FIG. 3A) has a specific thickness to yield the desired characteristic impedances z 3 , z 4 , and z 5 , respectively. Similarly, section “B” of shims  323 ,  324 , and  325  has a specific thickness to yield the desired characteristic impedances z 4 , z 5 , and z 6 , respectively. Accordingly, shims  323 ,  324 , and  325  each possess two different thicknesses, a specific thickness for section “A” to yield one desired characteristic impedance, and another specific thickness for section “B” to yield another characteristic impedance. 
     In the illustrated embodiment, the characteristic impedance z 3  is the 14.67-ohms output impedance of the impedance matching device  115 , the characteristic impedance z 4  is the 29.33-ohms that results from the first power splitter stage  230  (as shown in FIG.  2 A), the characteristic impedance z 5  is the 58.65-ohms that results from the second power splitter stage  235 , and the characteristic impedance z 6  is the 117.3-ohms that results from the third power splitter stage  240 . The characteristic impedance z 6  of 117.3-ohms is the desired load impedance for each antenna element in the illustrated embodiment, as previously discussed. It should be noted that the thickness of shim  323  through section “B” is the same thickness as shim  324  through section “A” because these sections of shims  323  and  324  possess the same characteristic impedance z 4 . Similarly, the thickness of shim  324  through section “B” is the same thickness as shim  325  through section “A” because these sections of shims  324  and  325  possess the same characteristic impedance z 5 . 
     Referring now to FIG. 3B, a cross-sectional view of each of the five transformation sections  210 - 240  of the outer conductor  305  is shown. The shims  321 - 325 , for each of the respective transformation sections  210 - 240 , are disposed on the inner surface of the outer conductor  305  and encircle the inner conductor  310 . In the illustrated embodiment, a shim  321 - 325  corresponding to one of the transformation sections  210 - 240  will have a specific thickness, thereby providing a particular separation distance between the inner surface of the shim  321 - 325  (indicated by the shaded region adjacent the inner surface of the outer conductor  305 ) and the inner conductor  310  of the impedance matching/power splitter device  125 . The varying of the separation distance between the inner surface of the shim  321 - 325  and the outer surface of the inner conductor  310  will cause each shim  321 - 325  to yield a different characteristic impedance for each of the five transformation sections  210 - 240  of the outer conductor  305 . By providing specific characteristic impedances for each transformation section  210 - 240  along the outer conductor  305 , the impedance matching/power splitter device  125  is capable of substantially matching the input impedance  205  (as seen from the transmitter  105 ) to the load impedance of each antenna element of the antenna array  130 . For the transformation sections  230 ,  235 , and  240 , the respective shims  323 ,  324 , and  325  have a specific thickness (denoted as  323 A,  324 A, and  325 A in FIG. 3B) through section “A” of the shim to yield the characteristic impedances z 3 , z 4 , and z 5 , respectively. Similarly, the shims  323 ,  324 , and  325  have another thickness (denoted as  323 B,  324 B, and  325 B in FIG. 3B) through section “B” of the shim to yield the characteristic impedances z 4 , z 5 , and z 6 , respectively. 
     Turning now to FIG. 4, tables are illustrated for determining the characteristic impedances z 1  and z 2  for the eighteen-degree transformation section  210  and the twelve-degree transformation section  215  of the impedance matching device  115 . In particular, table 1 provides normalized “step-down” ratio design criteria for the transformation sections  210 ,  215  when it is desired to reduce the input impedance  205  of the transmission network  100  to the desired output impedance of the impedance matching device  115 . Table 2, on the other hand, provides normalized “step-up” ratio design criteria for the transformation sections  210 ,  215  when it is desired to increase the input impedance  205  of the transmission network  100  to the desired output impedance of the impedance matching device  115 . The first column of these tables provides the ratio in which it is desired to either “step-down” (table 1) or “step-up” (table 2) the input impedance  205  (i.e., z input ) to achieve the desired output impedance of the impedance matching device  115  (i.e., z output ). Each column of the tables corresponding to the transformation sections  210  and  215  has a factor by which to multiply by the input impedance  205  (z input ) to determine the characteristic impedances z 1  and z 2  needed for each transformation section  210 ,  215  to yield the desired output impedance (z output ) of the impedance matching device  115 . 
     It will be appreciated that other step-down and step-up ratios may be derived in addition to the ratios provided in the tables of FIG.  4 . In the step-down transformation of the impedance matching device  115  provided in FIG. 2A, the ratio is 50/14.67, or approximately 3.41, which may be extrapolated from the ratios of “3” and “3.5” in table 1 of FIG. 4, if so desired. Furthermore, the order of the 18-degree and 12-degree sections may be reversed, as previously discussed. 
     When the characteristic impedances (z 1 -z 6 ) are obtained for each transformation section  210 - 240 , the thickness of the shims  321 - 325  that correspond to each transformation section  210 - 240  may be determined to yield the particular characteristic impedance (z 1 -z 6 ) for each transformation section  210 - 240 . The characteristic impedance (z 1 -z 6 ) is equal to 138 log (b/a), where b is the inside diameter of the outer conductor  305  and a is the outer diameter of the inner conductor  310 . Accordingly, the thickness of the shims  321 - 325  that correspond to each transformation section  210 - 240  may be determined by the inside diameter “b” of the outer conductor  305 . It should be noted that since transformation sections  230 ,  235 , and  240  provide power splitting capabilities and, therefore, yield two separate characteristic impedances (i.e., z 3  and z 4  for section  230 , z 4  and z 5  for section  235 , and z 5  and z 6  for section  240 ), that each of these transformation sections have two thicknesses. One thickness through section “A” of the transformation section (note FIGS. 3A and 3B) and another thickness through section “B” of the transformation section to yield the corresponding characteristic impedances z 3 -z 6 . 
     Turning now to FIG. 5, a side-view perspective of the impedance matching/power splitter device  125  is shown in accordance with another embodiment of the present invention. In this particular embodiment, as opposed to using shims  321 - 325  of differing thicknesses to vary the separation distance or gap between the inner and outer conductors, an outer conductor  505  is provided that has a series of five transformation sections  510 - 540  formed therein. Each transformation section  510 - 540  formed within the outer conductor  505  provides a specific separation distance or gap between the inner surface of the outer conductor  505  and the outer surface of the inner conductor  310 . The varying of the separation distance between the inner surface of the outer conductor  505  and the outer surface of the inner conductor  310  will cause the impedance matching transformer/power splitter device  125  to yield a different characteristic impedance (z 1 -z 6 ) for each of the five transformation sections  510 - 540  of the outer conductor  505 . The specific characteristic impedances (z 1 -z 6 ) for each transformation section  510 - 540  will enable the impedance matching/power splitter device  125  to substantially match the impedance as seen from the transmitter  105  to the load impedance of each antenna element of the antenna array  130 . In the illustrated embodiment, transformation sections  510  and  515  respectively correspond to the sections  210  and  215  of the impedance matching device  115  (note FIG.  2 B). The transformation sections  530 ,  535 , and  540  respectively correspond to the sections  230 ,  235 , and  240  of the power splitter device  120 . 
     Turning now to FIG. 6, a process  600  for designing an impedance matching/power splitter device  125  is shown according to one embodiment of the present invention. The process  600  commences at block  605 , where the input impedance of the transmission network  100  and the desired load impedance for each antenna element of the antenna array  130  is determined. Specifically, the input impedance of the transmission network  100  is the impedance as seen from the transmitter  105  and represents the input impedance  205  (as shown in FIG.  2 A). The desired load impedance for each antenna element of the antenna array  130  is determined by adjusting the feed point location for each of these antenna elements so as to provide each antenna element with a substantially equivalent impedance. That is, the location of the element feeds of the antenna array  130  may be adjusted from the center of the element until substantially equal impedance values are attained for each antenna element. The impedance for each antenna element is desirably as close to the input impedance  205  as possible such that the disparity between the input impedance  205  and the load impedance of each antenna element of the antenna array  130  is minimized. 
     At block  610 , the output impedance of the impedance matching device  115  (and, thus, the input impedance to the RF power splitter  120 ) is determined by dividing the desired load impedance for each antenna element of the antenna array  130  by the number of antenna elements. At block  615 , the characteristic impedances z 1  and z 2  for each transformation section  210  and  215  of the impedance matching device  115  are determined using the normalized “step-down” or “step-up” ratio design criteria in the tables of FIG. 4, as previously described. In addition to determining the characteristic impedances z 1  and z 2  of the impedance matching device  115 , the characteristic impedances z 3 -z 6  for the transformation sections  230 ,  235 , and  240  are determined. The characteristic impedance z 3  of transformation section  230  is the output impedance of the impedance matching device  115  (as determined at block  610 ). The characteristic impedance z 4  is double the characteristic impedance of z 3  because the transformation section  230  splits the current and power, and, thus doubles the impedance at this stage. Similarly the characteristic impedances z 5  and z 6  are double the characteristic impedances of z 4  and z 5 , respectively, because their respective transformation sections  235  and  240  splits the current and power, and, thus doubles the impedance as well at their respective stages. 
     Subsequent to determining the characteristic impedances z 1 -z 6  for each of the transformation sections  210 - 240  at block  615 , the size (i.e., gauge) of the inner conductor  310  is determined to match the output impedance of the transmitter  105  at block  620 . In the illustrated embodiment, the size of the inner conductor  310  is selected based upon the current handling requirements at the RF frequency in which the transmitter  105  is tuned. 
     After determining the size of the inner conductor  310  at block  620 , the separation or gap distance between the inner surface of the outer conductor  305  and the outer surface of the inner conductor  310  for each transformation section  210 - 240  is determined at block  625  based upon the characteristic impedances (z 1 -z 6 ) for each transformation section  210 - 240 . The characteristic impedance (z 1 -z 6 ) is equal to 138 log (b/a), where b is the inside diameter of the outer conductor  305  and a is the outer diameter of the inner conductor  310 . Accordingly, the thickness of the shims  321 - 325  that correspond to each transformation section  210 - 240  may be determined by the inside diameter “b” of the outer conductor  305 . 
     The process  600  continues at block  630 , where the inside diameter of the outer conductor  305  is determined from the gauge size that is used for the outer conductor  205 . Based upon the separation or gap distance determined between the inner surface of the outer conductor  305  and the outer surface of the inner conductor  310  determined at block  625 , the thickness for each shim  321 - 325  corresponding to each transformation section  210 - 240  of the outer conductor  305  is determined at block  635 . The thickness for each shim  321 - 325  is selected such that it will yield the desired separation or gap distance between the inner surface of the outer conductor  305  and the outer surface of the inner conductor  310 , thereby yielding the desired characteristic impedance for each transformation section  210 - 240  of the outer conductor  305 . 
     The particular embodiments disclosed above are illustrative only, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the invention. Accordingly, the protection sought herein is as set forth in the claims below.