CALIBRATION OF SYMMETRIC AND PARTIALLY-SYMMETRIC FIXTURES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority under 35 U.S. C. § 119(e) from U.S. Provisional Application serial number 60/836,489, filed on August 8, 2006 and U.S. Provisional Application serial number 60/916,872, filed on May 9, 2007 the contents of which are herein incorporated by reference in their entirety.

BACKGROUND

[0002] This disclosure relates to the calibration of fixtures and, more particularly to calibration of partially- symmetric and mirror-symmetric fixtures.

[0003] A fixture is commonly used to couple a test and measurement (T&M) instrument to a device under test (DUT). The fixture provides an interface between the T&M instrument and the DUT. For example, the T&M instrument may have coaxial connectors while the DUT has a planar microstrip interface. For measurements of the DUT, the fixture must be characterized in order to remove its effect on the measurements of the DUT. [0004] For a DUT with coaxial connections, the T&M instrument can be calibrated with off-the-shelf calibration kits. The calibration kits are available for many types of coaxial connectors. However, for DUTs in other environments such as a planar environment, calibration kits may not be available or may be highly expensive. For calibration kits that are available, multiple calibration standards may be required. For example, for a thru-reflect-line (TRL) calibration, a thru standard, reflect standards, and one or more line standards are needed, typically with multiple line standards. Such calibrations require multiple standards, multiple measurements of the standards, and math processing to combine the measurements together.

[0005] Accordingly, there remains a need for an improved system and method for calibrating fixtures.

SUMMARY

[0006] An aspect of the invention includes systems and methods for calibrating a fixture including measuring a plurality of parameters of the fixture; time-domain gating at least one of the measured parameters; and calculating parameters for a first section of the fixture and a second section of the fixture in response to the measured parameters and the time-domain gated parameter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIGURE 1 is a block diagram of a system for calibrating a fixture according to an embodiment of the invention.

[0008] FIGURE 2 is a flow graph representation of parameters of the fixture of FIGURE 1. [0009] FIGURE 3 is a flow graph representation of symmetric parameters of the fixture of FIGURE 1.

[0010] FIGURE 4 is an example of a time-domain representation of a parameter of the fixture of FIGURE 1.

[0011] FIGURE 5 is an example of a time-domain gated representation of a parameter of the fixture of FIGURE 1.

[0012] FIGURE 6 is a flowchart illustrating how a fixture is calibrated according to an embodiment of the invention.

[0013] FIGURE 7 is a flowchart illustrating examples of time-domain gating of FIGURE 6. [0014] FIGURE 8 is a flowchart illustrating additional examples of time-domain gating of FIGURE 6.

[0015] FIGURE 9 is a flowchart illustrating examples of the calculations of fixture parameters of FIGURE 6.

[0016] FIGURE 10 is a block diagram illustrating a system for calibrating a partially- symmetric fixture according to an embodiment of the invention.

[0017] FIGURE 11 is a flow graph representation of parameters of the partially- symmetric fixture of FIGURE 10.

[0018] FIGURE 12 is a flowchart illustrating how a fixture is calibrated using multiple time-domain gated parameters.

[0019] FIGURE 13 is a block diagram of a system for calibrating a differential fixture according to an embodiment of the invention.

[0020] FIGURES 14 and 15 are flow graph representations of common-mode and differential-mode parameters of the differential fixture of FIGURE 13. [0021] FIGURE 16 is a flowchart illustrating how a differential fixture is calibrated according to an embodiment of the invention.

DETAILED DESCRIPTION

[0022] Various embodiments of the invention will next be described with reference to the drawings. These embodiments enable characterization of fixtures, including mirror-

symmetric or partially-symmetric fixtures.

[0023] FIGURE 1 is a block diagram of a system for calibrating a fixture according to an embodiment of the invention. The system includes a fixture 20 coupled to a vector network analyzer (VNA) 10. Although a VNA 10 is illustrated in FIGURE 1, the VNA 10 can be replaced with any T&M instrument capable of measuring scattering parameters (S- parameters). For example, the T&M instrument can be an oscilloscope capable of making a time-domain reflectometry (TDR) measurement. In another example, the T&M instrument can be a dedicated calibration instrument for calibrating the fixture, rather than a general purpose T&M instrument.

[0024] Although S-parameters are used in this description for the characterization of components, calibrations, or the like, the parameters can take any form as desired. For example, transmission parameters (T-parameters), ABCD-parameters, admittance parameters

(Y-parameters), impedance parameters (Z-parameters), or the like can be used both as replacement with S-parameters or in combination.

[0025] In this embodiment, the VNA 10 is coupled to the fixture 20 through cables 12 and

14. A first port of the VNA 10 is coupled to a connector 16 on a first port of the fixture 20. A second port of the VNA 10 is coupled to the connector 18 on a second port of the fixture 20.

Accordingly, the VNA 10 can make two-port measurements of the fixture 20.

[0026] Although the fixture 20 has been described as having connectors 16 and 18 to connect to the VNA 10, other coupling can be used. For example, the fixture may have landing pads for probes that are coupled to the VNA 10. Any manner of coupling between the VNA 10 and the fixture 20 can be used.

[0027] The fixture 20 includes a transmission line 21 between the two connectors 16 and

18. The fixture 20 is symmetric about reference plane 26. Accordingly, fixture 20 includes a first section 22 and a second section 24 divided by the reference plane 26. The reference plane 26 need not correspond to a physical structure on the fixture 20. For example, the reference plane 26 can correspond to a location along the transmission line 21.

[0028] FIGURE 2 is a flow graph representation of parameters of the fixture of FIGURE 1.

Flow graph 30 represents the S-parameters of the fixture 20 as a whole. The fixture 20 S- parameters are designated Sf , where Sf _v represents the S-parameter response at port x due to port j. Accordingly, flow graph 30 represents the two-port S-parameters of the fixture 20. [0029] Flow graph 31 is equivalent to flow graph 30, both representing the S-parameters of the fixture 20. However, flow graph 31 includes S-parameters X and S-parameters Y

representing the S-parameters of the first section 22 and the second section 24 of the fixture 20. Reference plane 36 corresponds to the reference plane 26 of the fixture 20. The cascade of S-parameters X and Y are equivalent to the S-parameters of the fixture 20. [0030] FIGURE 3 is a flow graph representation of symmetric parameters of the fixture of FIGURE 1. Because the fixture 20 is assumed to be symmetrical, some assumptions can be made regarding the S-parameters X and Y. In this embodiment, the fixture 20 is assumed to be mirror-symmetric about reference plane 26, corresponding to reference plane 36 in the flow graphs. Because of the symmetry return losses on symmetrical sides of the fixture will be equivalent. Since the fixture 20 is mirror- symmetric, Sx π = Sy 22 and Sx 22 = Sy π. [0031] Similarly, because of the symmetry, the through S-parameters will be equivalent. Accordingly, SX ₂₁ = Sy ₁₂ and Sx ₁₂ = Sy ₂₁ . In other words, the through S-parameters from an edge of the fixture 20 towards the reference plane 36 are equivalent, and vice-versa. [0032] Furthermore, the sections of the fixture 20 are assumed to have reciprocal through responses. That is, SX21 = Sxπ and Sy2i = Sy 12. Using these assumptions S-parameters X and Y of the flow graph 31 can be substituted, resulting in S-parameters Z and Z . It should be noted that S-parameters Y have been replaced with S-parameters Z; however the ports are switched. Accordingly, flow graph of FIGURE 3 results in equation 1 :

[0034] Because of fixture symmetry, Sf _n = Sf ₂₂ . Because of fixture reciprocity, Sf 1 = Sf 2. Accordingly, equation 1 results in two independent equations, equations 2 and 3; however, there are three unknowns, Sx π, SX22, and SX21. Sx ₇ , ²

[0035] Sf ₂₁ = (2)

1 - &C

[0036] Sf ₁ = Sx _n + (3)

1 - Sx ₀₀

[0037] In an embodiment, time-domain gating can be used to determine Sxu. FIGURE 4 is an example of a time-domain representation of a parameter of the fixture of FIGURE 1. In this example, chart 50 is the impulse response of the reflection from port 1 of the fixture 20, or Sf i. A first region 52 may be due to the first port of the fixture 20. For example, it may be due to the transition from the connector 16 to the transmission line 21. The second region 54

may be due to the transition from the transmission line 21 to the connector 18.

[0038] As can be seen in the Sf u component of equation 1 , Sx u is not the only component of Sf π. Sf π includes an additional component due to Sx 22 and SX21. This additional component includes Sx2i ² , corresponding to the round trip contribution through S-parameters

Z reflected from reference plane 36 of FIGURE 3. Since SX ₂₁ likely includes a time delay, the additional component ofSfπ will be delayed in time relative to the Sxn component.

[0039] Accordingly, the first region 52 can substantially correspond to Sxn. Time-domain gating can be used to gate out the second region 54. The resulting measurement substantially corresponds to Sx π- Now that Sx π is known, it can be used with equations 2 and 3 above to calculate Sx 22 and SX21. For example, equation 2 is substituted into equation 3 resulting in equation 4:

[0040] Sf _n = Sx _n + Sx ₂₂ ^■ Sf ₂₁ (4)

[0041] Equation 4 is solved for Sx 22 in equation 5 :

[0042] Sx ₂₂ = ^{Sf SXn} (5)

[0043] Equation 5 is substituted into equation 2 in equation 6:

(6) [0045] Solving equation 6 for SX21 results in equations 7 and 8:

[0047] Sx ₂₁ = ^ Sf ₂₁ ^ - Sx ₂₂ ) (8)

[0048] Accordingly, Sx _n , Sx ₂₂ , and Sx _2I , all of the unknown S-parameters of S-parameters Z of FIGURE 3 are now known. Z is also known as it has the same component S-parameters as S-parameters Z. As a result, the fixture 20 is characterized, establishing a reference plane

36 corresponding to the reference plane 26 on the fixture 20.

[0049] Although the impulse response has been used as an example, other time-domain responses can be used. For example, a step response can be used. The step response can be time-domain gated to achieve a similar result.

[0050] FIGURE 5 is an example of a time-domain gated representation of a parameter of

the fixture of FIGURE 1. In this example, the impulse response of Sf u has been gated at a time 58 corresponding to the center of the fixture. As can be seen, the response of region 54 of FIGURE 4 has been gated out. Accordingly, the impulse response 60 now includes a substantial amount of the energy in Sf u due to Sx π.

[0051] FIGURE 6 is a flowchart illustrating how a fixture is calibrated according to an embodiment of the invention. An embodiment includes a method of calibrating a fixture. The method includes measuring parameters of the fixture in 70; time-domain gating at least one of the measured parameters 72; and calculating parameters for a first section of the fixture and a second section of the fixture in response to the measured parameters and the time-domain gated parameter in 74.

[0052] As described above, the measured parameters can be S-parameters; however, the parameters need not be in such a form. In another example, measuring of the parameters need not be in a frequency domain. The measurement of the parameters can be through a time-domain measurement. Any measurement technique resulting in parameters that can be transformed into S-parameters or other similar parameters can be used. [0053] Time-domain gating in 72 can include time-domain gating of one or more of the measured parameters. For example, as described above, the reflection from a first port of the fixture can be parameter that is time-domain gated. The frequency domain response oϊSfπ, or the measured reflection from a first port of the fixture, can be Fourier transformed into the time-domain impulse response.

[0054] In another example, the measurements can include an actual time-domain measurement of the first port of the fixture. This measurement can be independent of the measurements of the S-parameters. Accordingly, this time-domain measurement can be time- domain gated. Regardless of how obtained, the time-domain gated measurement can be Fourier transformed into the frequency domain. Accordingly in an embodiment, a frequency domain measurement representing Sx u can be obtained from Sf π- [0055] As described above, once the time-domain gating has resulted in one of the S- parameters of the first section of the fixture, only two unknowns remain. From the two independent equations, the other S-parameters for both the first section and the second section can be calculated. Although a first section and a second section have been described, either section of the fixture can be identified as the first section or the second section. [0056] In an embodiment, having characterized the first and second sections, the fixture can be used in the testing of a DUT. Referring back to FIGURE 1 , the DUT can be placed at a location on the transmission line 21 of the fixture 20 corresponding to the reference plane 26.

The calculated parameters for the first and second sections correspond to characterizations of those sections between their respective ports and the reference plane 26. Since the DUT is placed at the reference plane, the fixture has been characterized up to the connection point of the DUT.

[0057] In another embodiment, the fixture 20 can be split at the reference plane 26. A DUT with a substantially similar interface, such as transmission line 21, can be inserted. Since the fixture was characterized through the calculated parameters, the portions of the fixture are still characterized up to the reference plane and the DUT can be characterized. [0058] FIGURE 7 is a flowchart illustrating examples of time-domain gating 72 of FIGURE 6. As described above, a first reflection from the first port of the fixture can be time-domain gated in 76. Time-domain gating a second reflection in 78 will be described below.

[0059] FIGURE 8 is a flowchart illustrating additional examples of time-domain gating 72 of FIGURE 6. In one example, the method includes time-domain gating a reflection from a port of the fixture at a time substantially between a contribution of a first interface of the fixture and a contribution of a second interface of the fixture 114. As a result, the time- domain gated measurement can include a majority of the energy from the reflection of the first interface and a minority of the energy from the second interface of the fixture. The interfaces can be the connectors on the fixture. In addition, the interface can include additional transmission line portions, transitions, or the like. As a result, the contribution of the first or second interfaces can, but need not be limited to a single physical location. [0060] As described above, the reflection of the S-parameters of the first section of the fixture can be due to the reflection from various discontinuities or other attributes of the fixture up to a reference plane. The reference plane can be used to establish the time for the time-domain gating. Accordingly, in another example, the method includes time-domain gating a reflection using a time substantially corresponding to a reference plane of the fixture in 82. As a result, contributions to the reflection of the first section up to the reference plane can be taken into account. Since the reference plane divides the two sections of the fixture for the creation of the S-parameters, using the time corresponding to the reference plane can prevent the contribution of reflections looking into the reference plane towards the second port from contributing to the reflection of the S-parameters of the first section. Such reflections should be represented by the S-parameters of the second section. [0061] In another example, the method can include time-domain gating a reflection using a time substantially corresponding to physical location on the fixture corresponding to a

substantially uniform transmission line in 84. A substantially uniform transmission line is a transmission line having a substantially uniform impedance. Accordingly, the portion of the impulse response due to the substantially uniform transmission line can approach zero. Within the substantially uniform transmission line, reflections are minimized due to the substantially uniform impedance. Accordingly, any reflections due to components beyond the substantially uniform transmission line can be removed through time-domain gating. As a result, the time-domain gated reflection will approach the exact amount of the reflection of the S-parameters of the first section of the fixture.

[0062] FIGURE 9 is a flowchart illustrating examples of the calculations of fixture parameters of FIGURE 6. The method includes calculating a reflection for the first portion of the fixture in response to the time-domain gated parameter in 86; and calculating the parameters for a first section of the fixture and a second section of the fixture in response to the calculated reflection of the first portion in 88. As described above, the time-domain gated parameter corresponds to a reflection of the S-parameters for the first section of the test fixture. However, the remaining parameters of both the first and second section need to be determined. Accordingly, they are calculated using the measurements of the fixture and the calculated reflection.

[0063] FIGURE 10 is a block diagram illustrating a system for calibrating a partially- symmetric fixture according to an embodiment of the invention. Similar to the system of FIGURE 1, a VNA 10 is coupled to the fixture 101 through cables 12 and 14. In contrast to the fixture 20, fixture 101 is partially symmetric.

[0064] A partially-symmetric fixture is a fixture with a mirror-symmetric section divided by a reference plane and additional sections coupled to the mirror-symmetric section that may or may not be symmetric. In this embodiment, section 107 and section 103 are mirror- symmetric. However, connector 106 and connector 108 are different, and section 105 is between the mirror-symmetric sections 100 and 103 and the connector 108. The fixture 101 can still be divided into a first section 100 and a second section 102 at the reference plane 104. Accordingly, the calibration includes characterization of these sections. [0065] FIGURE 11 is a flow graph representation of parameters of the partially- symmetric fixture of FIGURE 10. An assumption is made in that Sx 22 = Sy π. In addition assumptions are made on reciprocity. Thus, SX21 = Sxn, Sy 21 = Sy n, and Sf2i = Sf n. Referring back to FIGURES 2, S-parameters X and Y represent the different sections of the fixture. Through substitution using the assumptions described above, S-parameters X become S-parameters Z, just as described with reference to FIGURE 3; however, S-parameters Y become S-

parameters Zy. The designation Zy is used to represent that it has substituted S-parameters; however, it still retains portions of the original S-parameters Y. Accordingly, S-parameters Z can represent the first section 100 and S-parameters Zy can represent the second section 102 of the fixture 101. As can be seen in the flow graphs, the unknown S-parameters are Sx π, Sx ₂ I, Sx ₂₂ , Sy ₂₁ , and Sy ₂₂ . [0066] Equation 9 represents the cascade of the S-parameters X and Y of FIGURE 2.

[0068] Similar to the symmetric fixture, the S-parameters of the entire fixture are measured. Sx u corresponds to the reflection of the first section 100 of fixture 101 looking into the first connector 106. Sy ₂₂ corresponds to the reflection of the second section 102 of the fixture 101 looking into the second connector 108. Sf _n and Sf ₂₂ can be time-domain gated to obtain Sx _n and Sy ₂₂ . With the assumptions described above and the time-domain gated Sx _n and Sy ₂₂ , the only remaining unknowns are Sx ₂ 1, Sy ₂ I, and Sx ₂₂ . [0069] Equation 9 yields three independent equations 10-12:

Sx ₁₂ - Sy _n - Sx ₂

[0070] - Sf _n Sx _n (10) 1 - Sx,, - Sv,,

[0073] Solving for Sx ₂₂ in the above equations yields equation 13:

[0075] Once Sx ₂₂ is known, equations 10 and 12 can be solved for Sx i ₂ and Sy n in equations 14 and 15:

[0078] The signs in equations 13, 15, and 15 affect the phase of those S-parameters. The

sign can be determined from the time-domain measurement and/or examining the resulting S- parameters for continuity of phase.

[0079] If Sx ₂₂ = 0 , then Sx ₁₂ , Sj ₁₂ can not be computed from (14) and (15). Instead, they can be resolved from

[0080] Sx _n - Sy _n = Sf _n (i6)

[0081] Additional knowledge of the relation between Sx ₁₂ and Sj ₁₂ may be needed to resolve Sx ₁₂ and Sy i ₂ . For example, if the fixture is through-symmetric, then Sx ₁₂ = Sj ₁₂ . In another example, if traces on the first portion and the second portion are uniform, but the trace on the first portion is twice as long as the trace in second portion, then Sx ₁₂ = Sj ₁₂ • Sj ₁₂ . Once such additional information is determined, Sxn and Sy ₁₂ can be resolved.

[0082] Referring back to FIGURES 1, 7, and 10 in an embodiment, a second reflection from a second port of the fixture is time-domain gated in 78. As described above with respect to FIGURE 4 and 5, a reflection from the port 1 of the fixture 20 of FIGURE 1 is time- domain gated. Similarly, in 76, the time-domain gated first reflection can be the reflection from the port at connector 106 of fixture 101 of FIGURE 10. Using the example fixture 101 of FIGURE 10, the second reflection can be from a second port of the fixture 101. That is, the reflection can be from the connector 108.

[0083] Furthermore, as described above, there are various techniques for performing the time-domain gating. For example, various points in time can be used to gate a parameter, various measurements can be used, or the like. When performing the time-domain gating for the reflections from the first and second ports in 76 and 78, identical techniques can, but need not be used.

[0084] Although described with respect to a partially-symmetric fixture, time-domain gating of multiple reflections need not be limited to partially-symmetric fixtures. For example, a symmetric fixture such as the fixture 20 of FIGURE 1 can be characterized using multiple time-domain gated reflections.

[0085] FIGURE 12 is a flowchart illustrating how a fixture is calibrated using multiple time-domain gated parameters. In an embodiment, the method includes calculating a reflection for the first portion of the fixture in response to a first time-domain gated parameter in 90; and calculating a reflection for the second portion of the fixture in response to a second time-domain gated parameter in 92. Just as the time-domain gated reflection from the first port at connector 106 can be used to obtain the reflection Sx;; of S-parameters Z, the time- domain gated reflection from the second port at connector 108 can be used to obtain the

reflection Sy 22 of S-parameters Zy.

[0086] The method also includes calculating the parameters for a first section of the fixture and a second section of the fixture in response to the calculated reflection of the first portion and the calculated reflection of the second portion in 94. Accordingly, the reflections Sx π and Sy ₂₂ can be used to calculate the parameters for both the first and second sections, even through the first and second portions are not mirror-symmetric.

[0087] FIGURE 13 is a block diagram of a system for calibrating a differential fixture according to an embodiment of the invention. Similar to embodiments described above, in this embodiment, the VNA 10 is coupled to the fixture 144 through cables 12 and 14. In contrast, the fixture 114 is a differential fixture. That is, it has two differential ports 139 and 141. Each port is formed by two connectors. Differential port 139 is formed by connectors 136 and 138. Differential port 141 is formed by connectors 140 and 142. Transmission lines 135 and 137 form the differential transmission line of the differential fixture 144. [0088] Measurements of parameters of the differential fixture 144 can be measured by the VNA 10. In this embodiment, the VNA 10 is illustrated as a two-port instrument. However, the differential fixture 144 is a four-port device. Accordingly, multiple two-port measurements can be made on the differential fixture 144 to form a four-port measurement. T & M instruments with a different number of ports can be used. For example, a VNA with four-ports can be used to directly measure the four-port parameters of the fixture 144. [0089] Once obtained, the four-port parameters can be separated into differential-mode parameters and common-mode parameters. Equation 17 describes the differential-mode and common-mode components of a four-port matrix.

Diff ModeStim. ComModeStim. sDD, 1,1 s vD-'D ^t -',Yl sDC _n sDC _ϊ2 sDD _n sDD _l2 ^" sDC, , sDC,

Diff. ModeStim. sDD ₀ , SDD ₀₀ sDC ' ₀ 2,1 sDC 22 sDD _2l SDD ₂₂ sDC " ₀ 2,1 sDC 22 sCD sCD _u sCC _n sCC sCD _n sCD _l2

Com .ModeStim . sCD ₀ , sCD ₀₀ sCC ₀ , sCC ₀₀ sCD _2l sCD ₂₂ sCC " ₀ 2,1 sCC 22

(17)

[0090] Parameters described as sDD are differential responses from differential-mode stimulation. Similarly, sCC parameters are common-mode responses from common-mode stimulation. Parameters sCD and sDC represent cross-mode responses. Accordingly, the differential-mode fixture parameters are sDD and the common-mode fixture parameters are sCC. [0091] FIGURES 14 and 15 are flow graph representations of common-mode and

differential-mode parameters, respectively, of the differential fixture of FIGURE 5. FIGURE 14 is a representation of the first and second sections of the common-mode response of the differential fixture 144. Xcm represents the first section and Xcm represents the second section divided by the reference plane 154. In this embodiment, the differential fixture 144 is assumed to be a mirror-symmetric fixture. The flow graph is similar to the flow graph of FIGURE 3 representing the single ended fixture 20 of FIGURE 1. Thus, Xcm is Xcm with the ports reversed, similar to Z and Z described above.

[0092] Since two-port S-parameters for the common-mode response of the sections of the fixture 144 have been obtained, the calculation of the various parameters sxc;;, sxc _2/ , and SXC ₂₂ can be performed as described above with respect to the single ended case. [0093] FIGURE 15 is a representation of the first and second sections of the differential- mode response of the differential fixture 144. Similar to the common-mode parameters described above, the first and second sections of differential-mode of the differential fixture 144. Accordingly, S-parameters Xdm and Xdm , divided by the reference plane 160, can be calculated from the differential parameters.

[0094] FIGURE 16 is a flowchart illustrating how a differential fixture is calibrated according to an embodiment of the invention. In this embodiment, the method includes converting the measured parameters into differential-mode parameters and common-mode parameters in 170; time-domain gating a first differential-mode reflection from a first port of the fixture in 172; and time-domain gating a first common-mode reflection from a first port of the fixture in 176. Accordingly, as described above, the time-domain gated parameters can be used to substitute for the additional unknown in the characterization of the respective differential and common-mode parameters.

[0095] In another embodiment, the fixture 144 could be a partially-symmetric fixture. Accordingly, the method can include time-domain gating a second differential-mode reflection from a second port of the fixture in 174; and time-domain gating a second common-mode reflection from a second port of the fixture in 178. Similar to embodiments described above, multiple time-domain gated measurements need not be limited to partially- symmetric fixtures.

[0096] Furthermore, an embodiment can include means for performing any of the above described operations. Examples of such means include the devices, systems, apparatus, configurations, or the like described above.

[0097] Another embodiment includes an article of machine readable code embodied on a machine readable medium that when executed, causes the machine to perform any of the above described operations. As used here, a machine is any device that can execute code. Microprocessors, programmable logic devices, multiprocessor systems, digital signal processors, personal computers, or the like are all examples of such a machine. [0098] Although transmission lines have been described above, a transmission line is not limited to any particular type. Accordingly, a transmission line can be a microstrip line, a coaxial cable, a waveguide, or the like.

[0099] Although particular embodiments have been described, it will be appreciated that the principles of the invention are not limited to those embodiments. Variations and modifications may be made without departing from the principles of the invention as set forth in the following claims.