Patent Publication Number: US-2015081238-A1

Title: RF Signal Meter

Description:
RELATED APPLICATIONS 
     The present application claims the benefit of U.S. provisional application Ser. No. 61/870,351, filed Aug. 27, 2013, the contents of which are hereby incorporated by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present application relates to measurement of radio-frequency signals, and to devices for carrying out such measurement. 
     BACKGROUND OF THE INVENTION 
     Various meters, such as the Agilent, Model—V3500A Handheld RF Power Meter, measure radio-frequency (RF) power, but not phase. Many meters have a restricted range of input frequencies. 
     Current reflectometers need four coupled ports and are expensive and not off-the-shelf. Moreover, impedance measurement can be difficult to do at high power levels representative of actual operation using conventional reflectometers. Examples of conventional RF impedance analyzers include the MKS Instruments Model: VI-Probe-4100; and the MKS Model: VI-Probe-350. 
     Phase measurements are often performed using six RF ports, which can require complex RF setups. A Six port reflectometer can require eleven constants for its calibration. These coefficients are used to express the magnitude of the emerging wave, and the amplitude and complex ratio of the incoming and emerging waves, which can also be used to extract the phase and impedance information. However, the increasing number of standards for terminations, computational effort and the cost make six port reflectometers unattractive for phase or magnitude measurements. 
     Many conventional meters are calibrated only for specific external couplers and cannot be used with customers&#39; existing couplers or with couplers better suited for the application than the specific coupler. There is, therefore, a need of a more flexible, less complex meter for RF power (or amplitude) and phase. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features, and advantages of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein: 
         FIG. 1  shows a block diagram of a system according to one embodiment; 
         FIG. 2  is a high-level diagram showing the components of a data-processing system according to one embodiment; and 
         FIG. 3  shows simulated losses of a coupler according to one embodiment. 
       The attached drawings are for purposes of illustration and are not necessarily to scale. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following description, some aspects will be described in terms that would ordinarily be implemented as software programs. Those skilled in the art will readily recognize that the equivalent of such software can also be constructed in hardware, firmware, or micro-code. Because data-manipulation algorithms and systems are well known, the present description will be directed in particular to algorithms and systems forming part of, or cooperating more directly with, systems and methods described herein. Other aspects of such algorithms and systems, and hardware or software for producing and otherwise processing the signals involved therewith, not specifically shown or described herein, are selected from such systems, algorithms, components, and elements known in the art. Given the systems and methods as described herein, software not specifically shown, suggested, or described herein that is useful for implementation of any aspect is conventional and within the ordinary skill in such arts. 
       FIG. 1  shows a block diagram of a radio-frequency (RF) system, including a meter  100  and related components. RF source  110  provides a signal to antenna  120 . Coupler  130  is a four-port coupler, e.g., supplied separately from the meter  100 . A portion of the signal from source  110  passes along the “FWD” line and a portion of any reflections from antenna  120  passes along the “REFL” line. Meter  100  includes two more couplers  140  and  150 . In one embodiment, the couplers  140  and  150  comprise microstrip directional couplers. The couplers  140 ,  150  provide advantages over resistive attenuators since the couplers provide improved bandwidth and low insertion-loss. This ensures that the scalar power measurements will not be adversely affected during calibration and measurement. The microstrip couplers  140 , 150  are preferably etched onto a printed circuit board contained within the meter  100  to act as a transmission line, which requires matching to reduce loss. The microstrip couplers  140 ,  150  optionally include mitered 90 degree bends to reduce the effect of the bends on the impedance of the transmission line. 
     The FWD and REFL signals have their amplitudes or powers measured by detection units  145 ,  155 . The forward line from each coupler  140 ,  150  provides energy to phase detector  160 . Units  145 ,  155 ,  160  provide data of measurements of the RF signal to processor  186 . Processor  186  can perform error compensation and calibration processing, then provide magnitude, phase, or impedance- mismatch information. 
     Meter  100  can work with an external customer-supplied coupler, such as coupler  130 . Prior meters are designed and calibrated to work only with a particular coupler. However, different RF signals can require different couplers, thereby limiting the usefulness of such coupler-specific meters. An external coupler has to meet the power requirements of the devices attached to it and be operative in the correct signal frequency range. In an example, meter  100  measures magnitude of signals between 1 MHz and 6 GHz and phase between 1 MHz and 2.7 GHz. 
     In one embodiment, detection units  145  and  155  each comprise a demodulating logarithmic amplifier, such as the ANALOG DEVICES Model 8318. The ANALOG DEVICES Model 8318 used to measure amplitude is described by ANALOG DEVICES thus: “As a measurement device, Pin VOUT is externally connected to VSET to produce an output voltage, V OUT , which is a decreasing linear-in-dB function of the RF input signal amplitude.” Different measurement devices can be used for different frequency ranges. A segmentation approach can be used to determine how much error is present at a given frequency for a given meter  100  configuration. 
     Meter  100  can be calibrated in the field for a particular coupler  130 . This is done using a known source and known load. In various aspects, all calibration is algorithmic. The frequency of the known source can be provided to processor  186 , e.g., via user interface system  230 ,  FIG. 2 , as can the dB rating of external coupler  130 . Calibration loads can include 50 ohms, open, and short. The processor  186  can produce and later use calibration tables to compensate for error from external coupler  130  and internal couplers  140 ,  150 . Separate look-up tables may be used for power and phase. 
     Phase calibration uses forward and reflected power. 0° and 180° reference signals can be measured into a known load. S-parameters can be measured and phase information derived from those and known configurations of the components, e.g., the reference-signal frequency and system characteristic impedance. 
     For power, calibration, attenuation levels can be measured, or attenuation curves provided by manufacturers can be used. These can be inverted to determine the coupler-input power level corresponding to a given coupler output. 
     Calibration parameters can be stored within meter  100  (e.g., in data storage system  240 ,  FIG. 2 ) or on an external device such as a personal computer. Different sets of calibration parameters can be stored for different external couplers  130 . The calibration can take into account the characteristics of couplers  130 ,  140 ,  150 , and produce a single set of calibration data that will compensate for nonidealities in any of these, or other components of the signal path in coupler  130  or meter  100 . 
     It has been observed that the directivity of the external coupler  130  is of particular importance in determining its measurement accuracy. In one embodiment, calibration of the external coupler  130  may be performed as described below. 
     The following is the general S-parameter equation for b 3  (reflected wave at port 3) in a directional 4-port coupler with the source at port 1, forward-coupled line at port 3, reverse-coupled line at port 2, and the load at port 4: 
         b   3   =s   31   a   1   +s   32   a   2   +s   33   a   3   +s   34   a   4    (1)
 
         b   3   =s   31   a   1   +s   32 Γ 2   s   21   a   1   +s   34 Γ 4   b   4   +s   32 Γ 2   s   24 Γ 4   b   4   +s   33   a   3    (2)
 
         b   3   =s   31   a   1   +s   32 Γ 2 ( s   21   a   1   +s   24 Γ 4   b   4 )+ s   33   a   3   +s   34 Γ 4   b   4    (3)
 
     where:
 
b i =the reflected wave at port i.
 
a i =the incident wave at port i.
 
Γ i =the reflection coefficient for port i.
 
s 31 a 1 —Forward coupled power from P1 to P3: very large compared to other signals.
 
S 32 Γ 2 —This is multiplied by all power terms incident to P2 to give the contribution of this power to that incident to P3.
 
s 21 a 1 —Power emergent from port 1 multiplied by s 21  gives power incident to P2 resulting from a 1 .
 
s 24 Γ 4 b 4 —Note that Γ 4 b 4 =a 4 , this is the power reflected from the DUT. So multiplied by s 24  gives the power incident to P2 resulting from a 4 .
 
s 33 a 3 —This is the power incident to P3 resulting from reflected power at P3. With matched detector this is close to zero.
 
s 34 Γ 4 b 4 —Power at P3 resulting from a 4 =Γ 4 b 4 =reflected power from the load/DUT. In a good directional coupler (high directivity) this is very small.
 
     Several properties of the directional coupler  130  can simplify the above equations. For highly matched detectors, a 3 =a 2 ≈0. Also, loose coupling gives b 4 ≈a 1 =√{square root over (P 1  )} since only a small amount of power is coupled. Finally, the coupler is also assumed to be a low-loss device, which gives |s 32 |=|s 41 |≈1. Also, the coupling factor is K c =|s 24 | −2 =|s 31 | −2  and the directivity is related to the s-parameters as √K d K c =|s 21 | −1 =|s 34 | −1 . These simplifications give: 
     
       
         
           
             
               
                 
                   
                     b 
                     3 
                   
                   = 
                   
                     
                       
                         s 
                         31 
                       
                        
                       
                         a 
                         1 
                       
                     
                     + 
                     0 
                     + 
                     0 
                     + 
                     
                       
                         s 
                         34 
                       
                        
                       
                         Γ 
                         4 
                       
                        
                       
                         b 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     3 
                   
                   = 
                   
                     
                       
                         
                           
                             P 
                             1 
                           
                         
                         
                           
                             K 
                             c 
                           
                         
                       
                        
                       
                         ∠θ 
                         1 
                       
                     
                     + 
                     
                       
                         1 
                         
                           
                             
                               K 
                               d 
                             
                              
                             
                               K 
                               c 
                             
                           
                         
                       
                        
                       
                          
                         
                           Γ 
                           4 
                         
                          
                       
                        
                       
                         
                           P 
                           1 
                         
                       
                        
                       
                         ∠θ 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     3 
                   
                   = 
                   
                     
                       
                         
                           P 
                           1 
                         
                         
                           K 
                           c 
                         
                       
                     
                      
                     
                       [ 
                       
                         
                           1 
                            
                           
                             ∠θ 
                             1 
                           
                         
                         + 
                         
                           
                             
                                
                               
                                 Γ 
                                 4 
                               
                                
                             
                             
                               
                                 K 
                                 d 
                               
                             
                           
                            
                           
                             ∠θ 
                             4 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     The power at port 3 is then given by squaring the magnitude of b 3 , which takes on a minimum and maximum value due to the two phases. The maximum is given when θ 1 =θ 4  when the magnitudes are added, and the minimum occurs when the two components are 180 degrees out of phase per equation (7) below. 
     
       
         
           
             
               
                 
                   
                     P 
                     3 
                   
                   = 
                   
                     
                       
                         
                           P 
                           1 
                         
                         
                           K 
                           c 
                         
                       
                        
                       
                         [ 
                         
                           1 
                           ± 
                           
                             
                                
                               
                                 Γ 
                                 4 
                               
                                
                             
                             
                               
                                 K 
                                 d 
                               
                             
                           
                         
                         ] 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Similarly, the power at port 2 is found by using the s-parameter equation for b 2  with the same simplifications: 
     
       
         
           
             
               
                 
                   
                     b 
                     2 
                   
                   = 
                   
                     
                       
                         s 
                         21 
                       
                        
                       
                         a 
                         1 
                       
                     
                     + 
                     
                       
                         s 
                         22 
                       
                        
                       
                         a 
                         2 
                       
                     
                     + 
                     
                       
                         s 
                         23 
                       
                        
                       
                         a 
                         3 
                       
                     
                     + 
                     
                       
                         s 
                         24 
                       
                        
                       
                         a 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     2 
                   
                   = 
                   
                     
                       
                         s 
                         21 
                       
                        
                       
                         a 
                         1 
                       
                     
                     + 
                     0 
                     + 
                     0 
                     + 
                     
                       
                         s 
                         24 
                       
                        
                       
                         Γ 
                         4 
                       
                        
                       
                         b 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     2 
                   
                   = 
                   
                     
                       
                         
                           
                             P 
                             1 
                           
                         
                         
                           
                             
                               K 
                               d 
                             
                              
                             
                               K 
                               c 
                             
                           
                         
                       
                        
                       
                         ∠θ 
                         1 
                       
                     
                     + 
                     
                       
                         
                            
                           
                             Γ 
                             4 
                           
                            
                         
                         
                           
                             K 
                             d 
                           
                         
                       
                        
                       
                         
                           P 
                           1 
                         
                       
                        
                       
                         ∠θ 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     2 
                   
                   = 
                   
                     
                       
                         
                           P 
                           1 
                         
                       
                       
                         
                           K 
                           c 
                         
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             1 
                             
                               
                                 K 
                                 d 
                               
                             
                           
                            
                           
                             ∠θ 
                             1 
                           
                         
                         + 
                         
                           
                              
                             
                               Γ 
                               4 
                             
                              
                           
                            
                           
                             ∠θ 
                             4 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     2 
                   
                   = 
                   
                     
                       
                         
                           P 
                           1 
                         
                         
                           K 
                           c 
                         
                       
                        
                       
                         [ 
                         
                           
                              
                             
                               Γ 
                               4 
                             
                              
                           
                           ± 
                           
                             1 
                             
                               
                                 K 
                                 d 
                               
                             
                           
                         
                         ] 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In a reflectometer measurement, the reflected power reading is divided by the forward power reading, and the resulting fraction is square-rooted to give the reflection coefficient magnitude. This gives the equation: 
     
       
         
           
             
               
                 
                   
                      
                     
                       Γ 
                       
                         4 
                         , 
                         measured 
                       
                     
                      
                   
                   = 
                   
                     
                       
                         
                           P 
                           2 
                         
                         
                           P 
                           3 
                         
                       
                     
                     = 
                     
                       
                         
                            
                           
                             Γ 
                             4 
                           
                            
                         
                         ± 
                         
                           1 
                           
                             
                               K 
                               d 
                             
                           
                         
                       
                       
                         1 
                         ± 
                         
                           
                              
                             
                               Γ 
                               4 
                             
                              
                           
                           
                             
                               K 
                               d 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Which can be made clearer by pulling out a |Γ 4 | term from the numerator: 
     
       
         
           
             
               
                 
                   
                      
                     
                       Γ 
                       
                         4 
                         , 
                         measured 
                       
                     
                      
                   
                   = 
                   
                     
                        
                       
                         Γ 
                         4 
                       
                        
                     
                      
                     
                       [ 
                       
                         
                           1 
                           ± 
                           
                             1 
                             
                               
                                  
                                 
                                   Γ 
                                   4 
                                 
                                  
                               
                                
                               
                                 
                                   K 
                                   d 
                                 
                               
                             
                           
                         
                         
                           1 
                           ± 
                           
                             
                                
                               
                                 Γ 
                                 4 
                               
                                
                             
                             
                               
                                 K 
                                 d 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Equation (14) demonstrates how the directivity and the magnitude of the return loss (−20 log 10 |Γ 4 |) can adversely affect the measurement accuracy of the reflection coefficient of the DUT (device under test). It is also shows that the forward measurement gains accuracy as return loss decreases, while the reverse measurement loses accuracy as return loss decreases. Higher coupler directivity increases accuracy in all cases. 
     It is also important to note that both the coupling factor and the input power level have no influence on the measurement of the reflection coefficient magnitude. Therefore, these parameters may be adjusted to meet the requirements of the detectors  145 ,  155  without affecting the measurement accuracy. In a preferred embodiment, the detectors  145 ,  155  are closely matched to a 50 ohm system. The forward and reflected power measurements may require a further calibration to correct for the external coupler  130  and the power being supplied by the system generator. 
     In one embodiment, the processor calculates the value of 
     
       
         
           
             
               
                 P 
                 1 
               
               
                 
                   K 
                   c 
                 
               
             
             . 
           
         
       
     
     With a constant-power generator this will be a constant value, and will allow the correction of both the forward and reverse measurements due to the coupling of the external coupler  130 . 
     In one embodiment, the calibration of the external coupler  130  will take place as a separate stage from the calibration of the detectors  145 ,  155 . This separation simplifies the calibration of the external coupler  130 , since only one power level from the generator is needed to characterize the coupling coefficient. 
       FIG. 2  is a high-level diagram showing the components of a data-processing system for analyzing data and performing other analyses described herein. The system includes a data processing system  210 , a peripheral system  220 , a user interface system  230 , and a data storage system  240 . The peripheral system  220 , the user interface system  230  and the data storage system  240  are communicatively connected to the data processing system  210 . Processor  186  can include one or more of systems  210 ,  220 ,  230 ,  240 . 
     The data processing system  210  includes one or more data processing devices that implement the processes of the various aspects, including the example processes described herein. The phrases “data processing device” or “data processor” are intended to include any data processing device, such as a central processing unit (“CPU”), a desktop computer, a laptop computer, a mainframe computer, a personal digital assistant, a Blackberry™, a digital camera, cellular phone, or any other device for processing data, managing data, or handling data, whether implemented with electrical, magnetic, optical, biological components, or otherwise. 
     The data storage system  240  includes one or more processor-accessible memories configured to store information, including the information needed to execute the processes of the various aspects, including the example processes described herein. The data storage system  240  can be a distributed processor-accessible memory system including multiple processor-accessible memories communicatively connected to the data processing system  210  via a plurality of computers or devices. On the other hand, the data storage system  240  need not be a distributed processor-accessible memory system and, consequently, can include one or more processor-accessible memories located within a single data processor or device. 
     The phrase “processor-accessible memory” is intended to include any processor-accessible data storage device, whether volatile or nonvolatile, electronic, magnetic, optical, or otherwise, including but not limited to, registers, floppy disks, hard disks, Compact Discs, DVDs, flash memories, ROMs, and RAMs. 
     The phrase “communicatively connected” is intended to include any type of connection, whether wired or wireless, between devices, data processors, or programs in which data can be communicated. The phrase “communicatively connected” is intended to include a connection between devices or programs within a single data processor, a connection between devices or programs located in different data processors, and a connection between devices not located in data processors. In this regard, although the data storage system  240  is shown separately from the data processing system  210 , one skilled in the art will appreciate that the data storage system  240  can be stored completely or partially within the data processing system  210 . Further in this regard, although the peripheral system  220  and the user interface system  230  are shown separately from the data processing system  210 , one skilled in the art will appreciate that one or both of such systems can be stored completely or partially within the data processing system  210 . 
     The peripheral system  220  can include one or more devices configured to provide digital content records to the data processing system  210 . For example, the peripheral system  220  can include digital still cameras, digital video cameras, cellular phones, or other data processors. The data processing system  210 , upon receipt of digital content records from a device in the peripheral system  220 , can store such digital content records in the data storage system  240 . 
     The user interface system  230  can include a mouse, a keyboard, another computer, or any device or combination of devices from which data is input to the data processing system  210 . In this regard, although the peripheral system  220  is shown separately from the user interface system  230 , the peripheral system  220  can be included as part of the user interface system  230 . 
     The user interface system  230  also can include a display device, a processor-accessible memory, or any device or combination of devices to which data is output by the data processing system  210 . In this regard, if the user interface system  230  includes a processor-accessible memory, such memory can be part of the data storage system  240  even though the user interface system  230  and the data storage system  240  are shown separately in  FIG. 9 . 
     In view of the foregoing, aspects of the invention provide improved magnitude and phase measurement. A technical effect is to convert an RF signal to power and phase, and to determine impedance mismatch of source  110  and an RF load such as antenna  120 . Processor  186 , described above, can include a data processing system  210  and one or more of systems  220 ,  230 , or  240 . 
     As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method, or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware aspect, an entirely software aspect (including firmware, resident software, micro-code, etc.), or an aspect combining software and hardware aspects that may all generally be referred to herein as a “service,” “circuit,” “circuitry,” “module,” and/or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     A computer program product can include one or more storage media, for example; magnetic storage media such as magnetic disk (such as a floppy disk) or magnetic tape; optical storage media such as optical disk, optical tape, or machine readable bar code; solid-state electronic storage devices such as random access memory (RAM), or read-only memory (ROM); or any other physical device or media employed to store a computer program having instructions for controlling one or more computers to practice method(s) according to various aspects(s). 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage mediwn may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code and/or executable instructions embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, or any suitable combination of appropriate media. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages. The program code may execute entirely on the user&#39;s computer (device), partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). The user&#39;s computer or the remote computer can be non- portable computers, such as conventional desktop personal computers (PCs), or can be portable computers such as tablets, cellular telephones, smartphones, or laptops. 
     Computer program instructions can be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner. The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified herein. 
       FIG. 3  shows simulated results of a coupler such as coupler  140 ,  150 . The S41 trace shows the amount of RF energy coupled from the input (from coupler  130 ) to the phase detector  160 . 
     The invention is inclusive of combinations of the aspects described herein. References to “a particular aspect” and the like refer to features that are present in at least one aspect of the invention. Separate references to “an aspect” or “particular aspects” or the like do not necessarily refer to the same aspect or aspects; however, such aspects are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to “method” or “methods” and the like is not limiting. The word “or” is used in this disclosure in a non-exclusive sense, unless otherwise explicitly noted. 
     The invention has been described in detail with particular reference to certain preferred aspects thereof, but it will be understood that variations, combinations, and modifications can be effected by a person of ordinary skill in the art within the spirit and scope of the invention.