Abstract:
An in-line directional radio-frequency (“RF”) power meter for measuring power and other parameters in a transmission line. The meter simultaneously measures complex voltage-waves traveling in the forward and reverse directions of a connected transmission line and processes measured voltages to compute forward and reverse power, standing wave ratio, and impedance values. The apparatus includes a microprocessor having microcode for digitally computing RF power parameters, and a field programmable gate array (“FPGA”) having microcode for executing complex Fast Fourier Transforms (“FFT”) to calculate voltages and frequencies, a microprocessor with attached firmware to make a series of complex calculations relative to sensed electrical values in the transmission line and to pass certain calculated values to the device to communicate RF power parameters to a user. The configuration of the apparatus allows for measurement of RF power parameters in a relatively economical package.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to systems that measure transmission power within a radio frequency medium. More particularly, the present invention relates to apparatuses and methods for measuring radio frequency (“RF”) voltage, power, impedance and other relevant parameters in an RF power transmission system to allow for optimization of a transmission power source. 
     BACKGROUND OF THE INVENTION 
     Currently available apparatuses that measure power parameters in a RF power transmission system typically utilize inductive type pickup coils positioned transverse to a connected transmission line. The coils sense voltage variations related to forward- or reverse-traveling voltage waves on the transmission line and this voltage is rectified and used to drive an analog meter displaying a human perceptible value. However, these types of devices are not capable of measuring complex impedance which is an important quantity in RF power calculations. 
     In addition, current instruments generally use electrical assemblies containing an inductive pickup coil, a resistor-capacitor frequency compensator, and a diode rectifier to provide a direct current (“DC”) signal related to forward- and reverse-traveling waves on the transmission line. A deficiency with this type of design is that the assembly will only accommodate a relatively limited frequency range of, for example, 25-60 MHz or a ratio of approximately 2.5:1, with a “feasible” ratio of 5:1. Additionally, such configurations accurately measure a relatively small range of RF power (e.g. 150 to 1000 Watts or a ratio of about 7:1). 
     These aforementioned limitations result in several different assemblies being required to accommodate even a modest range of frequencies and RF power amplitudes, and such assemblies are relatively expensive due to precise machining and high quality componentry required to achieve a high quality, high directivity directional coupler. Hence, what is needed in the industry is a relatively inexpensive RF meter that is able to accurately measure all of the RF power parameters required to optimize a radio frequency transmissions source. 
     SUMMARY OF THE INVENTION 
     In summary, the invention includes a coupler connected to a RF power transmission system, a filter to compensate for reception of voltage signals through the coupler, an analog to digital (“A-D”) converter for digitizing the received voltage signals from the coupler, a microprocessor having microcode for digitally computing RF power parameters, a field programmable gate array (“FPGA”) having microcode for executing complex Fast Fourier Transforms (“FFT”) responsive to microprocessor command signals, and a display device for displaying RF power parameters in human comprehendible values. 
     In the aforementioned system, acceptable power parameters may be obtained by connecting a relatively inexpensive semi-directional coupler such as a coupled microstrip for wide-frequency-band use to a transmission line, sensing right and left radio frequency voltage signals over an acceptable frequency range, filtering the received right and left signals to partially compensate for the frequency dependent coupling, and using FFT&#39;s and other calculations to calculate RF power parameters such as V F , V R , S 11 , SWR, P F , P R , P d  and Z, and displaying those results on a human perceptible display. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       An RF power meter and method incorporating the features of the apparatus are depicted in the attached drawings which form a portion of the disclosure and wherein: 
         FIG. 1  is a block diagram of the preferred embodiment of the apparatus; 
         FIG. 2  is a detailed diagram of the hardware signal processing module of the apparatus shown in  FIG. 1 ; 
         FIG. 3  is a further electrical diagram of the RF connectors, semi-directional coupler, and the compensating filters for each right and left channel; 
         FIG. 4  is a top level flow chart of the steps of the method implemented in the apparatus of  FIG. 1  to obtain preferred power parameters; 
         FIG. 5  is a flow chart of an algorithmic example for calculating an ambiguous frequency estimate; and, 
         FIG. 6  is a flow chart of an algorithm for refining parameters related to estimating frequency in block  76  of  FIG. 4 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to the drawings for a better understanding of the function and structure of the system, it will be shown generally that the preferred embodiment 4 shown in  FIG. 1  includes a coupler  12 , sometimes referred to herein as a “semi-directional” coupler, a pair of connectors such as an input connector  10  and output connector  11  connecting the coupler  12  to a transmission system  5 , a pair of filters  13 ,  14  to partially compensate for sensing limitations of the coupler  12  in each side or channel of the semi-directional coupler (hereinafter referred to as “left” and “right” sides of the coupler), an A-D converter  16  for digitizing filtered left voltage waveforms V FL    36  and for digitizing filtered right voltage waveforms V FR    37 , and a signal processing module  39  for processing signal waveforms, displays  22 ,  23 , and a user interface  24 . The preferred embodiment 4 is optimized for transmitter frequencies bounded between 1.8 MHz and 450 MHz and for an analog-to-digital converter capable of sampling at rates of less than or equal to 65 mega-samples per second with 14 bits of resolution. Further, the processing module  39  utilizes a Fourier Transform size of 1024 points. However, the system is not so limited to these frequencies, sampling rates, number of bits, or Fourier Transform size and may be varied as may be understood to accommodate other variants of the herein described system. 
     The apparatus  4  is configured to be positioned “in-line” with regard to the transmission medium  8  by installing it between the transmitter  6  and load  7  of, for example, a coaxial transmission line  8   b  that is attached to an antenna. In particular, the apparatus becomes part of the RF transmission line  8  of the RF power transmission system  5  and therefore passes full-power RF signals during operation of the apparatus. The apparatus optimizes the operation of the transmitter by maximizing power delivered to the load and measures the absolute magnitude of the voltage- and power-waves traveling in the forward and reverse directions on the coaxial transmission line  8   b  of the RF power transmission system  5 . The apparatus  4  measures forward- and reverse-traveling power (P f  and P r ); Standing Wave Ratio (“SWR”); real and imaginary parts of the load impedance (Z); delivered power (P d ); forward- and reverse-traveling voltage (V f  and V r ); and a complex scattering parameter S 11 . 
     In operation, a radio frequency (RF) transmitter  6  is connected to the input connector  10  via connector  9   a  and a coaxial transmission line  8   b  leading to a load  7  is connected to the output connector  11  via connector  9   b . Voltage waves travel in the forward and reverse direction on the transmission line  8  from the output connector  11  to the load  7 . The forward direction is defined as from the transmitter  6  to the load  7 . The reverse direction is defined as from the load  7  to the transmitter  6 . The apparatus measures the complex (real and imaginary) components of the forward- and reverse-traveling waves and uses these measurements to compute other parameters of interest. 
     Referring now to  FIG. 2 , the signal processing module  39  includes micro-computing device A  19  and B  21 , such as inexpensive and readily available 8 or 16 bit microprocessors, an FPGA  17 , and a clock generator  18 . As is known in the art, FPGAs can be configured to process complex equations at high speed rates and are relatively easy to program with today&#39;s FPGA design tools. FPGA  17  is configured to include processing logic structure to execute FFT algorithms and to compute various measured frequencies of V FR    37  and V FL    36 . Similarly, devices  19  and  21  either include onboard programmable memory or are configured to communicate with other programmable processor memory within module  39 . Such memory is loaded with mathematical equations, calibration data, and algorithmic processing steps as will be described. Module  39  is a typical printed circuit wire board (“PWB”) connecting such components, as is also known in the art. The inventor expects that the herein described methods and algorithms are readily compiled for execution by either devices  19  and  21 , but in practice device  21  would be dedicated to passing data and controlling displays  22 ,  23 , and user interface  24 , and USB communications port  38 , if utilized, and device  19  would be dedicated to performing the herein described calculations, except for FFT algorithms which would be executed by the programmed state machine operation of FPGA  17 . 
     As may be now seen in  FIG. 3 , the semi-directional coupler  12  is shown to have a structure similar to a parallel-strip coupler such as a microstrip. The apparatus will perform its claimed operations with a parallel-strip coupler, but is not limited to this device. As noted above, the semi directional coupler can be a directional coupler but does not have to be of very high quality or directivity. Directional couplers are passive devices which couple part of the transmission power by a known amount as the signal passes through the coupler and out through another port, often by using two transmission lines set close enough together so energy passing through one transmission line is coupled to the other transmission line. Hence, the coupler is not required to be a high quality (i.e. having “high directivity”) coupler, which significantly reduces the cost of the apparatus. The signal that is passed to the load enters the coupler  12  through the input connector  10  and exits through the output connector  11 . The coupled output from the coupler  12  is used to obtain information (such as frequency and power level) of the transmitted signal without interrupting the main power flow in the system (except for a slight power reduction). 
     As shown, the coupled line  42  of the coupler  12  provides a left output voltage VL (or “V L ”)  33  and a right output voltage VR (or “V R ”)  34 . These two voltages are related to the forward and reverse traveling waves on the coaxial transmission line that is connected to output connector  11 . The coupling properties of the coupler  12  typically vary with frequency. For the case of a microstrip type coupler that is physically small compared to a measured wavelength, if the frequency is doubled while the magnitude of the forward and reverse traveling waves on the coaxial transmission line remain constant, the voltages V L    33  and V R    34  will approximately double. The left filter  13  network includes resistors  26 ,  27  and a capacitor  28  to effectively form an RC input circuit. The purpose of this filter is to attempt to compensate for the frequency dependent nature of the semi-directional coupler  12  and to provide an energy storage element  28  to enhance performance of the two channel analog-to-digital converter  16  when digitizing V FL    36 . Similarly to the left filter  13 , the right filter  14  network consists of resistors  29 ,  31  and a capacitor  32  and provides the same function as filter  13 , but for signal V R    34 . 
     Referring now to  FIG. 4 , while also referring back to  FIGS. 1-3 , it may be seen generally that signals V L    33  and V R    34  are received  72  by the apparatus via connectors  10  and  11  as previously described. After being filtered  73 , V FL    36  and V FR    37  (“F” referring to post filtered signals), signals V FL  and V FR  are digitized  74  as time-series samples at N different sample rates. The number of sample rates required is a function of the specified operating frequency range of the apparatus and the maximum sample-rate capability of the A/D converter  16 . For the preferred embodiment, three (N=3) sample rates of 65-, 64-, and 63 mega-samples/second are sufficient to compute a non-ambiguous frequency estimate for a signal whose frequency is bounded between 0-500 mega-Hertz. The V FL  V FR  samples are then converted into the frequency domain using a set of FFT calculations  76  to obtain a sufficiently large set of ambiguous frequency estimates to later compute  79  a non-ambiguous frequency estimate of the signal represented by the voltages V FL    36  and V FR    37 . Variable coefficients are identified from a calibration table  82 , stored in memory for use by microprocessor  19  and used in the final stages of the process. The values in the calibration table are established by making measurements to the apparatus or its components and is done as part of the manufacturing process (see paragraph N, infra). Complex amplitudes of the V FL  and V FR  signals are then calculated  83 , and using these complex Fourier Transform components describing V FL  and V FR , along with a frequency-dependent mathematical transform, compensations  84  for the poor performance of the semi-directional coupler  12  are made. The apparatus then computes  87  the forward-traveling voltage amplitude V F , reverse-traveling voltage amplitude V R , complex scattering parameter S 11 , forward-traveling power P F , reverse-traveling power P R , delivered power P d , and complex load impedance Z, and displays the result  86 . The process is continually refreshed  88  to maintain accurate readings and ensure result consistency. 
     Referring now to  FIG. 5 , block  76  of  FIG. 4  can be further shown in the preferred embodiment as refined into a trio of sampling sets  111 ,  112 , and  113 . Assuming an optimized transmitter bounded between 1.8 MHz and 450 MHz with an A-D converter capable of sampling rates of less than or equal to 65 mega-samples per second with 14 bits of resolution, A-D converter  16  is configured  91 - 92  to a digitizing rate of 65 samples/sec and samples of V FL  and V FR  are taken  94 . Multiple complex FFT&#39;s are then executed by FPGA  17  to calculate  96  an ambiguous frequency estimate (F 65 ) at that sampling rate. A calculation of the statistical means and variances of amplitude variables associated with F 65  is then made  101  and stored  102  for future use. That process  111  is then repeated using a sampling rate of 64 samples/sec  112  and 63 samples/sec  113 . As shown, the processes in blocks  111 ,  112 , and  113  may be performed in series or in parallel depending upon the quantity and capabilities of an A-D converter, and the speed and availability of micro-processors  19 ,  21  and FPGA  17 . 
     In greater particularity, the following processing steps A-N, as executed and controlled by device  19 , disclose the iterative processing sequences of blocks  71 - 87  of  FIG. 4 , and as associated with the preferred embodiment the steps shown in block  76  of  FIG. 5  that yield the above described power parameters of step  87 .
         A. The micro-computing device A  19  sets the clock generator  18  such that the two channel analog-to-digital converter (A/D)  16  samples at a rate of 65 mega-samples/second.   B. The A/D  16  simultaneously samples voltages V FL    36  and V FR    37  and converts 1024 analog samples to digital values for both V FL  and V FR . These two sets of 1024 values are routed to the field-programmable gate array (FPGA)  17  and are referred to as V 65   FL (n) and V 65   FR (n) respectively, where n refers to the nth sample and ranges from 0 to 1023.   C. The FPGA  17  performs a 1024-point complex Fourier transform. The Fourier transform is defined by the following equation:       

     
       
         
           
             
               
                 
                   
                     X 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       65 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         N 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         w 
                         n 
                       
                       ⁢ 
                       
                         x 
                         n 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             nk 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             j 
                             / 
                             N 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁡ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
         
         
           
             
               
                 Where, in the above equation the variables and constants have the following definitions: 
                 j=√{square root over (−1)}, 
                 N=size of the Fourier transform=1024, 
                 x n =V 65   FL (n)+V 65   FR (n), 
                 w n =1−1.93*cos(2πn/N)+1.29*cos(4πn/N)−0.388*cos(6πn/N)+0.0322*cos(8πn/N), 
                 V 65   FL (n)=n th  time-series point from the analog-to-digital converter  16  representing voltage V FL    36 , 
                 V 65   FR (n)=n th  time-series point from the analog-to-digital converter  16  representing voltage V FR    37 , and 
                 X 65   k =k th  complex component of the Fourier Transform (0≦k≦N). 
               
             
             D. The FPGA  17  examines the 1024 complex Fourier components X 65   0 , X 65   1  . . . X 65   1023 , selects the Fourier component of largest magnitude, and reports the associated subscript. The subscript is denoted by bn 65  and ranges from 0 to 1023. The subscript, bn 65 , is reported to the micro-computing device A  19  of  FIG. 2 . During these calculations, FPGA  17  reports p 65  to the micro-computing device A  19  of  FIG. 2 , where p 65 =(1024−bn 65 ) module 1024. The FPGA also reports the complex Fourier components X 65   bn65  and X 65   p65  to the micro-computing device A  19  of  FIG. 2 . 
             E. The micro-computing device A  19  computes complex values XL 65 , XR 65 , and scalar values DBL 65 , DBR 65  from the following equations and stores these values in internal memory:
 
 XL 65 =X 65 bn65 +conj( X 65 p65 )  Equation (2 A )
 
 XR 65 =j *(conj( X 65 bn65 )− X 65 p65 )  Equation (2 B )
 
             Where j=√{square root over (−1)}, and 
             the operator conj( ) denotes complex conjugate.
 
 DBL 65=10*log 10 ( XL 65*conj( XL 65))  Equation (3 A )
 
 DBR 65=10*log 10 ( XR 65*conj( XR 65))  Equation (3 B )
 
             F. The process of paragraphs B, C, D, and E are repeated five times so that the micro-computing device A  19  has a total of six independent values of XL 65 , XR 65 , DBL 65 , and DBR 65  stored in memory. These parameters are denoted by XL 65   i , XR 65   i , DBL 65   i , and DBR 65   i , where the subscript, i, ranges from 1 to 6. The micro-computing device A  19  stores the last value of bn 65  and p 65 . 
             G. The micro-computing device A  19  sets the clock generator  18  such that the two channel analog-to-digital converter  16  samples at a rate of 64 mega-samples/second. The process of paragraphs B, C, D, and E are conducted six times with notation changes (e.g. bn 65 , XR 65   p65  becomes bn 64  and XR 64   p64  respectively) so that the micro-computing device A  19  has a total of six independent values of XL 64 , XR 64 , DBL 64 , and DBR 64  stored in memory. These parameters are denoted by XL 64   i , XR 64   i , DBL 64   i , and DBR 64   i , where the subscript, i, ranges from 1 to 6. The micro-computing device A  19  also stores the last value of bn 64  and p 64  reported by the FPGA  17 . 
             H. The micro-computing device A  19  sets the clock generator  18  such that the two channel analog-to-digital converter  16  samples at a rate of 63 mega-samples/second. The process of paragraphs B, C, D, and E are conducted six times with notation changes (e.g. bn 65 , X 65   p65  becomes bn 63  and X 63   p63  respectively) so that the micro-computing device A  19  has a total of six independent values of XL 63 , XR 63 , DBL 63 , and DBR 63  stored in memory. These parameters are denoted by XL 63   i , XR 63   i , DBL 63   i , and DBR 63   i , where the subscript, i, ranges from 1 to 6. The micro-computing device A  19  also stores the last value of bn 63  and p 63  reported by the FPGA  17 . 
             I. The micro-computing device A  19  computes six values μL 65 , μL 64 , μL 63 , μR 65 , μR 64 , and μR 63 , using the following equations: 
           
         
       
    
     
       
         
           
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     L 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     65 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBL 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           65 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       A 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     L 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     64 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBL 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           64 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       B 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     L 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     63 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBL 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           63 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       C 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     65 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBR 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           65 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       D 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     64 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBR 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           64 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       E 
                     
                     ) 
                   
                 
               
             
             
               
                 
                   
                     μ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     63 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         DBR 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           63 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       4 
                       ⁢ 
                       F 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     The micro-computing device A  19  compares the six results computed in Equations (4A) through (4F) and determines the largest result. If the largest result is either μL 65 , μL 64 , or μL 63 , the micro-computing device A  19  computes the statistical variances V 65 , V 64 , and V 63  from the following set of equations: 
     
       
         
           
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     65 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBL 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 65 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               65 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     64 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBL 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 64 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               64 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     63 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBL 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 63 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               63 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
           
         
       
     
     If the largest result is either μR 65 , μR 64 , or μR 63 , the micro-computing device A  19  computes V 65 , V 64 , and V 63  from the following set of equations: 
     
       
         
           
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     65 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBR 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 65 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               R 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               65 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     64 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBR 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 64 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               R 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               64 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     63 
                   
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         6 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               DBR 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 63 
                                 i 
                               
                             
                             - 
                             
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               R 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               63 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
           
         
       
         
         
           
             J. The micro-computing device A  19  computes three frequencies (F 65 , F 64 , and F 63 ) from the following equations:
           Compute F 65 :   If bn 65  is less than 513, then F 65 =bn 65 *65 MHz/1024.   If bn 65  is greater than 512, then F 65 =(1024−bn 65 )*65 MHz/1024.   Compute F 64 :   If bn 64  is less than 513, then F 64 =bn 64 *64 MHz/1024.   If bn 64  is greater than 512, then F 64 =(1024−bn 64 )*64 MHz/1024.   Compute F 63 :   If bn 63  is less than 513, then F 63 =bn 63 *63 MHz/1024.   If bn 63  is greater than 512, then F 63 =(1024−bn 63 )*63 MHz/1024.   
         
             K. The micro-computing device A  19  uses a decision algorithm as shown in  FIG. 6  to further refine the aliased frequency estimates F 65 , F 64 , and F 63 . 
             L. The micro-computing device A  19  computes intermediate results and the frequency estimate (FE) using the algorithm defined below:
           Compute Roll 65 :   If F 65  is less than or equal to (32.5 MHz−F 65 ), then Roll 65 =F 65 .   If F 65  is greater than (32.5 MHz−F 65 ), then Roll 65 =32.5 MHz−F 65 .   Compute Roll 63 :   If F 63  is less than or equal to (31.5 MHz−F 63 ), then Roll 63 =F 63 .   If F 63  is greater than (31.5 MHz−F 63 ), then Roll 63 =31.5 MHz−F 63 .   Compute DF:   If Roll 65  is greater than or equal to Roll 63 , then DF=F 65 −F 64 .   If Roll 65  is less than Roll 63 , then DF=F 64 −F 63 .   
         
           
         
       
    
     Using the values shown in Table 1.0 below, the micro-computing device A  19  selects the row with the Delta value closest to DF and selects C 1  and C 2  from this row: 
     
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 1.0 
               
               
                   
               
               
                 Delta (MHz)  
                 C 1   
                 C 2   
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 0 
                 1 
               
               
                 1 
                 1 
                 −1 
               
               
                 −1 
                 1 
                 1 
               
               
                 2 
                 2 
                 −1 
               
               
                 −2 
                 2 
                 1 
               
               
                 3 
                 3 
                 −1 
               
               
                 −3 
                 3 
                 1 
               
               
                 4 
                 4 
                 −1 
               
               
                 −4 
                 4 
                 1 
               
               
                 5 
                 5 
                 −1 
               
               
                 −5 
                 5 
                 1 
               
               
                 6 
                 6 
                 −1 
               
               
                 -6 
                 6 
                 1 
               
               
                 7 
                 7 
                 −1 
               
               
                 −7 
                 7 
                 1 
               
               
                 8 
                 8 
                 −1 
               
               
                   
               
             
          
         
       
         
         
           
             Compute FE (Frequency Estimate) 
             If Roll 65  is greater than or equal to Roll 63 , then FE=C 1 *65 MHz+C 2 *F 65   
             If Roll 65  less than Roll 63 , then FE=C 1 *64 MHz+C 2 *F 64   
             Note: The error in the frequency estimate will typically be less than the resolution of the 65-MHz Fourier Transform (65 MHz/1024˜0.0635 MHz). 
           
         
       
    
     Two examples are provided below to help clarify the algorithm defined in paragraph L. 
     Example #1 
     
         
         
           
             Assume the transmitter frequency is 1.91 MHz. This results in F 63 =1.907 MHz, F 64 =1.938 MHz, and F 65 =1.904 MHz. These three frequencies are processed by the algorithm of paragraph L as shown below:
           Compute Roll 65 :   F 65  is less than (32.5 MHz−F 65 ), so Roll 65 =F 65 =1.904 MHz   Compute Roll 63 :   F 63  is less than (31.5 MHz−F 63 ), so Roll 63 =F 63 =1.907 MHz   Compute DF:
               Roll 65  is less than Roll 63 , so DF=F 64 −F 63 =0.0303 MHz   
               Selecting the row in Table 1 with the Delta value closest to DF results in selecting the top row. Selecting C 1  and C 2  from the top row results in C 1 =0 and C 2 =1.   Compute FE (Frequency Estimate):   Roll 65  less than Roll 63 , so FE=C 1 *64 MHz+C 2 *F 64 =0*64 MHz+1*1.938 MHz=1.938 MHz. The frequency estimate is (FE=1.938 MHz), whereas the true frequency is 1.91 MHz. The error in the estimate (0.0275 MHz) is within the expected tolerance of the algorithm (˜0.0635 MHz).   
         
           
         
       
    
     Example #2 
     
         
         
           
             Assume the transmitter frequency is 500 MHz. This results in F 63 =3.999 MHz, F 64 =12 MHz, and F 65 =19.995 MHz. These three frequencies are processed by the algorithm of paragraph L as shown below:
           Compute Roll 65 :   F 65  is greater than (32.5 MHz−F 65 ), so Roll 65 =(32.5 MHz−F 65 )=12.505 MHz   Compute Roll 63 :   F 63  is less than (31.5 MHz−F 63 ), so Roll 63 =F 63 =3.999 MHz   Compute DF:
               Roll 65  is greater than Roll 63 , so DF=F 65 −F 64 =7.995 MHz   
               Selecting the row in Table 1 with the Delta value closest to DF results in selecting the bottom row. Selecting C 1  and C 2  from the bottom row results in C 1 =8 and C 2 =−1.   Compute FE (Frequency Estimate):   Roll 65  is greater than Roll 63 , so FE=C 1 *65 MHz+C 2 *F 65 =8*65 MHz−1*19.995=500.005 MHz. The frequency estimate is (FE=500.005 MHz) whereas the true frequency is 500 MHz. The error in the estimate (0.005 MHz) is within the expected tolerance of the algorithm (˜0.0635 MHz).   
         
             M. The micro-computing device A  19  picks the minimum variance Fourier samples for further processing. This is done by comparing the values V 65 , V 64 , and V 63  from paragraph I and picking the one of least magnitude. If V 63  is the least, then the micro-computing device A  19  computes the complex values VP 2 , VP 3  and the phase coefficient, PC, from the following:
 
 PC =(−1) INT(2*FE/63) ,
 
 VP 2=Real( XL 63 1 )+ PC *Imaginary( XL 63 1 ), and
 
 VP 3=Real( XR 63 1 )+ PC *Imaginary( XR 63 1 ),
 
             where XL 63   1  and XR 63   1  are results generated in paragraph H, and FE is the frequency estimate computed in paragraph L. The operator INT(x) denotes the integer portion of x. The expressions Real(x) and Imaginary(x) denote the real and imaginary parts respectively of the complex variable x. If V 64  is the least, then the micro-computing device A  19  computes the complex values VP 2 , VP 3  and the phase coefficient, PC, from the following
 
 PC =(−1) INT(2*FE/64) ,
 
 VP 2=Real( XL 64 1 )+ PC *Imaginary( XL 64 1 ), and
 
 VP 3=Real( XR 64 1 )+ PC *Imaginary( XR 64 1 ),
 
             where XL 64   1  and XR 64   1  are results generated in paragraph G, and FE is the frequency estimate computed in paragraph L. The operator INT(x) denotes the integer portion of x. The expressions Real(x) and Imaginary(x) denote the real and imaginary parts respectively of the complex variable x. If V 65  is the least, then the micro-computing device A  19  computes the complex values VP 2 , VP 3  and the phase coefficient, PC, from the following:
 
 PC =(−1) INT(2*FE/65) ,
 
 VP 2=Real( XL 65 1 )+ PC *Imaginary( XL 65 1 ), and
 
 VP 3=Real( XR 65 1 )+ PC *Imaginary( XR 65 1 ),
 
             where XL 65   1  and XR 65   1  are results generated in paragraph F, and FE is the frequency estimate computed in paragraph L. The operator INT(x) denotes the integer portion of x. The expressions Real(x) and Imaginary(x) denote the real and imaginary parts respectively of the complex variable x. 
             N. The micro-computing device A  19  computes parameters s and κ from the following where the parameters α, β, and γ 0  will be defined later. 
           
         
       
    
     
       
         
           
             
               
                 
                   s 
                   = 
                   
                     
                       γ 
                       0 
                     
                     ⁢ 
                     
                       
                         α 
                         + 
                         
                           VP 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             3 
                             / 
                             VP 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         1 
                         + 
                         
                           β 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           VP 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             3 
                             / 
                             VP 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   κ 
                   = 
                   
                      
                     
                       
                         1 
                         + 
                         s 
                       
                       
                         1 
                         - 
                         s 
                       
                     
                      
                   
                 
               
             
           
         
       
     
     The micro-computing device A  19  computes the scattering parameter S 11 , the magnitude of the forward-direction-traveling and reverse-direction-traveling voltage waveforms using the following equations:
 
If κ≦1.1 then
 
               S   11     =       γ   0     ⁢         α   +     VP   ⁢           ⁢     3   /   VP     ⁢           ⁢   2         1   +     β   ⁢           ⁢   VP   ⁢           ⁢     3   /   VP     ⁢           ⁢   2         .             If κ&gt;1.1 then
 
               S   11     =       γ   i     ⁢         α   +     VP   ⁢           ⁢     3   /   VP     ⁢           ⁢   2         1   +     β   ⁢           ⁢   VP   ⁢           ⁢     3   /   VP     ⁢           ⁢   2         .             | V   f   |=|q   11   VP 2 +q   12   VP 3| | V   r   |=|V   f   ∥S   11 |         where S 11  is defined as the complex ratio of the reverse-direction-traveling voltage to the forward-direction-traveling voltage waveform on the coaxial transmission line, VP 3  and VP 2  are results from paragraph M, and the operator |x| denotes magnitude of the complex variable x. The parameters α, β, γ 0 , γ i , q 11 , and q 12  are determined from measurements made as part of the manufacturing process. These parameters are a function of frequency and consequently must be measured over the operating frequency range of the apparatus and stored in memory of the micro-computing device A  19 , or in other connected memory device, as a calibration table (see block  82  of  FIG. 4 ). The required frequency-measurement-interval depends on characteristics of the semi-directional coupler  12 . Empirical results for a semi-directional coupler similar to a microstrip have shown that sufficient performance accuracy (approximately ±3% error in power estimates and 30 dB directivity) can be obtained by linearly interpolating between results obtained with values of α, β, γ 0 , γ i , q 11 , and q 12  measuring at 250-kHz intervals over the frequency range from 1.7 MHz to 500 MHz. The micro-computing device A  19  then computes the SWR (Standing Wave Ratio) on the transmission-line connected to the apparatus&#39;s output connector  11  using the following equation:       
     
       
         
           
             SWR 
             = 
             
               
                 1 
                 + 
                 
                    
                   
                     S 
                     11 
                   
                    
                 
               
               
                 1 
                 - 
                 
                    
                   
                     S 
                     11 
                   
                    
                 
               
             
           
         
       
         
         
           
             where |S 11 | denotes magnitude of complex quantity S 11 .
 
The micro-computing device A  19  computes the magnitude of the forward-direction-traveling power and the reverse-direction-traveling power on the coaxial transmission line connected to the apparatus&#39;s output connector  11  using the following equations:
 
           
         
       
    
     
       
         
           
             
               
                 
                   
                     
                       P 
                       f 
                     
                     = 
                     
                       
                         
                            
                           
                             V 
                             f 
                           
                            
                         
                         2 
                       
                       
                         Z 
                         0 
                       
                     
                   
                   , 
                   
                       
                   
                   ⁢ 
                   and 
                 
               
             
             
               
                 
                   
                     
                       P 
                       r 
                     
                     = 
                     
                       
                         
                            
                           
                             V 
                             r 
                           
                            
                         
                         2 
                       
                       
                         Z 
                         0 
                       
                     
                   
                   , 
                 
               
             
           
         
       
         
         
           
             where P f  and P r  are the forward- and reverse-traveling power on the coaxial transmission line connected to the output connector  11  of the apparatus. The parameter, Z 0 , is the characteristic impedance of the transmission line connected to the output connector  11  of the apparatus. The micro-computing device A  19  computes the delivered power P d  using the following equation:
 
 P   d   =P   f   −P   r ,
 
             where P f  and P r  are defined as above. The micro-computing device A  19  computes the complex impedance of the load attached to the output connector  11  of the apparatus using the following equation: 
           
         
       
    
     
       
         
           
             Z 
             = 
             
               
                 Z 
                 0 
               
               ⁢ 
               
                 
                   1 
                   + 
                   
                     S 
                     11 
                   
                 
                 
                   1 
                   - 
                   
                     S 
                     11 
                   
                 
               
             
           
         
       
         
         
           
             The micro-computing device A  19  sends the computed magnitudes V f , V r , P f , P r , P d  and the computed complex quantities S 11 , VP 2 , VP 3  and Z to the micro-computing device B  21  and to the general-purpose PC-type USB (Universal Serial Bus) port  38 . Micro-computing device B  21  coordinates with the User Interface  24  and presents the user-requested data on the Analog Display  22  and the Digital Display  23 . 
           
         
       
    
     The process is then restarted with paragraph A. The entire process (paragraphs A-N) requires less than 5 milliseconds to complete. Averaging can be used to improve accuracy of the measured and computed parameters V f , V r , P f , P r , P d , Z and S 11    
     Example Method of Determining Parameters α, β, γ i , γ 0 , q 11 , and q 12    
     There are many methods of determining α, β, γ i , γ 0 , q 11 , and q 12 . The following method was used in developing the preferred embodiment to prove its utility and absolute accuracy. The parameters are frequency dependent and therefore must be measured at discrete intervals over the frequency range of the apparatus. The number of intervals required depends on characteristics of the semi-directional Coupler  12 . A discrete frequency spacing of 0.25 MHz from 1.7 MHz to 500 MHz was found to be more than adequate for a semi directional coupler resembling a microstrip coupler 0.1 meters long.
         A. Connect a reference device of impedance Z 0  to the apparatus&#39; input connector  10 , where Z 0  is the desired reference impedance. For example, use a 50-Ohm resistor for the reference device if the apparatus is intended to be used with a 50-Ohm characteristic-impedance coaxial transmission line connected to its output connector  11 . Apply a sinusoidal voltage of desired frequency to the apparatus&#39;s output connector  11 . Operate the apparatus and use the results of paragraph N (reported via the USB port  38 ) to compute the complex parameter β as shown below.       

     
       
         
           
             β 
             = 
             
               - 
               
                 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
         
         
           
             B. Connect a reference device of impedance Z 0  to the apparatus&#39;s output connector  11 , where Z 0  is the desired reference impedance. Apply a sinusoidal voltage of desired frequency and known RMS (Root Mean Square) amplitude, V cal , to the apparatus&#39;s input connector  10 . Operate the apparatus and use the results of paragraph N (reported via the USB port  38 ), and V cal  to compute the complex parameters α and q 11 , and scalar parameter q 12  as shown below. 
           
         
       
    
     
       
         
           
             
               
                 
                   α 
                   = 
                   
                     - 
                     
                       
                         VP 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                       
                         VP 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     q 
                     12 
                   
                   = 
                   
                      
                     
                       
                         V 
                         cal 
                       
                       
                         
                           
                             VP 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           β 
                         
                         + 
                         
                           VP 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                     
                      
                   
                 
               
             
             
               
                 
                   
                     q 
                     11 
                   
                   = 
                   
                     
                       q 
                       12 
                     
                     β 
                   
                 
               
             
           
         
       
         
         
           
             C. Connect a non-radiating reference device of infinite impedance to the apparatus&#39;s output connector  11 . Apply a sinusoidal voltage of desired frequency to the apparatus&#39;s input connector  10 . Operate the apparatus and use the results of paragraph N (reported via the USB port  38 ) to compute the complex parameter γ i  as shown below. 
           
         
       
    
     
       
         
           
             
               γ 
               i 
             
             = 
             
               
                 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 + 
                 
                   β 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
               
                 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 + 
                 
                   α 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   VP 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
         
         
           
             D. Connect a non-radiating reference device of zero impedance to the apparatus&#39;s output connector  11 . Apply a sinusoidal current of desired frequency to the apparatus&#39;s input connector  10 . Operate the apparatus and use the results of paragraph N (reported via the USB port  38 ) to compute the complex parameter γ 0  as shown below. 
           
         
       
    
     
       
         
           
             
               γ 
               0 
             
             = 
             
               - 
               
                 ( 
                 
                   
                     
                       VP 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     + 
                     
                       β 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       VP 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   
                     
                       VP 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                     + 
                     
                       α 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       VP 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
         
         
           
             Note: Averaging can be used to enhance accuracy of the computed parameters α, β, γ i , γ 0 , q 11 , and q 12 . 
           
         
       
    
     As may now be understood, the afore-described power meter exhibits improved accuracy, directivity, bandwidth, power range, and construction cost relative to other modern systems. The apparatus measures, processes, and displays forward- and reverse-traveling voltage and power waves on a coaxial transmission line of a RF power transmission system where an RF source sends forward RF signals to an RF load. Additionally, the meter computes and displays the following relevant power information: (a) forward- and reverse-traveling power; (b) Standing Wave Ratio (“SWR”); (c) real and imaginary parts of the load impedance; (d) delivered power; (e) forward- and reverse-traveling voltage; and (f) a complex scattering parameter S 11 . By providing these parameters in the disclosed configuration, the system avoids the limitations and difficulties of current systems and exhibits features and advantages heretofore not obtainable. For example, the system can accommodate a much larger frequency range (e.g. 1.8 MHz to 500 MHz or a ratio greater than 270:1) with a feasible ratio exceeding 300:1. Further, the apparatus accommodates a large range of power (e.g. 3000 watts to 1 watt or a ratio of 3000:1) with a feasible ratio exceeding 10,000:1. The semi-directional coupler utilized does not have to have high directivity and so is simpler, requires no machining, and is less expensive to manufacture than the required high directivity directional coupler of current devices. 
     While the apparatus has been shown in embodiments described herein, it will be obvious to those skilled in the art that the apparatus is not so limited but may be modified with various changes that are still within the spirit of the apparatus.