Abstract:
A method is provided for eliminating the source harmonic component from VNA measurements of the output of a device under test (DUT). A standard vector measurement, GHx, is first measured from the DUT using the VNA. The value GHx is composed of two elements, the DUT&#39;s harmonic response to a fundamental input from the source, and the DUT&#39;s linear response to the harmonic input from the source. The harmonics from the source which are linearly passed by the DUT, GNx, are then measured with the VNA. The output harmonic generated by the DUT, Hx, is then calculated using vector subtraction according to the equation Hx=GHx−GNx. The output harmonic Hx will then be free from source harmonic components.

Description:
CROSS-REFERENCE TO PROVISIONAL APPLICATION 
     This Patent Application claims the benefit of Provisional Application No. 60/098,864, filed Sep. 2, 1998 has been expired. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method for determining a harmonic response of a device, and more 5 particularly, to a method for determining a more accurate harmonic response of a device over a dynamic range not limited by the stimulus source harmonic level. 
     2. Background 
     Harmonic measurements are of significant importance in many microwave, millimeter wave, and radio frequency (RF) applications including wireless communications. Excessive harmonic generation by components such as amplifiers or other nonlinear components in a communications device can lead to violations of spectrum rules set by the Federal Communications Commission (FCC), failed performance specifications, interference with other channels, or other problems. Harmonic measurements have been made by using a conventional spectrum analyzer, but this approach can be quite slow and the results are of only limited accuracy. Therefore, conventional methods of harmonic measurements using spectrum analyzers may be undesirable in a high throughput manufacturing environment in which both speed and accuracy of harmonic measurements are required. 
     To satisfy the requirements of speed and accuracy in harmonic measurements in a high throughput manufacturing environment, measurement techniques have been developed by using conventional vector network analyzers. However, a problem associated with conventional non-ratioed techniques for measuring the harmonic responses of a device by using typical vector network analyzers is that the internal signal sources of typical vector network analyzers are usually not very “clean.” The internal signal source of a typical vector network analyzer may generate a source harmonic in the range of −30 dB to −40 dB relative to the source fundamental frequency signal component. Although a source harmonic in the range of −30 dB to −40 dB relative to the source fundamental frequency component may not be regarded as a high harmonic level per se, the presence of such source harmonic can seriously affect the ability to accurately measure the harmonic response of a device. The presence of stimulus source harmonics can seriously limit the dynamic range of the measurements and the accuracy of the measurement results. 
     Therefore, there is a need for a method for measuring the harmonic response of a device with enhanced accuracy by using a typical vector network analyzer which may contain a source that has harmonics in addition to the source fundamental frequency component during the measurement of the device. Furthermore, there is a need for a method for measuring the harmonic response of a device to a fundamental frequency input with enhanced dynamic range that is not limited in measurement accuracy or dynamic range by the stimulus source harmonics. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, a method is provided for determining the harmonic output of a DUT relative to the fundamental frequency output of the DUT. The method allows VNA calibration calculations to be made to eliminate source harmonics from DUT harmonic output measurements or at least to mitigate the effect of the source harmonics on the DUT harmonic output measurements. 
     Vector quantities used to determine the harmonic response of a DUT relative to an input fundamental frequency component are illustrated in FIG.  1 . An output from the DUT is composed of two elements, the DUT&#39;s harmonic response to a fundamental input from the source, and the DUT&#39;s linear response to the harmonic input from the source. The vector sum of the DUT output responses, GHx, includes all composite harmonics from the DUT normally measured directly. The letter “x” in GHx represents a whole number, so if GHx is composed of second and third harmonics it will be a composite of GH2 and GH3. Harmonics from the source which are linearly passed by the DUT, GNx, are also readily measured with a VNA. In the method in accordance with the present invention, an output harmonic generated by the DUT, Hx, is calculated using vector subtraction according to the equation Hx=GHx−GNx. The output harmonic Hx will be free from source harmonic components and provide a more accurate measurement of parameters for the DUT. 
     When VNAs are used to measure harmonics in a conventional manner, a non-ratioed mode is used. But because of reliance of a VNA on ratioing to produce phase data, non-ratioed measurements can be noisy and inaccurate, and incapable of being used in a manner where the source harmonic contribution is characterized as a vector and mathematically removed. Accordingly, the method in accordance with the present invention provides for ratioing to obtain more accurate phase measurement results. To obtain the output harmonics Hx generated by the DUT relative to the source harmonic, the desired vector equation Hx=GHX−GNx can be used as described above. To obtain an output harmonic Hx′ relative to the source fundamental, the general Hx measurements are multiplied by a relative source harmonic level, that is, a ratio of a scalar harmonic measurement SH determined from a through line to a scalar fundamental measurement SF from the through line, or SH/SF. To obtain an output harmonic Hx″ relative to an output fundamental, the general Hx measurement is multiplied by the relative source harmonic level and then divided by the magnitude of a linear fundamental gain GN 1  of the DUT as described in more detail to follow. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will be described with respect to particular embodiments thereof, and references will be made to the drawings in which: 
     FIG. 1 is a vector diagram illustrating the relationship of the measured vector quantities GHx and GNx to the computed vector quantity Hx representing the harmonic response of a device obtained by the method according to the present invention; 
     FIG. 2 is a simplified diagram illustrating a typical vector network analyzer with two terminals connected to a through line to establish normalization factors and a relative source harmonic level; and 
     FIG. 3 is a simplified diagram illustrating a device under test connected to the terminals of the typical vector network analyzer to perform the process steps in the method for determining the harmonic response of the device according to the present invention. 
    
    
     DETAILED DESCRIPTION 
     For the method in accordance with the present invention, the output harmonic Hx of the DUT is established relative to the source harmonic, the source fundamental, and the output fundamental. To do so, several general steps are performed using a VNA as outlined in the following paragraphs. 
     I. Establishing Modes For Calculations 
     With the source fundamental frequency range covering frequencies from f 0  through f 1 , labeled here as [f 0 ,f 1 ], then the following shorthand can be established for modes used in subsequent calculations: 
     
       
         MODE {N 1 }: source [f 0 ,f 1 ], receiver [f 0 ,f 1 ] 
       
     
     
       
         MODE {N 2 }: source [2f 0 ,2f 1 ], receiver [ 2 f 0 , 2 f 1 ] 
       
     
     
       
         MODE {N 3 }: source [3f 0 ,3f 1 ], receiver [ 3 f 0 , 3 f 1 ] 
       
     
     
       
         MODE {H 2 }: source [f 0 ,f 1 ], receiver [ 2 f 0 ,  2 f 1 ] 
       
     
     
       
         MODE {H 3 }: source [f 0 ,f 1 ], receiver [ 3 f 0 ,  3 f 1 ] 
       
     
     The numbers 2 and 3 multiplied by the frequency ranges f 0 -f 1  indicate that the second and third harmonics are used respectively. The measurements and calculations described below utilize the second and third harmonics, but other source harmonic levels may be used as long as the measurement ratios determined according to the present invention are not excessively noisy. 
     To assure measurement accuracy in determining source harmonics, the source power level should be constant during measurements using the above modes. Because the source harmonics are a function of power 
     In an embodiment in which the DUT to be measured is a two-port device, a test setup is established as shown in FIG.  2 . In FIG. 2, a through line  2  is connected to the terminals  4  and  6  of a VNA  8  to establish a plurality of normalization factors and a relative source harmonic level before the DUT is connected to the VNA for subsequent measurements as shown in FIG.  3 . As shown, the VNA includes a source  12  connectable through couplers  14  to terminals  4  and  6 . A receiver  16  then receives signals from the DUT as well as source  12 . 
     II. Connection of Through Line To Establish Normalizations and Relative Source Harmonic Levels 
     In an embodiment in which the DUT to be measured is a two-port device, a test setup is established as shown in FIG.  2 . In FIG. 2, a through line  2  is connected to the terminals  4  and  6  of a VNA  8  to establish a plurality of normalization factors and a relative source harmonic level before the DUT is connected to the VNA for subsequent measurements. 
     To establish the normalization factors, S 21  measurements are first acquired from the through line with the system in modes N 1 , N 2 , N 3 , H 2  and H 3 . The S 21  values are stored as NS21N1, NS21N2, NS21N3, NS21H2 and NS21H3 respectively. These values will be used to normalize later DUT measurements. Note that the S 21  measurements could be trivially replaced by S 12  measurements if that is the requested parameter. For one-port S 11  or S 22  measurements, appropriate normalization is provided with a short. 
     The received signal, also referred to as the b 2  signal, is measured in modes N 1 , H 2  and H 3 . These b 2  values are stored as b 2 (N 1 ), b 2 (H 2 ) and b 2 (H 3 ) respectively. 
     To account for receiver power deviations from a flat level, an additional mode NO is defined in which voltage measurements b 2 (NO A ), b 2 (NO B ) and b 2 (NO C ) are made to normalize the b 2 (N 1 ), b 2 (H 2 ) and b 2 (H 3 ) values. The N 0  mode is established with the source  12  and receiver  14  operating over the same frequency range, such as f 0 -f 1 , as the mode being normalized, but with the source power level set at approximately 0 dBm. Note that it is possible that b 2 (N 0 ) could be measured and stored as a global vector in the VNA at factory calibration time, since it is not likely to change over time on a scale that would cause errors in unratioed measurements. 
     Relative source harmonic levels Ox for the second and third harmonics are computed from the b 2  values b 2 (N 1 ), b 2 (H 2 ) and b 2 (H 3 ) as follows: 
     
       
           O   2 = b   2 ( H   2 ) /b   2 ( N   1 ) 
       
     
     
       
           O   3 = b   2 ( H   3 ) /b   2 ( N   1 ) 
       
     
     The relative source harmonic levels O 2  and O 3  are scalar quantities without phase information. 
     III. Connection Of DUT And Measurement In Normal Mode 
     After the normalization factors and the relative source harmonic levels are established, the through line is disconnected and the DUT  10  is connected to the terminals  4  and  6  of a VNA  8  as shown in FIG.  3 . Once the DUT  10  is connected, S 21  measurements are made in the normal modes N 1 , N 2  and N 3 . The normalization values NS21N1, NS21N2 and NS21N3 are then applied respectively to obtain transfer coefficients GN1, GN2 and GN3. The GNx vector quantities GN1, GN2 and GN3 are the linear gains that the source fundamental, the second source harmonic and the third source harmonic will experience through the DUT, respectively. 
     In an embodiment in which the DUT is a nonlinear amplifier, it is desirable that the input source harmonic be at a sufficiently low power level such that the amplifier operates either within the linear region or close to the linear region at the harmonic frequency to obtain the transfer coefficients GN2 and GN3. For example, the power level for the source harmonic during the step of obtaining the transfer coefficient GN2 for the second harmonic may be set at approximately −4 dBc relative to the power level of a carrier signal at the fundamental frequency. 
     IV. Measurement of DUT In Harmonic Mode 
     While the DUT is connected to the VNA, S 21  measurements are also made in the harmonic modes H 2  and H 3 . The normalization values NS21H2 and NS21H3 are then applied respectively to obtain transfer coefficients GH2 and GH3. The GHx values GH2 and GH3 are the DUT output harmonics relative to the source fundamental. 
     V. Computation Of Corrections 
     With the measurements described above, the DUT output harmonic levels relative to the source harmonic component, the source fundamental frequency component, and the DUT output fundamental frequency component are calculated as follows: 
     A: Output Harmonic Hx Relative To Source Harmonic Component 
     
       
           H   2   =GH 2 −GN 2 
       
     
     
       
           H   3   =GH 3 −GN 3 
       
     
     B: Output Harmonic Hx′ Relative To Source Fundamental Frequency Component 
     
       
           |H   2   ′|=|GH 2 −GN 2| O   2   
       
     
     
       
           |H   3   ′|=|GH 3 −GN 3 |O   3   
       
     
     The computed values |H 2 ′| and |H 3 ′| are scalar quantities since phase information was not available for the Ox values O 2  and O 3 . Alternatively, with only the magnitude of Ox available, the values Hx′ could be calculated as vector quantities with the phase of Hx used for the phase of Hx′. 
     C: Output Harmonic Hx″ Relative To Output Fundamental Frequency Component 
     
       
           |H   2   ″|=|GH 2 −GN 2 |O   2 / |GN 1| 
       
     
     
       
           |H   3   ″|=|GH 3 −GN 3 |O   3 / |GN 1| 
       
     
     Again the computed values |H 2 ″| and |H 3 ″| are scalar quantities, but the values Hx″ can be calculated as vector quantities with the phase of Hx/GNx used for the phase of Hx″. 
     VI. Establishing Phase 
     Establishing the phase of harmonic components is particularly relevant for measurements of matching networks for power amplifier design. There is no direct method of establishing phase of the source fundamental relative to its harmonic. However, phase measurements can be made using a phase standard. 
     One phase standard which may be used in accordance with the present invention is a conventional shunt diode with sufficient RF power applied to it so that the diode starts clipping one side of the waveform. Based on a Fourier analysis, the second and third harmonic components from the DUT must be 180° out of phase relative to the source fundamental. The Fourier analysis is performed with a top-clipped cosine waveform with the reference phase being 0° for the source fundamental frequency component, which has a period T. The Fourier expansion is performed on a period centered at the origin and the clipping time is from −x to +x. Because this waveform represents an even function, only the cosine terms are present in the Fourier expansion. The Fourier coefficients are thus expressed as:                a   n     =                    4   T            ∫   0   x            cos        (       2      π                 x     T     )            cos        (       2      π                 n                 t     T     )               t           +                                4   T            ∫   x     T   /   2              cos        (       2      π                 t     T     )            cos        (       2      π                 nt     T     )               t                       =                      2        cos        (       2      π                 x     T     )           n                 π            sin        (       2      n                 π                 x     T     )         +                                  1   π          [           -   1       n   +   1            sin        (       2        (     n   +   1     )        π                 x     T     )         +         -   1       n   -   1            sin        (       2        (     n   -   1     )        π                 x     T     )           ]       ,                                  
     For the first harmonic or fundamental,          a   1     =           2        cos        (       2      π                 x     T     )         n          sin        (       2      π                 x     T     )         +       1   π          [         1   2          (     -     sin        (       4      π                 x     T     )         )       +   1   -       2      x     T       ]                                
     Since 0&lt;x&lt;T/4, this term will be positive, and the phase reference for the fundamental is 0°. 
     For the second harmonic          a   2     =           cos        (       2      π                 x     T     )       π          sin        (       4      π                 x     T     )         +       1   π          [           -   1     3          sin        (       6      π                 x     T     )         +         -   1     1          sin        (       2      π                 x     T     )           ]                                
     Since 0&lt;x&lt;T/4, it is easy to show that a 2 &lt;=0 and decreasing, and the phase shift is 180°. 
     For the third harmonic,          a   3     =           2        cos        (       2      π                 x     T     )           3      π            sin        (       6      π                 x     T     )         +       1   π          [           -   1     4          sin        (       8      π                 x     T     )         +         -   1     2          sin        (       4      π                 x     T     )           ]                                
     Since 0&lt;x&lt;T/4, it is easy to show that a 3 &lt;=0, and the phase shift is 180°. 
     For the fourth harmonic,          a   4     =           cos        (       2      π                 x     T     )         2      π            sin        (       8      π                 x     T     )         +       1   π          [           -   1     5          sin        (       10      π                 x     T     )         +         -   1     3          sin        (       6      π                 x     T     )           ]                                
     If 0&lt;x/T ≦0.17, then a 4 &lt;=0 and the phase shift is 180°. If x/T≧0.17 indicating more severe clipping of the cosine waveform, a 4 &gt;0 and the phase shift is 0°. Therefore, the phase shift for the fourth harmonic relative to the phase of the fundamental frequency component depends upon the severity of clipping produced by the nonlinear DUT. 
     Measurements of Hx will acquire the phase angles φx needed for calculating the phase components of Hx′ and Hx″. The phase angles measured for Hx are preferably referenced to a 0° reference plane established at the fundamental. With the standard being the shunt diode described above and the fundamental referenced to 0° at the standard, the correction angles 180°−φ2 and 180°−φ3 for the second and third harmonics can be applied to obtain the phases of the vector quantities Hx′ and Hx″. The use of an absolute phase reference plane eliminates the effect of any extra line length at the output of the DUT. The extra line length at the output of the DUT produces unreferenced output phases because of the different phase shifts experienced through the extra line length by the different harmonic signals. 
     To determine the harmonic phases in accordance with the present invention, a calibration standard, such as the shunt diode described above, is connected to the VNA With the standard connected, S 21  measurements are made in modes H 2  and H 3 . The normalization vector values NS21H2 and NS21H3 are then applied to the H 2  and H 3  measurements respectively to obtain corrected transfer coefficients termed GH2C and GH3C. S 21  measurements are further made with the standard connected in mode {N 1 } to obtain the transfer coefficient GN 1 . Next phase offsets POx are calculated as follows: 
     
       
           ∠PO   2 =∠ref 2   −∠GH 2 C+∠GN 1 
       
     
     
       
           ∠PO   3 =∠ref 3   −∠GH 3 C+∠GN 1 
       
     
     wherein ∠PO 2  and ∠PO 3  are the harmonic phase responses of the DUT at the second and third harmonics respectively, ∠ref 2  and ∠ref 3  are 180° as calculated using Fourier series analysis for the shunt diode, ∠GH2C and ∠GH3C are the phases of the corrected harmonic transfer coefficients GH2C and GH3C after normalization, and ∠GN1 is the phase of the transfer coefficient GN1 at the fundamental frequency. 
     After the harmonic phase responses ∠PO 2  and ∠PO 3  are obtained, the vector harmonic responses H 2 ′ and H 3 ′ of the DUT at the second and third harmonics to the input fundamental frequency component are obtained respectively according to the following relationships: 
     
       
           H   2 ′=( GH 2 −GN 2)(1 ∠PO   2 ) O   2   
       
     
     
       
           H   3 ′=( GH 3 −GN 3)(1 ∠PO   3 ) O   3   
       
     
     In a similar manner, the vector harmonic outputs H 2 ″ and H 3 ″ of the DUT at the second and third harmonics relative to the output fundamental frequency component are obtained respectively according to the following relationships: 
     
       
           H   2 ″=( GH 2 =GN 2)(1 ∠PO   2 ) O   2 / GN 1 
       
     
     
       
           H   3 ″=( GH 3 =GN 3)(1 ∠PO   3 ) O   3 / GN 1 
       
     
     The harmonic responses of the DUT to the input fundamental frequency component as well as the harmonic outputs of the DUT relative to the output fundamental frequency component are thus obtained as vector quantities with magnitude and phase information. 
     The present invention has been described with respect to particular embodiments thereof, and numerous modifications can be made which are within the scope of the invention as set forth in the claims.