Abstract:
Novel excitation signals are specifically designed for testing a high-frequency mixer such that all of the desired intermodulation products are measurable after being converted by a sampling frequency converter. This is achieved by using excitation frequencies which are equal to an integer multiple of the sampling frequency of the sampling frequency convertor plus or minus small frequency offsets. The offset frequencies are carefully choosen such that the frequencies of all the significant intermodulation products after being converted by the sampling frequency converter are within the bandwidth of the sampling frequency converter output.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is entitled to the benefit of Provisional Application Ser. No. 60/673,889, filed on Apr. 19, 2005. 

   FEDERALLY SPONSORED RESEARCH 
   Not Applicable 
   SEQUENCE LISTING OR PROGRAM 
   Not Applicable 
   BACKGROUND OF THE INVENTION 
   1. Field of Invention 
   The present invention relates to a method and an apparatus to characterize the behaviour of high-frequency mixers under large-signal operating conditions. 
   2. Description of the Related Art 
   In “The Return of the Sampling Frequency Converter,” 62nd ARFTG Conference Digest, USA, December 2003, Jan Verspecht explains how sampling frequency converters are used in “Large-Signal Network Analyzers” (LSNAs) in order to characterize the behaviour of high-frequency devices-under-test (DUTs). It is explained in the above reference that the measurement capabilities of any prior art LSNA are limited to the use of periodic signal excitations and periodically modulated carrier signals. The above excitation signals are often sufficient for a practical characterization of microwave amplifier components. This limitation makes it impossible, however, to measure all of the significant intermodulation products which are typically generated between a local oscillator signal and a radio-frequency (RF) signal at the signal ports of a mixer. As such the prior art LSNA can in general not be used for the characterization of mixers. 
   BRIEF SUMMARY OF THE INVENTION 
   With the present invention one will apply novel excitation signals that are specifically designed such that all of the desired intermodulation products will be measurable after being converted by the sampling frequency converter of the LSNA. This new method allows to measure all of the relevant intermodulation products that are needed to characterize fundamental and harmonic mixers. This is achieved by using excitation frequencies which are equal to an integer multiple of the local oscillator frequency of the sampling frequency converter plus or minus small frequency offsets. The offset frequencies are carefully choosen such that the frequencies of all the significant intermodulation products can easily be measured after being converted by the sampling frequency converter. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  Schematic of an LSNA 
   

   DETAILED DESCRIPTION 
   For reasons of simplicity a three-port Large-Signal Network Analyzer (LSNA) is used in the following to illustrate the method of this invention. Extensions to more signal ports or simplifications whereby signal ports are being eliminated can easily be derived. In general an LSNA is used to measure the travelling voltage waveforms as they occur at the signal ports ( 1 ),( 2 ) and ( 3 ) of a high-frequency device-under-test ( 4 ) (DUT) under a large signal excitation.  FIG. 1  shows a mixer ( 4 ) with an RF input signal terminal ( 2 ), a local oscillator input terminal ( 1 ) and with an intermediate frequency signal terminal ( 3 ). The RF signal is generated by a synthesizer ( 5 ) and the local oscillator signal is generated by a second synthesizer ( 6 ). The intermediate frequency signal port is terminated in an impedance ( 7 ). The bandwidth of the signals which are used for an LSNA characterization may be as high as 50 GHz. In order to measure these high-frequency signals, they are sensed by a test-set ( 8 ) that usually contains several couplers ( 9 ), ( 10 ), ( 11 ), ( 12 ), ( 13 ) and ( 14 ). The sensed signals, which are related to the travelling voltage waves as they appear in both directions of the signal terminals ( 1 ), ( 2 ) and ( 3 ) are send to the input ports of a sampling frequency converter ( 15 ). The sampling frequency converter ( 15 ) converts all of the frequencies to a lower frequency bandwidth, typically in the MHz range. The converted signals are then digitized by an analog-to-digital converter ( 16 ). The complex values of the spectral components are calculated by a digital signal processor ( 17 ). The signal processor ( 17 ) performs time to frequency domain transformations and performs all of the calculations that are used for calibration of the data. 
   In prior art one starts by choosing the fundamental frequency of the excitation signal, which is noted f c . Next one calculates a sampling frequency f s  that is used by the LSNA sampling downconvertor. The frequency f s  is chosen such that the sampled high-frequency signal is converted into an a piori determined lower intermediate frequency, noted f if . The relationship between f s , f c  and f if  is given by
 
 f   if =Modulo( f   c   ,f   s ).  (1)
 
   In equation (1) Modulo(x, y) refers to the remainder of x divided by y. This procedure requires that the downconverter sampling frequency f s  is variable and can be set with a high precision. 
   As explained in the “The Return of the Sampling Frequency Converter,” 62nd ARFTG Conference Digest, USA, December 2003, Jan Verspecht the measurement capability of any prior art LSNA that is based on the above explained principle is limited to the use of pure periodic excitations and periodically modulated carrier signals. 
   With the present invention one will use a different approach that allows to extend the applicability of an LSNA to mixer applications. Consider a sampling downconverter with a fixed sampling frequency f s . Suppose that one wants to measure the intermodulation products that are generated by a mixer that is excited by a set of multitone signals that contain spectral components at the frequencies f 1 , f 2 , . . . , f N . In stead of calculating a sampling frequency which will result in a set of measurable intermediate frequencies at the output of the sampling frequency converter, one will keep f s  constant and one will slightly shift the frequencies of the multitone excitation signals to a corresponding set of new frequencies g 1 , g 2 , . . . , g N  such that (1) is valid for “i” going from 1 to N, with P i  an integer number.
 
 g   i   =P   i   .f   s   +Δf   i   (1)
 
In other words, one will shift each excitation frequency such that it has a frequency offset Δf i  relative to an integer multiple of the sampling frequency f S . The value of Δf i  is typically much smaller than the value f s . In the following will be explained how a good value for Δf i  can be chosen.
 
   Consider that one wants to measure the complex value of an intermodulation product of a specific order with respect to each of the excitation frequencies g 1 . This order is indicated by the set of integer coefficients k 1 . The frequency of this intermodulation product, noted f IP [k 1 ,k 2 , . . . ], is given by
 
 f   IP   [k   1   ,k   2   , . . . ]=k   1   .g   1   +k   2   g   2    . . . +k   N   .g   N   (2)
 
   Substitution of (1) in (2) and a rearrangement of the terms results in the following.
 
 f   IP   [k   1   ,k   2 , . . . ]=( k   1   .P   1   +k   2   .P   2   + . . . +k   N   .P   N ) .f   s +( k   1   Δf   1   +k   2   .Δf   2   + . . . +k   N   .Δf   N )  (3)
 
   The values of Δf i  are chosen such that the value of the linear combination (k 1 .Δf 1 +k 2 .Δf 2 + . . . +k N . Δf N ) is within the output bandwidth of the sampling frequency converter ( 15 ). As a result the intermodulation product with frequency f IP [k,k 2 , . . . ] will appear at the output of the sampling frequency converter ( 15 ) at a specific frequency, noted f IF [k 1 ,k 2 , . . .], that is given by:
 
 f   IF   [k   1   ,k   2 , . . . ]=Mod( f   IP   [k   1   ,k   2   , . . . ],f   s )= k   1   .Δf   1   +k   2   .Δf   2   + . . . +k   N   .Δf   N   (4)
 
   It will always be possible to choose the values of Δf i  such that the above is valid for a whole range of significant intermodulation products. One will further choose the values Δf i  such that the resulting linear combinations result in a set of frequencies which can easily be characterized by the analog-to-digital converter ( 16 ). The set of frequencies Δf i  will e.g. be chosen such that there is a minimum distance between any two frequency converted intermodulation products. This avoids interference between two spectral components caused by phase noise. One can also choose ΔF i  such that all intermodulation products fall on an exact bin of the discrete Fourier transform as calculated by the digital signal processor ( 17 ). 
   Note that in practice the difference between g i  and f i  can be made sufficiently small such that one will be able to characterize the travelling voltage waveforms as they occur at the mixer signal terminals under conditions which are close enough to the desired operating conditions in order to extract the desired information of the mixer. 
   The following examples illustrates the above. 
   Consider that one wants to measure the intermodulation products up to the 4 th  order at the signal terminals of a mixer with a local oscillator frequency (f 1 ) of 10 GHz and an RF signal frequency (f 2 ) of 9.9 GHz. Further suppose that f s  equals 20 MHz and that the output bandwidth of the sampling frequency converter ( 15 ) is 4 MHz. One starts by choosing P 1 =500, Δf 1 =1 MHz, P 2 =495 and Δf 2 0.99 MHz. This results in actually applied frequencies given by g i =10.001 GHz (for the local oscillator signal) and g 2 =9.90099 GHz (for the RF signal). Note that the deviation between the ideal frequencies and the actual applied frequencies is only 0.01%. The first two columns of Table 1 represent the respective k 1  and k 2  indices, the third column gives the actual RF frequencies of the respective intermodulation product up to the 4 th  order, and the second column gives the corresponding frequencies as they appear at the output of the sampling frequency converter ( 15 ). Note that only positive frequencies are being considered. 
   As can be concluded from Table 1, all of the considered intermodulation products appear at the output of the sampling frequency converter ( 15 ) at a frequency within the sampling frequency converter ( 15 ) output bandwidth of 4 MHz and with a minimum separation between any two tones of 10 kHz. This result was achieved by carefully choosing Δf 1  and Δf 2 . The difference between the desired frequencies f 1  and f 2  and the actual frequencies g 1  and g 2  is minimized by carefully choosing the values P 1  and P 2 . 
   Note that for the example above the ratio between Δf 1  and Δf 2  was chosen to be exactly the same as the ratio between f 1  and f 2 . This is convenient but it is not necessary. The advantage is that, in this case, the ratio between any two intermodulation frequencies is exactly the same before and after frequency conversion. As a result the time domain waveforms at the output of the sampling frequency converter ( 15 ) are copies of the actual RE time domain waveforms where the only difference is in the time scales. 
   Another more advanced example is given in what follows. Assume that one wants to characterize a mixer ( 4 ) that is excited by a local oscillator signal ( 6 ) having a frequency equal to 1 GHz, and by an input signal ( 5 ) that is a periodically modulated carrier with a frequency of 1.1 GHz, with the modulation frequency equal to 1 kHz. For this example one will assume that the sampling frequency f s  equals 20 MHz, as was the case in the previous example, and that the output bandwidth of the sampling frequency converter ( 15 ) is 4 MHz. Further assume that one wants to measure all of the intermodulation products generated at the mixer terminals ( 1 ), ( 2 ) and ( 3 ) upto the first order for the local oscillator signal ( 6 ), upto the second order for the input signal ( 5 ) carrier frequency and upto the fourth order for the input signal ( 5 ) modulation frequency. 
   To measure all of the abovementioned intermodulation products by means of the sampling frequency converter ( 15 ) that runs at 20 MHz, one will slightly shift the above specified local oscillator ( 6 ) and input signal ( 5 ) frequencies as follows. The local oscillator signal ( 6 ) is approximated by making g 1  equal to 50*20 MHz+1 MHz, which equals 1.001 GHz, only 0.1% different from the original 1 GHz frequency. Next one approximates the input signal ( 5 ) by making g 2  equal to 55*20 MHz+1.1MHz, which equals 1.1011 GHz, only 0.11% different from 1.1 GHz, and one makes g 3  equal to 1 kHz, which is exactly equal to the modulation frequency. Referring to equation (1) this implies that P 1  equals 50, Δf 1  equals 1 MHz, P 2  equals 55, Δf 2  equals 1.1 MHz, P 3  equals 0 and Δf 3  equals 1 kHz. 
   As a result of the nonlinear behavior of the mixer ( 4 ), the response signals generated at the terminals ( 1 ), ( 2 ) and ( 3 ) of the mixer will contain many intermodulation products. The frequencies of these intermodulation products upto the abovementioned orders, before and after being frequency converted by the sampling frequency converter ( 15 ), are shown in Table 2. The first 3 columns represent the respective orders of the intermodulation products, upto the first order for the local oscillator signal ( 6 ) (k 1  ranging from −1 to 1), upto the second order for the input signal ( 5 ) carrier (k 2  ranging from 0 to 2), and upto the fourth order for the input signal ( 5 ) modulation (k 3  ranging from −4 to 4). 
   The second column represents the actual frequencies of the respective intermodulation products, and the fourth column represents the frequencies of the respective intermodulation products as they appear at the output of the sampling frequency converter ( 15 ). By carefully choosing the frequencies g 1 , g 2  and g 3 , all of the response signals at the output of the sampling frequency converter ( 15 ) are unique and are within the sampling frequency converter ( 15 ) output bandwidth of 4 MHz. As such the amplitude as well as the phase of all of the intermodulation products can easily be determined by digitizing the output signals generated by the sampling frequency converter ( 15 ) by means of a analog-to-digital converter ( 16 ) and by calculating the discrete Fourier transform of the digitized signals by means of a digital signal processor ( 17 ). 
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Intermodulation Product Indices and Corresponding Frequencies 
             
             
               (example 1) 
             
           
        
         
             
               k 1   
               k 2   
                 
               f IP [k 1 , k 2 ] 
               f IF [k 1 , k 2 ] 
             
             
                 
             
           
        
         
             
               −1  
               2 
               9.80098 
               GHz 
               980 
               kHz 
             
             
               −1  
               3 
               19.70197 
               GHz 
               1970 
               kHz 
             
             
               0 
               0 
               0 
               GHz 
               0 
               kHz 
             
             
               0 
               1 
               9.90099 
               GHz 
               990 
               kHz 
             
             
               0 
               2 
               19.80198 
               GHz 
               1980 
               kHz 
             
             
               0 
               3 
               29.70297 
               GHz 
               2970 
               kHz 
             
             
               0 
               4 
               39.60396 
               GHz 
               3960 
               kHz 
             
             
               1 
               −1  
               0.10001 
               GHz 
               10 
               kHz 
             
             
               1 
               0 
               10.00100 
               GHz 
               1000 
               kHz 
             
             
               1 
               1 
               19.90199 
               GHz 
               1990 
               kHz 
             
             
               1 
               2 
               29.80298 
               GHz 
               2980 
               kHz 
             
             
               1 
               3 
               39.70397 
               GHz 
               3970 
               kHz 
             
             
               2 
               −2  
               0.20020 
               GHz 
               20 
               kHz 
             
             
               2 
               −1  
               10.10101 
               GHz 
               1010 
               kHz 
             
             
               2 
               0 
               20.00200 
               GHz 
               2000 
               kHz 
             
             
               2 
               1 
               29.90299 
               GHz 
               2990 
               kHz 
             
             
               2 
               2 
               39.80398 
               GHz 
               3980 
               kHz 
             
             
               3 
               −1  
               20.10201 
               GHz 
               2010 
               kHz 
             
             
               3 
               0 
               30.00300 
               GHz 
               3000 
               kHz 
             
             
               3 
               1 
               39.90399 
               GHz 
               3990 
               kHz 
             
             
               4 
               0 
               40.00400 
               GHz 
               4000 
               kHz 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Intermodulation Product Indices and Corresponding Frequencies 
             
             
               (example 2) 
             
           
        
         
             
               k 1   
               k 2   
               k 3   
               f IP [k 1 , k 2 , k 3 ] (Hz) 
               f IP [k 1 , k 2 , k 3 ] (Hz) 
             
             
                 
             
           
        
         
             
               0 
               0 
               1 
               1000 
               1000 
             
             
               0 
               0 
               2 
               2000 
               2000 
             
             
               0 
               0 
               3 
               3000 
               3000 
             
             
               0 
               0 
               4 
               4000 
               4000 
             
             
               −1 
               1 
               −4 
               100096000 
               96000 
             
             
               −1 
               1 
               −3 
               100097000 
               97000 
             
             
               −1 
               1 
               −2 
               100098000 
               98000 
             
             
               −1 
               1 
               −1 
               100099000 
               99000 
             
             
               −1 
               1 
               0 
               100100000 
               100000 
             
             
               −1 
               1 
               1 
               100101000 
               101000 
             
             
               −1 
               1 
               2 
               100102000 
               102000 
             
             
               −1 
               1 
               3 
               100103000 
               103000 
             
             
               −1 
               1 
               4 
               100104000 
               104000 
             
             
               1 
               0 
               −4 
               1000996000 
               996000 
             
             
               1 
               0 
               −3 
               1000997000 
               997000 
             
             
               1 
               0 
               −2 
               1000998000 
               998000 
             
             
               1 
               0 
               −1 
               1000999000 
               999000 
             
             
               1 
               0 
               0 
               1001000000 
               1000000 
             
             
               1 
               0 
               1 
               1001001000 
               1001000 
             
             
               1 
               0 
               2 
               1001002000 
               1002000 
             
             
               1 
               0 
               3 
               1001003000 
               1003000 
             
             
               1 
               0 
               4 
               1001004000 
               1004000 
             
             
               0 
               1 
               −4 
               1101096000 
               1096000 
             
             
               0 
               1 
               −3 
               1101097000 
               1097000 
             
             
               0 
               1 
               −2 
               1101098000 
               1098000 
             
             
               0 
               1 
               −1 
               1101099000 
               1099000 
             
             
               0 
               1 
               0 
               1101100000 
               1100000 
             
             
               0 
               1 
               1 
               1101101000 
               1101000 
             
             
               0 
               1 
               2 
               1101102000 
               1102000 
             
             
               0 
               1 
               3 
               1101103000 
               1103000 
             
             
               0 
               1 
               4 
               1101104000 
               1104000 
             
             
               −1 
               2 
               −4 
               1201196000 
               1196000 
             
             
               −1 
               2 
               −3 
               1201197000 
               1197000 
             
             
               −1 
               2 
               −2 
               1201198000 
               1198000 
             
             
               −1 
               2 
               −1 
               1201199000 
               1199000 
             
             
               −1 
               2 
               0 
               1201200000 
               1200000 
             
             
               −1 
               2 
               1 
               1201201000 
               1201000 
             
             
               −1 
               2 
               2 
               1201202000 
               1202000 
             
             
               −1 
               2 
               3 
               1201203000 
               1203000 
             
             
               −1 
               2 
               4 
               1201204000 
               1204000 
             
             
               1 
               1 
               −4 
               2102096000 
               2096000 
             
             
               1 
               1 
               −3 
               2102097000 
               2097000 
             
             
               1 
               1 
               −2 
               2102098000 
               2098000 
             
             
               1 
               1 
               −1 
               2102099000 
               2099000 
             
             
               1 
               1 
               0 
               2102100000 
               2100000 
             
             
               1 
               1 
               1 
               2102101000 
               2101000 
             
             
               1 
               1 
               2 
               2102102000 
               2102000 
             
             
               1 
               1 
               3 
               2102103000 
               2103000 
             
             
               1 
               1 
               4 
               2102104000 
               2104000 
             
             
               0 
               2 
               −4 
               2202196000 
               2196000 
             
             
               0 
               2 
               −3 
               2202197000 
               2197000 
             
             
               0 
               2 
               −2 
               2202198000 
               2198000 
             
             
               0 
               2 
               −1 
               2202199000 
               2199000 
             
             
               0 
               2 
               0 
               2202200000 
               2200000 
             
             
               0 
               2 
               1 
               2202201000 
               2201000 
             
             
               0 
               2 
               2 
               2202202000 
               2202000 
             
             
               0 
               2 
               3 
               2202203000 
               2203000 
             
             
               0 
               2 
               4 
               2202204000 
               2204000 
             
             
               1 
               2 
               −4 
               3203196000 
               3196000 
             
             
               1 
               2 
               −3 
               3203197000 
               3197000 
             
             
               1 
               2 
               −2 
               3203198000 
               3198000 
             
             
               1 
               2 
               −1 
               3203199000 
               3199000 
             
             
               1 
               2 
               0 
               3203200000 
               3200000 
             
             
               1 
               2 
               1 
               3203201000 
               3201000 
             
             
               1 
               2 
               2 
               3203202000 
               3202000 
             
             
               1 
               2 
               3 
               3203203000 
               3203000 
             
             
               1 
               2 
               4 
               3203204000 
               3204000