Abstract:
Novel excitation signals are specifically designed for testing a nonlinear device-under-test such that all of the desired intermodulation products are measurable after being converted by a sampling frequency convertor. 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 convertor are within the bandwidth of the sampling frequency convertor output.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is entitled to the benefit of Provisional Application Ser. No. 60/673,889, filed on Apr. 19 th , 2005. 
     
    
     FEDERALLY SPONSORED RESEARCH  
       [0002]     Not Applicable  
       SEQUENCE LISTING OR PROGRAM  
       [0003]     Not Applicable  
       BACKGROUND OF THE INVENTION  
       [0004]     1. Field of Invention  
         [0005]     The present invention relates to a method and an apparatus to characterize the behaviour of high-frequency devices-under-test (DUTs) under large-signal operating conditions.  
         [0006]     2. Description of the Related Art  
         [0007]     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  
       [0008]     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 convertor 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 convertor 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 convertor. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]      FIG. 1  Schematic of an LSNA  
     
    
     DETAILED DESCRIPTION  
       [0010]     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. In  FIG. 1  the DUT ( 4 ) is a mixer with an RF input signal port ( 2 ), a local oscillator input port ( 1 ) and with an intermediate frequency signal port ( 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 ).  
         [0011]     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 ports ( 1 ), ( 2 ) and ( 3 ) are send to the input ports of a sampling frequency convertor ( 15 ). The sampling frequency convertor ( 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 convertor ( 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.  
         [0012]     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) 
 
         [0013]     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.  
         [0014]     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 DUT 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 convertor, 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) 
 
         [0015]     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.  
         [0016]     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 i . This order is indicated by the set of integer coefficients k i . 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) 
 
         [0017]     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 convertor. As a result the intermodulation product with frequency f IP [k 1 ,k 2 , . . . ] will appear at the output of the sampling frequency convertor 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 convertor ( 15 ). 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 ). 
 
         [0018]     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 DUT signal ports under conditions which are close enough to the desired operating conditions in order to extract the desired information of the DUT.  
         [0019]     The following example illustrates the above.  
         [0020]     Consider that one wants to measure the intermodulation products up to the 4 th  order at the signal ports 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 convertor is 4 MHz.  
         [0021]     One starts by choosing P 1 =500, Δf 1 =1 MHz, P 2 =495 and Δf 2 =0.99 MHz.  
         [0022]     This results in actually applied frequencies given by g 1 =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 convertor. Note that only positive frequencies are being considered.  
         [0023]     As can be concluded from Table 1, all of the considered intermodulation products appear at the output of the sampling frequency convertor at a frequency within the convertor 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, and f 2  and the actual frequencies g 1  and g 2  is minimized by carefully choosing the values P 1  and P 2 .  
         [0024]     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 convertor are copies of the actual RF time domain waveforms where the only difference is in the time scales.  
                                                               TABLE 1                           Intermodulation Product Indices and Corresponding Frequencies            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