Abstract:
A method for determining a waveform expected to be received by a device under test, the method including outputting a waveform generated by a waveform generation section of an arbitrary waveform and function generator at an output of the arbitrary waveform and function generator; sending the waveform generated by the waveform generation section to the device under test through a cable; monitoring a waveform at the output by a waveform monitoring section of the arbitrary waveform and function generator; and determining by the waveform monitoring section a transformed waveform expected to be received at the device under test based on the generated waveform being modified by the cable.

Description:
TECHNICAL FIELD 
     This disclosure relates to an arbitrary waveform and function generator, more specifically, an arbitrary waveform and function generator that de-embeds the effects of a coaxial cable upon the measurement and/or monitoring of the output waveform without any knowledge of the device under test. 
     BACKGROUND 
     Arbitrary Waveform and Function Generator (AFG) instruments are widely utilized for generating continuous/burst user-defined mathematical function waveform signals for electronic circuit design and testing. Typically, an AFG instrument has an output impedance of 50 ohms over its operating frequency range. The load impedance of a device under test (DUT) impacts the actual output signal of an AFG instrument. 
     During a typical operation, a low insertion-loss cable is generally used to connect the AFG to a DUT. For low frequencies and matching loads, the waveform monitoring function of the AFG works well with a minor cable attenuation that is easy to compensate. However, at high frequencies, i.e., when the cable length is comparable to the signal wave length and the load impedance of a DUT is mismatched with the AFG output impedance, the measurement results in the local output point of the AFG might be quite different than the actual signals loaded to the remote point of the DUT, due to the impedance transformation of the transmission line, which will be called the cable effect hereinafter. 
     SUMMARY 
     Some embodiments of the disclosed technology include a method for determining a waveform expected to be received by a device under test, the method including outputting a waveform generated by a waveform generation section of an arbitrary waveform and function generator at an output of the arbitrary waveform and function generator; sending the waveform generated by the waveform generation section to the device under test through a cable; monitoring a waveform at the output by a waveform monitoring section of the arbitrary waveform and function generator; and determining by the waveform monitoring section a transformed waveform expected to be received at the device under test based on the generated waveform being modified by the cable. 
     Some embodiments of the disclosed technology include an arbitrary waveform and function generator, including a waveform generation section configured to generate a waveform at an output; and a waveform monitoring section configured to monitor the waveform at the output. The waveform monitoring section includes a waveform de-embedding processor configured to determine a transformed waveform expected to be received at the device under test based on the generated waveform being modified by the cable, and a display configured to display the transformed waveform. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a traditional arbitrary waveform and function generator. 
         FIG. 2  illustrates an arbitrary waveform and function generator according to aspects of the disclosed technology. 
         FIG. 3  illustrates a method for de-embedding the cable effect from an acquired waveform. 
         FIG. 4  illustrates a block diagram of a waveform de-embedding module of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION 
     In the drawings, which are not necessarily to scale, like or corresponding elements of the disclosed systems and methods are denoted by the same reference numerals. 
       FIG. 1  illustrates a typical design of an AFG  100 . The AFG  100  includes a signal generation section  101  and a waveform monitoring section  102 . The signal generation section  101  generates a signal to send to the DUT. The waveform monitoring section  102  monitors the signal generated by the signal generation section  101  at a local test point on the output  104  on the AFG. 
     In the signal generation section  101 , a waveform signal, such as a sine function waveform signal or a user-defined arbitrary waveform signal, is digitized at a specific time/phase interval and a specific vertical resolution, and is saved to the Digitized Waveform Memory  108 . The Time/Phase to Address Mapper  106  functions at a specific clock, received from the System Clock  116 , to access the Digitized Waveform Memory  108  to output a digitized waveform at the correct time/phase intervals for achieving the user-specified signal waveform frequency. 
     The digitized waveform is then output from the Digitized Waveform Memory  108  to a Digital-to-Analog Converter (DAC)  110  to convert the digitized waveform to an analog signal. The analog signal is sent through a waveform reconstruction filter  112  and output to an amplifier  114  to scale the analog signal to a user-required amplitude. This analog signal is sent through the output  104  to a remote DUT location through a coaxial cable. 
     As mentioned above, the waveform monitoring section  102  monitors the signal generated by the signal generation section  101  at a local test point on the output  104  on the AFG. 
     The high impedance amplifier  118  may vary its gain/attenuation to produce an appropriate output signal amplitude. Then, an anti-aliasing filter  120  removes the high frequency noise beyond the bandwidth of the Analog-to-Digital Converter (ADC)  122 . The ADC  122  converts the analog signal received to a digitized waveform. The digitized waveform is acquired by a Waveform Acquisition Controller  124  and stored in the Waveform Acquisition Memory  126 . Synchronization block  130  generates a trigger signal  132  to ensure that the acquisition is accomplished in a complete signal period. The acquired digitized waveform stored in the Waveform Acquisition Memory  126  is sent to the Waveform Display Controller  128  for waveform display and/or monitoring on the AFG. 
     For example, using the configuration of the AFG shown in  FIG. 1 , a sine waveform signal is acquired at a local test point on the output  104 . The acquisition starts at a 0° phase and ends at a 360° phase using a trigger  132  through a Waveform Acquisition Controller  124 . The digitized acquired waveform is stored in the Waveform Acquisition Memory  126  and sent to the Waveform Display Controller  128 . However, the acquired waveform may be quite different from the remote waveform at the DUT connected to the AFG through a coaxial cable, due to the cable effect. That is, the acquired waveform at the AFG test point will not depict the actual waveform received at the DUT, since this waveform has been subjected to the cable effect. 
     According to embodiments of the present invention, as seen in  FIG. 2 , a Waveform De-embedding Module  202  may be used in an AFG  200 . As discussed in further detail below, the Waveform De-embedding module  202  may de-embed the cable effect from the acquired waveform to retrieve the waveform actually present at the DUT for waveform display and/or monitoring. 
     Using the AFG  200  depicted in  FIG. 2 , the cable effect can be de-embedded from the monitored waveform without knowledge of the DUT. This allows the waveform monitoring and testing to virtually move to the DUT from the AFG. 
     Initially, when an AFG is setup with a specific cable and DUT, the measurements to de-embed the cable effect goes through two steps. First, a calibration is run, and second, the de-embedding of the cable effect for the various signals. 
       FIG. 3  depicts a method for de-embedding the cable effect according to some embodiments of the disclosed technology. The cable effect can be de-embedded from either a sine waveform or another type of waveform. 
     Initially, when the AFG is setup with a specific cable and DUT, a calibration is run. In operation  300 , the voltage at the output  104  is measured for a sine signal of the frequency of f with a coaxial cable that is terminated with a matching load, i.e., with a load equal to the characteristic impedance Z C  of the coaxial cable. This measurement provides the complex measurement result of the nominal output V mea   _   nom  of the AFG  200  through synchronous acquisition, i.e. V mea   _   nom  can be expressed in a complex format as shown in equation (1):
 
 V   mea   _   nom =Abs( V   mea   _   nom ) e   jAngle(V     mea—nom     )   (1)
 
where the synchronous trigger signal is used as a reference phase.
 
     In operation  302 , the voltage at the output  104  is measured for the sine signal of the frequency f with the coaxial cable terminated with an open load through synchronous acquisition, i.e., the signal is fully reflected by the load, which provides the measurement of V mea   _   open . This measurement may be used with V mea   _   nom  to determine the complex ratio k o , as shown in equation (2): 
                     k   o     =         V   mea_open       V   mea_nom       =     1   +     e       -   2     ⁢           ⁢     l   ⁡     (     α   +     j   ⁢           ⁢   β       )                       (   2   )               
where α is the unknown attenuation coefficient of the coaxial cable, β the unknown waveform number of the coaxial cable, and l the unknown length of the coaxial cable.
 
     Then in operation  304 , the whole frequency range of the AFG  200  is scanned to characterize k o  of coaxial cable with an open load at a specified frequency step of Δf, which is normally frequency-dependent. That is, V mea   _   nom  and V mea   _   open  are scanned over the entire frequency range at the specified frequency step. The data collections of k o (2πf) for multiple frequency points are needed for de-embedding non-sine wave signals because they occupy a frequency range rather than a single frequency point of a sine signal. These values are then stored in a coefficient table on a memory (not shown) of the AFG  200 . 
     In operation  306 , the voltage at the output  104  is measured for the sine signal of the frequency f with the coaxial cable terminated with a user load, i.e., the DUT to determine V mea   _   load . The complex ratio k l  is calculated then using equation (3): 
                     k   l     =         V   mea_load       V   mea_nom       =     1   +       e       -   2     ⁢           ⁢     l   ⁡     (     α   +     j   ⁢           ⁢   β       )           ⁢         Z   DUT     -     Z   C           Z   DUT     +     Z   C                       (   3   )               
where Z DUT  is the unknown input impedance of DUT.
 
     In operation  308 , the whole frequency range of the AFG  200  is scanned to characterize k l  at a specified frequency step of Δf, which is normally frequency-dependent. That is, V mea   _   load  is scanned over the entire frequency range at the specified frequency step. The data collections of k l (2πf) for multiple frequency points are needed for de-embedding non-sine wave signals because they occupy a frequency range rather than a single frequency point of sine signal. These values are then stored in a coefficient table on a memory (not shown) of the AFG  200 . 
     After the values for k o  and k l  are stored in the coefficient table of the memory on the AFG, the AFG may then begin de-embedding for actual signals generated. That is, the AFG will first determine in step  310  whether a sine signal or an arbitrary signal is generated by the signal generation section  101 . 
     In operation  312 , if a sine signal is generated, then the coefficients k o  and k l  may be looked up at the user-set frequency point of signal generation to calculate the signal that is actually received at the DUT at the remote end of the coaxial cable, using equation (4): 
                     V   DUT     =       2   ⁢           ⁢     V   mea_nom     ⁢       Z   DUT         Z   DUT     +     Z   C         ⁢     e     -     l   ⁡     (     α   +     j   ⁢           ⁢   β       )             =         V   mea_nom     ⁢         k   o     +     k   l     -   2           k   o     -   1           =       V   mea_nom     ⁢     k   d                   (   4   )               
i.e., V DUT  is de-embedded or retrieved from the measurement results at the output  104  of AFG  200  and k d  is a de-embedding coefficient which is equal to
 
     
       
         
           
             
               
                 
                   k 
                   o 
                 
                 + 
                 
                   k 
                   l 
                 
                 - 
                 2 
               
               
                 
                   
                     k 
                     o 
                   
                   - 
                   1 
                 
               
             
             . 
           
         
       
     
     In operation  314 , if an arbitrary (non-sine) waveform signal is generated, the Fourier Transform of V mea   _   nom  of the time domain format is calculated to get V mea   _   nom (2πf) of the frequency domain format and the measurement results may be computed in frequency domain to get V DUT (2πf). That is, the k o  and k l  coefficients at all frequency points over the frequency range are used. Then, the inverse Fourier Transform of V DUT  (2πf) is calculated to get the actual waveform V DUT  in time domain as seen in equation (5): 
                     V   DUT     =         ℱ     -   1       ⁢     {       V   DUT     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       }       =         ℱ     -   1       ⁢     {         V   mea_nom     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       ⁢           k   o     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       +       k   l     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       -   2             k   o     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       -   1           }       =       ℱ     -   1       ⁢     {         V   mea_nom     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )       ⁢       k   d     ⁡     (     2   ⁢   π   ⁢           ⁢   f     )         }                   (   5   )               
i.e. V DUT  is de-embedded or retrieved from the measurement result at the output  104  of AFG  200  to predict the actual waveform received at the DUT through the coaxial cable using the waveform de-embedding module  202  shown in  FIG. 2 .
 
     Alternatively, it is feasible to use a well-designed pulse signal or arbitrary waveform signal to accelerate the above measurement process of frequency scanning. The procedure is almost the same except for calculating the Fourier Transform of V mea   _   nom  , V mea   _   open  and V mea   _   load  , k o  and k l  in frequency domain instead of repeating the calculations on the basis of frequency point by point while scanning the frequency range. It is noted here that this Pulse method helps to save the measurement time but at the cost of accuracy since it is more sensitive to noises. 
       FIG. 4  depicts a block diagram of the De-Embedding module  202  shown in  FIG. 2  with three separate paths. The first path measures V mea   _   nom , V mea   _   open , and V mea   _   load , as discussed above in operations  300 ,  302  and  306 , using a sine wave of a single frequency. As seen in  FIG. 4 , the acquired waveform  400  is sent to a plurality of switches in the first path. The first switch  402 , when enabled, measures V mea   _   nom  with a matched load using the acquired waveform, as discussed above in operation  300 . The second switch  404 , when enabled, measures V mea   _   open  with an open load using the acquired waveform, as discussed in operation  302 . The third switch  406 , when enabled, measures V mea   _   load  using the acquired waveform, with the coaxial cable terminated with a user load of DUT, as discussed in operation  306 . 
     As in operations  302  and  306 , V mea   _   open  is divided by V mea   _   nom  using divider  408 , and V mea   _   load  is divided by V mea   _   nom  using divider  410 , to calculate k o  and k l , respectively. The Waveform De-Embedding module  202  calculates k d  using the equation 
     
       
         
           
             
               
                 
                   k 
                   o 
                 
                 + 
                 
                   k 
                   l 
                 
                 - 
                 2 
               
               
                 
                   
                     k 
                     o 
                   
                   - 
                   1 
                 
               
             
             , 
           
         
       
         
         
           
              as discussed above in operation  312 . This then provides the de-embedded coefficient at a single frequency. 
           
         
       
    
     However, as discussed above in operations  304  and  308 , the whole frequency range is scanned to characterize k o  and k 1  at specified frequency steps. The frequency scanning only needs to run a single time prior to waveform de-embedding for a specific setup of cable and DUT. This retrieves the frequency-dependent calibration/de-embedding function of k d (2πf) stored as a coefficient table, discussed above, in the system for later sine and arbitrary waveform monitoring/testing. 
     In the second path, if the de-embed switch  410  is enabled, the acquired waveform can be sent to the de-embedding calculation path through switch  414 . For a sine signal, the signal goes to the multiplier  416  through the sine-selected switch  414  for amplitude scaling and phase offset for de-embedding at one single signal frequency and then goes through switches  418  and  412  to Waveform Display Controller (not shown) for display. For an arbitrary signal, the signal goes to FFT  420  for converting to the signal in frequency domain through the arbitrary-selected switch  414 . Then the signal in the frequency domain format goes to the multiplier  422  for amplitude scaling and phase offset for de-embedding over the signal frequency range. And then the de-embedded signal in frequency domain goes to inverse FFT  424  for converting to the signal in time domain. Then the de-embedded signal in time domain goes through switches  418  and  412  to the Waveform Display Controller (not shown) for display. 
     In the final path, if the de-embed switch  410  is not enabled, then the acquired waveform can be sent to the Waveform Display Controller (not shown) for display through switch  412 . 
     A de-embedding emulation example of the disclosed technology is shown below using an AFG having only a signal generation section and an oscilloscope. 
     First, a sine wave of 10 MHz, 1 Vpp, 50 Ohm termination for the AFG was set. The AFG&#39;s trigger out signal was used for triggering the oscilloscope&#39;s acquisition. A coaxial cable connected from the AFG to a termination of 50 Ohm. A high impedance probe with an oscilloscope channel was used to measure the voltage at the AFG&#39;s output, i.e. V mea   _   nom  (note: a test window was cut into the cable for the probe&#39;s contacting, which applies for the below discussed probe testing). 
     The cable was then disconnected to leave the cable as Open to measure the voltage at AFG output to determine V mea   _   open  through a high impedance probe with an oscilloscope channel. The cable was then connected to a DUT to measure the voltage at AFG output to determine V mea   _   load  and measure the actual voltage at DUT through a high impedance probe with an oscilloscope channel. Then, the de-embedded voltage at the AFG, i.e. V DUT , was calculated using the above disclosed method of  FIG. 3  and compared with the voltage actually measured at the DUT. This resulted in an amplitude error of less than 11% and a phase error of less than 3° for the de-embedded voltage waveform, versus the actual voltage waveform produced at the remote DUT location. 
     It may be concluded that the cable effect then can be de-embedded through the above disclosed technology without any knowledge of DUT and effectively make the waveform monitoring/testing virtually move to DUT from the instrument, which was called “Virtual Monitoring.” Additionally, based on the above disclosed technology, it is feasible to enhance AFG to have the capability of compensation/pre-emphasis for improving output distortions for various DUTs. That is, an accurate depiction of the test signal received at the DUT based on the signal generated by the signal generation section  101  can be viewed by a user. 
     According to some examples, Waveform De-embedding Module  202  may include various hardware elements, software elements, or a combination of both. Examples of hardware elements may include devices, logic devices, components, processors, microprocessors, circuits, processor circuits, circuit elements (e.g., transistors, resistors, capacitors, inductors, and so forth), integrated circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), memory units, logic gates, registers, semiconductor device, chips, microchips, chip sets, and so forth. Examples of software elements may include software components, programs, applications, computer programs, application programs, device drivers, system programs, software development programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, functions, methods, procedures, software interfaces, application program interfaces (API), instruction sets, computing code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. Determining whether an example is implemented using hardware elements and/or software elements may vary in accordance with any number of factors, such as desired computational rate, power levels, heat tolerances, processing cycle budget, input data rates, output data rates, memory resources, data bus speeds and other design or performance constraints, as desired for a given example. 
     Having described and illustrated the principles of the disclosed technology in a preferred embodiment thereof, it should be apparent that the disclosed technology can be modified in arrangement and detail without departing from such principles. We claim all modifications and variations coming within the spirit and scope of the following claims.