Abstract:
A test and measurement instrument including an input configured to receive a reflected and/or transmitted pulse signal from a device under test, a reference clock input configured to receive a reference signal, the reference signal being asynchronous from the reflected pulse signal, a phase reference module configured to acquire samples of the reference signal, a sampling module configured to acquire samples of the reflected pulse signal; and a controller configured to determine a scattering parameter of the device under test based on the acquired samples of the reference signal and the acquired samples of the reflected pulse signal.

Description:
TECHNICAL FIELD 
       [0001]    This disclosure relates to determining the reflection coefficients, transmission coefficients, and scattering parameters of an unknown device under test using an asynchronous phase reference, fast impulse, and an electrical sampling scope. 
       BACKGROUND 
       [0002]    Test and measurement systems with time domain solutions are limited. Currently, time domain reflectometers and transmitometers are only useable up to approximately 50 GHz. Vector network analyzers, while having a higher bandwidths, are extremely expensive. 
         [0003]    Embodiments of the disclosed technology address these and other limitations in the prior art. 
       SUMMARY 
       [0004]    Some embodiments of the disclosed technology are directed toward a test and measurement instrument, including an input configured to receive a reflected or transmitted pulse signal from a device under test; a reference clock input configured to receive a reference signal, the reference signal being asynchronous from the reflected pulse signal; a phase reference module configured to acquire samples of the reference signal; a sampling module configured to acquire samples of the reflected and/or the transmitted pulse signal; and a controller configured to determine the reflection and transmission coefficients of the device under test based on the acquired samples of the reference signal and the acquired samples of the reflected and/or transmitted pulse signals. 
         [0005]    Some embodiments of the disclosed technology are directed toward a method for determining scattering parameters of a device under test, including receiving a reflected pulse signal from a device under test; receiving a transmitted pulse from a device under test; receiving a reference signal, the reference signal being asynchronous from the reflected pulse signal; acquiring samples of the reference signal; acquiring samples of the transmitted and/or reflected pulse signals; and determining a scattering parameter of the device under test based on the acquired samples of the reference signal and the acquired samples of the reflected pulse signal. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1  illustrates an arrangement of test and measurement equipment suitable for implementing an acquisition method of the disclosed technology. 
           [0007]      FIG. 2  depicts a method for determining the scattering parameter of a device under test using the disclosed technology. 
           [0008]      FIG. 3  shows a full scale of the calculated impulse and sampled data using the method of  FIG. 2 . 
           [0009]      FIG. 4  shows a zoomed in region where ripples are still visible in the impulse response of the calculated impulse and sampled data using the method of  FIG. 2 . 
           [0010]      FIG. 5  shows a zoomed in region of the main pulse of the calculated impulse and sampled data using the method of  FIG. 2 . 
           [0011]      FIG. 6  illustrates an arrangement of test and measurement equipment suitable for implementing an acquisition method of the disclosed technology when the device under test has multiple input and output ports. 
       
    
    
     DETAILED DESCRIPTION 
       [0012]    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. 
         [0013]      FIG. 1  depicts an arrangement of a test and measurement system with an electrical sampling module in accordance with the disclosed technology. A pulse source  100  is connected to a high-speed photo diode  102 . The pulse source  100  is preferably an optical pulse source such as, for example, a Calmar Mode Locked Laser. Other types of pulse sources may be used to provide the pulse. The pulse source, however, should be highly stable. The photo diode  102  is connected to one port  104  of a resistive divider  106 . The second port  108  of the resistive divider  106  is connected to a electrical sampling module  110 . The third port  112  of the resistive divider  106  is connected to either a device under test (DUT)  114  or the calibration standards (when performing calibrations). 
         [0014]    The output from the sampling module  110  is sent to an analog-to-digital (ADC) converter  116  to digitize the sampled outputs from the sampling module  110  and are passed to a controller  118  for further processing, discussed below, and for storage in memory  120 . The controller  118  may be a general purpose processor with software, a microcontroller, an ASIC, an FPGA, etc. 
         [0015]    A phase reference module  122  is also provided that receives a reference clock  124  signal. The reference clock  124  is preferably a highly stable reference frequency. The reference clock  124  is preferably a sine-wave. The sine-wave is spectrally pure, meaning that it has low phase-noise, or equivalently, that it has low jitter. The frequency of the reference clock  124  is not critical for reasons discussed below. The reference clock  124  may be internal or external to the test and measurement instrument. 
         [0016]    The phase reference module  122  internally splits the reference clock into two replicas, and samples them at quadrature, or 90° apart, to produce one pair of sampled analog values per sample. Analog-to-digital converters (ADC)  126  and  128  digitize the sampled analog values from the phase reference module  122 . These digitized sampled values are sent to controller  118  and memory  120  for processing and storage, respectively. Because both the pulse source  100  and the reference clock  124  are highly stable, the phase between the two devices should drift linearly with respect to each other. So any phase difference that deviates from the measured linear drift between the two is caused by the time-base of the measurement system and can be corrected, as discussed in more detail below. 
         [0017]    Calibration coefficients are determined and stored in the memory  120  for processing the signals from the DUT  114 . To determine the calibration coefficients, measurements are determined when port three  112  of the divider  106  is terminated using three known terminations, usually open, shorted, and 50 Ohm load. The same procedure described below with respect to the DUT  114  is performed to determine the calibration standards when port three  112  of the resistive divider  106  is open, shorted, or connected to a known load. This may be done, for example, at regular time intervals and stored in the memory  120 . 
         [0018]    During operation, the pulse source  100  sends a pulse signal through the diode  102  to the resistive divider  106 . The resistive divider  106  then divides the signal to be sent to the DUT  114  (or the calibration standards during calibration) and the sampling module  110 . The sampling module  110  receives the impulse signal from the resistive divider and also receives a reflected signal of the impulse signal received at the DUT  114  back through the resistive divider  106 . That is, the impulse signal is reflected from the DUT  114  and also received at the sampling module  110 . This measured signal is used to calculate the reflection coefficient, S11, of the DUT  114  without the use of a vector network analyzer. The reflection coefficient may then be de-embedded from received signals of the DUT for other calculations by the test and measurement instrument. 
         [0019]    The impulses of four different test signals are measured over a time period T. This time period includes the original impulse, as well as the reflected signal coming from the DUT  114  or the calibration standards. Although the original impulse does not strictly need to be measured, such a measurement makes aligning the reflected signal easier. For each impulse measurement, the phase-reference module  122  must also be used to capture the reference signal from the reference clock  124 . That is, during time period T, the reflected test signals are measured as well as the reference signal from the reference clock  124 . 
         [0020]    Preferably, multiple acquisitions of each of the four measurements should be taken. The more data that is received, the lower the noise level present in the post processed waveform. 
         [0021]      FIG. 2  depicts the method for determining the reflection coefficient of the DUT  114 . 
         [0022]    In step  200 , all of the measured impulses are corrected for time-based errors using an asynchronous correction algorithm, as discussed in U.S. Pat. No. 7,746,058, titled SEQUENTIAL EQUIVALENT—TIME SAMPLING WITH AN ASYNCHRONOUS REFERENCE CLOCK, filed Mar. 21, 2008, which is incorporated herein by reference in its entirety. 
         [0023]    That is, the impulse and phase of the reference clock signal are measured during time period T. The in-phase and quadrature components of the reference clock signal are plotted. The resulting Lissajou is fit with an ellipse to calculate the phase. Since the phase has a linear progression, it is unwrapped and the phase data is fitted with a line. Deviations from the line is the jitter present in the system. By converting radians to seconds, the signal received by the sampling module  110  can be time-corrected based on the deviations from the line. 
         [0024]    The time-corrected data is now no longer uniformly spaced. Each point has its own unique timestamp. The time-corrected pulse is then resampled to be uniformly spaced. To do this, the time-corrected pulses of the signal received by the sampling module  110  are aligned by fitting the initial pulse with a Gaussian function. The location of the center of the Gaussian function is used as the reference point to realign the data. As mentioned above, because the corrections of the time base shift the sample locations in time, the impulse data no longer has uniformly spaced sampled points. This needs to be corrected, so the Fourier transform can be taken in the next step. The multiple acquisition are then averaged together to reduce the noise. The averaging and resampling of the time base may be performed by taking a numerical convolution of the data with a Gaussian impulse, as described in more detail below. 
         [0025]    In operation  202 , all the pairs (t,y) of all the measured waveforms are placed into one data record [T,Y]. The vector T consists of non-uniformly spaced time points and the vector Y consists of the amplitude data. A uniformly spaced sampling grid, t={t0, t1, t2, . . . , ti}, is chosen, where ti=i*Δt. 
         [0026]    For each time interval ti, the integral 
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         [0000]    is computed in operation  204  to determine the amplitude of the pulse at each time interval ti to resample the data. This is a convolution of a function (Y) with Gaussian impulse. The value σ determines the rise-time of the impulse. This integral acts as the averaging over the data. Using a Gaussian function also makes the bandwidth calculations easier. Since the function Y is sampled Yi, the integral needs to be computed numerically. For small rise-times, the tails of the Gaussian decay rapidly and only a small region of integration needs to be used, which results in an increase speed in computation. 
         [0027]    By choosing the rise-time of the Gaussian, the filter bandwidth can be adjusted to have minimal impact on the measured data so that y(ti)≈Y(ti), i.e., the smaller the rise-time, the larger the effective bandwidth of the filter. There is a practical limit, however, in that if the rise-time is made too small, then the filter becomes too narrow and not enough sampled data is used for any given point. This results in a noisy looking plot because not enough of the noise has been averaged out. 
         [0028]    In operation  206 , the Fast Fourier Transform (FFT) is taken of Yi. 
         [0029]    Correcting the time base, resampling, and averaging the data produces one uniform time vector and four impulse measurement amplitude vectors, where the three calibration vectors may be stored from a previous measurement. For the calibration step the FFT is taken so the data is in the frequency domain. 
         [0000]    Since the calibration standards are pre-stored in the memory  120 , as discussed above, only the reflection coefficient of the DUT  114  is unknown. Standard calibration correction algorithms in the frequency domain may be used to correct the measurement of the DUT  114 . These algorithms use the pre-measured calibration standards to correct for unknown distortions in the measurement system. 
         [0030]    To calculate the actual reflection based on a non-ideal measurement in operation  208 , three known reference standards are used, usually a short, open and load. The reflection coefficient of each of these standards is known so the measured reflection can be compared to the actual reflection for each of the calibration standards. In one port DUT Network Analysis there are three error terms, usually referred to as source match, directivity and reflection tracking errors. Three equations are set up, comparing the known standards to the measure results, where each of these three equations has three unknowns (directivity, source match and reflection tracking). The three equations are solved for the three unknowns and use them to correct for the s-parameters of the DUT. 
         [0031]    Therefore, the S11 S-parameter, the reflection coefficient, is determined using an electrical sampling scope, rather than a vector network analyzer. The above-discussed method and system may also be used to measure a transmitted signal from a DUT, rather than a reflected signal. 
         [0032]      FIGS. 3-6  show the calculated impulse using the method of  FIG. 2 . For this method, a convolution rise-time of 0.5 pS was chosen. This corresponds to a filter that has a loss of only 0.05 dB at 100 GHz, so the impact of the convolution is quite small over the bandwidth of interest. 
         [0033]    The above-discussed disclosed technology is not limited to measuring a single port. The above systems and methods can be extended to measure the scattering parameters of a multiple port DUT. To extend the above-discussed method and systems to multiple ports, the method discussed above would be performed for each port. 
         [0034]    For multiport scattering parameters one possible setup would be as shown in  FIG. 6 . Here the impulse laser is routed to the N-photo-diodes  102 ,  600 ,  602  using an optical switch  604 . Each of the diodes  102 ,  600 ,  602  is connected to the DUT  114  and, a divider  106 ,  610 ,  612 , and a sampler  110 ,  606 , and  608 , respectively, as in the one-port case. The reflection coefficients, as before, are determined by measuring the impulse at the nth sampler  608  when the optical pulse is incident on the nth diode  602 . The transmission coefficient can also be measured from port n−1 to port n by measuring the n−1 sampler  606  when the pulse is incident on the nth diode  602 . For each port a reflection calibration and through calibration needs to be made. A modification needs to be made to the calibration method, when before three known reflections (short, open and load) were used, now a known through is used. The through needs to be measured from each of the n-ports to the other n−1 ports. The calibration is as before where the errors are solved for by solving a system of equations. 
         [0035]    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. I claim all modifications and variations coming within the spirit and scope of the following claims.