Multi-rate data for S-parameter extraction

Abstract

A device configured to determine an S-parameter of a communication channel, comprising: a physical interface configured to send and receive signals over a communication channel under test; and a processor that is configured to execute instructions which, when executed, cause the processor to: to capture a first waveform corresponding to a first data pattern sent from a transmitter over the communication channel at a first data rate and to determine a first impulse response from the captured first waveform; to calculate a first transfer function from the first impulse response; to capture a second waveform corresponding to a second data pattern transmitted by the sender over the communication channel at a second data rate and to determine a second impulse response from the captured second waveform; to calculate a second transfer function from the second impulse response; and to combine the first and second transfer functions to determine the S-parameter of the communication channel.

Description

RELATED REGISTRATIONS

[0001] This application is a continuation and claims priority over preliminary US patent application No. 62 / 801,619, which was filed on February 5, 2019. TECHNICAL AREA

[0002] This disclosure relates to testing and measuring instruments, in particular to the use of an oscilloscope for characterizing a signal path. BACKGROUND

[0003] Document DE 195 27 730 A1 concerns a method for correcting erroneous transfer coefficients between two of N measurement channels of a measuring instrument for circuit networks. The method aims to reduce the number of calibration measurements required from N to N. 2 - 1 Calibration measurements by forming triangular combinations from the N measurement channels and by combining these only requiring the measurement of a transmission coefficient in one transmission direction.

[0004] Document US 2013 / 0003804A1 describes a method for compensating for network-induced impairment of an electrical signal. The method involves measuring the impaired electrical signal, sending and measuring a pulse signal through the network, estimating the resulting network impairment transfer function, and thereby correcting the impairment of the electrical signal.

[0005] High-speed serial data links are frequently used for communication between electrical devices. As the bit rate increases, the simulation and measurement of these high-speed serial data links generally requires the use of S-parameters to characterize the components in the link for embedding and de-embedding operations. In the Fig. For example, in the serial data link shown in Figure 1, the output impedance (s22) of the transmitter (Tx) 10, the input impedance (s11) of the receiver (Rx) 14, and the complete S-parameters of the channel 12 are all required to fully characterize and simulate the link. The result is typically that the signals at the receiver can be adapted to preserve the signal at the transmitter by eliminating the effects of the channel and terminations, a process known as de-embedding.

[0006] Traditionally, performing this type of S-parameter measurement for characterizing two- or multi-port networks required a vector network analyzer (VNA) or a time-domain reflectometry (TDR) system with a sampling oscilloscope. Real-time oscilloscopes are also commonly used for troubleshooting, testing, and measuring high-speed serial data links. A real-time oscilloscope can be used in conjunction with a step signal generator to perform a time-domain transmission (TDT) or time-domain reflection (TDR) measurement of a link. This approach has a bandwidth limitation because a step signal has a linearly decreasing energy across the frequency range on the dB scale.

[0007] Furthermore, it is often necessary to characterize the transmitter and the channel, as the receiver interacts with the combination of transmitter and channel. Most transmitters contain signal generators capable of producing stepped signals and various NRZ / PAM4 data patterns. An NRZ (Non-Return-To-Zero) data pattern represents the binary high and low states transmitted by specific and constant DC voltages. It can also be referred to as PAM-2, as it represents two-stage pulse amplitude modulation. A PAM4 data pattern generally transmits 2 bits per symbol, thus halving the bandwidth required for a given data rate.

[0008] When a step-shaped signal is used to extract S-parameters, the accuracy and frequency range of the result are limited by the energy of the step signal at higher frequencies. However, the more random NRZ / PAM4 data patterns, such as PRBS13 (pseudorandom binary sequence 13) for NRZ and PRBS12Q for PAM4, have even higher energy at even higher frequencies. Most of the pseudorandom NRZ / PAM4 data patterns exhibit a greater number of transitions, which carry more radio frequency energy, than a step signal, which has one transition if only the rising or falling edge is counted, or two transitions if both the rising and falling edges are counted.

[0009] Embodiments of the disclosed devices and methods remedy deficiencies in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 shows an embodiment of a channel between a transmitter and a receiver. Fig. Figure 2 shows a comparison of a captured waveform and an unembedded waveform on a real-time oscilloscope. Fig. Figure 3 shows a flowchart of a process for determining an S-parameter of a communication channel. Fig. Figure 4 shows an extracted impulse response from a signal captured by an oscilloscope. Fig. Figure 5 shows a comparison of the magnitude spectra of the extracted impulse and an ideal impulse at a first data rate. Fig. Figure 6 shows magnitude spectra of an ideal pulse at different data rates. Fig. Figure 7 shows the magnitude, phase, impulse and step responses of an S-parameter transfer function. Fig. Figure 8 shows a comparison of an eye diagram for a captured waveform and an eye diagram for an unembedded waveform. Fig. Figure 9 shows a block diagram of a device that can determine an S-parameter of a communication channel. DETAILED DESCRIPTION

[0010] The embodiments presented here can utilize test instruments such as real-time oscilloscopes and sampling oscilloscopes (collectively, “scopes”), which in certain test configurations, such as transmitter tests and receiver calibration tests, replace the one described in Fig. The receiver shown in Figure 1 (“Rx”) can capture waveforms. Once the receivers are in place, probes with telescopes are sometimes used to capture the signal transmitted from the transmitter over the channel. This setup can be used for troubleshooting and system verification.

[0011] A real-time telescope can capture a continuous time waveform of a data pattern, regardless of whether the data pattern repeats or not. A captured NRZ waveform is in Fig. Figure 2 is shown with a data rate of fb1 = 10 Gb / s. A sampling scope can only capture repeating data patterns because, to achieve high bandwidths, sampling scopes typically use time-equivalent sampling, which depends on the pattern repeating. In most cases, the transmitters are capable of sending repeating patterns. It can be assumed that a repeating pattern is available for S-parameter extraction. In some cases, the transmitter is a signal generator, such as a bit error rate tester (BERT), an arbitrary waveform generator (AWG), a pulse pattern generator (PPG), etc.

[0012] As in Fig. As can be seen in Figure 2, the captured waveform 20 differs from the actual unembedded waveform 22 due to the characteristics of the communication channel. If the channel is characterized by determining its S-parameters, the device can apply these characteristics to unembed the channel's effects in order to obtain a more accurate waveform of the received signal.

[0013] Fig. Figure 3 shows the complete process for determining the S-parameter of a communication channel. Initially, at 30, a first data pattern with an initial data rate is sent over the communication channel. The telescope then detects at 32 in Fig. 3 the first waveform, in this case the one in Fig. The recorded waveform shown in Figure 2 is used to determine the impulse response from the first waveform, which is here referred to as the first impulse response. In this disclosure, the terms "impulse" and "impulse response" may be used interchangeably.

[0014] The impulse response can be determined from the captured waveform using an existing industry-standard algorithm that extracts the impulse response from the averaged pattern waveform based on linear matching. See IEEE, “IEEE 802.3ba 40Gb / s and 100Gb / s Ethernet Standard”, http: / / www.ieee802.org / 3 / , 2010, the contents of which are hereby incorporated by reference. A real-time scope can perform software clock recovery, which reduces trigger jitter. See Kan Tan, “Clock recovery for signals with spread spectrum clock through lossy channels”, DesignCon 2016, Santa Clara, CA, 2016, the contents of which are hereby incorporated by reference. The scope can then resample the waveform based on the data rate, and the bit pattern can be detected if the bit pattern is not precisely known.Since a real-time telescope can often capture multiple pattern repetitions in a single acquisition, averaging can be performed between these repetitions to obtain a cleaner, averaged waveform. A sampling telescope can be configured to obtain averaged pattern waveforms.

[0015] Fig. Figure 4 shows the extracted impulse response 44, which is taken from the in Fig. The waveform shown in section 2 was determined. The unit interval (UI) is 100 ps. Fig. Figure 4 shows the non-ideal impulse shape at the main pointer and a large discontinuity about 2.5 ns after the main pointer at 46, which may be due to all-around reflections.

[0016] Fig. Figure 5 shows the spectrum for the extracted impulse response 52, the so-called time domain transmission, and the spectrum of an ideal pulse 50, here referred to as the ideal waveform at the same data rate, which is a rectangular pulse. The ideal pulse width can be the inverse of the data rate. There are zeros, i.e., zero on the linear scale, negative infinity on the dB scale, at multiples of the data rate of [fb1, 2*fb1, 3*fb1] = [10, 20, 30] GHz for the magnitude spectrum of the ideal pulse. This results from the sin(x) / x profile for the rectangular waveform.

[0017] In order to Fig. Returning to step 3, the process then calculates a first transfer function at step 34 based on the spectrum of the first waveform. The S-parameter, or transfer function H_transfer_1 in the frequency domain, is the ratio between the spectrum of the captured waveform H_tdt_1 and the spectrum of the ideal waveform H_ideal_1. H_transfer_1 is well-defined at the frequency points, except at those frequency points where H_ideal_1 has zero values.

[0018] In addition to the data rate of fb1, which in this example was 10 Gb / s, the transmitter can also operate at 36 of Fig. 3. Send the same or a different data pattern at a different data rate fb2. The second data rate fb2 should be chosen such that the zeros in its pulse spectrum, which are multiples of fb2, differ from the multiples of fb1 within the frequency range of interest. For example, let fb2 = 12.5 Gb / s. Here, zeros are located at [12.5, 25] GHz within the 30 GHz range. The process captures at 38 in Fig. 3. The second set of waveforms is calculated, and the corresponding second impulse response is determined. Using the same process as described above, the process calculates the value at 40 of Fig. 3 a second transfer function H_transfer_2 with valid values, except at the frequency points where H_ideal_2 has zeros. Fig. Figure 6 shows the magnitude spectra of the ideal pulses at different data rates, where 50 is the ideal pulse at fb1, which in this example was 10 Gb / s, and 54 is the ideal pulse at fb2, which in this example was 12.5 Gb / s.

[0019] In order to Fig. Returning to step 3, the process combines the first and second transfer functions at step 42 to determine an S-parameter of the channel. Since the valid data of the transfer functions H_transfer_1 and H_transfer_2 overlap over significant frequency spans, this overlap can be used to align the phase response and eliminate the difference in group delays between the two transfer functions. For example, the phase of H_transfer_1 and H_transfer_2 can be subtracted between DC and ¾ * min(fb1, fb2), and the process can perform phase unwinding. The process can then use line matching on the unwound phase difference to obtain a group delay difference value. The individual group delay difference can be added to the phase of H_transfer_2 by adding an additional group delay.

[0020] Once the two transfer functions are phase-aligned, the zero points in one of the transfer functions at these frequency points can be replaced by the valid data of the other transfer function. At the superposition frequency points where both transfer functions have valid data, they can be combined with appropriate weighting. If, in one embodiment, H_ideal_1 has a higher energy than H_ideal_2 at certain frequencies, then H_transfer_1 will be weighted more heavily than H_transfer_2 when the two are combined.

[0021] Other variations and modifications fall within the scope of embodiments and claims. For example, the process can use more than two data rates. Using more data rates increases the accuracy of the transfer functions because better coverage of the frequency points is achieved. For any given frequency point, there is at least some more reliable data available, since H_ideal_n generally has high energy. Averaging all valid values ​​of the transfer function at each frequency point will improve the results.

[0022] Fig. Figure 7 shows the resulting transfer function, represented as an S-parameter. It has clean results up to 30 GHz and a level close to -40 dB. The upper left sub-graph shows the magnitude response in the frequency domain (Figure 60). The upper right sub-graph shows the phase response in the frequency domain (Figure 62). The lower left sub-graph shows the impulse response in the time domain (Figure 64). The lower right sub-graph shows the step response in the time domain (Figure 66). On the same timeline, where the discontinuity in the impulse response is shown in Fig. Figure 4 shows the discontinuity in the impulse response and the step response in Fig. 7.

[0023] The S-parameter can be used to design an embedding filter in the scope, equalizers in transmitters, equalizers in receivers, or in design simulation using other electronic design automation tools. Equalizer design in a transmitter can pre-compensate for signal path degradation, resulting in a higher-quality signal at the end of the channel. This allows the receiver to detect the bit sequence with a lower bit error rate.

[0024] The in Fig. The S-parameter shown in Figure 7 is used, for example, to design an embedding filter in a real-time telescope. The embedding waveform 22 obtained by applying the embedding filter to the captured waveform 20 was then Fig. 2 shown. Fig. Figure 8 shows the eye diagrams derived from the captured waveform at 70 and the eye diagram derived from the unembedded waveform at 72.

[0025] The approach for extracting S-parameters from multi-rate data utilizes both real-time and sampling scopes to obtain S-parameters that characterize the combined impact on signal integrity from the transmitters and channels. This approach employs typical high-speed serial data transmitters for NRZ and PAM4 signaling, which can generate PRBS data patterns. By using multiple data rate settings, the resulting S-parameter is accurate at all measured frequency points. The higher energy level at high frequencies enables this approach to achieve greater dynamic range over a wider bandwidth. For example, embodiments of the disclosed technology can measure S-parameters up to 30 GHz and down to -40 dB levels.

[0026] This method for determining the S-parameters of a communication channel can be implemented in a processor within the scope itself, since most available scopes have integrated computing capabilities, in both real-time and sampling scopes. Alternatively, the device can include a testing instrument such as an oscilloscope operating under computer control. Fig. Figure 9 shows a block diagram of such a device. While the embodiment of Fig. 9. While all parts of the system are shown in a single system, it should be noted that the various elements may be distributed between a computer and an oscilloscope. Fig.9 The device 80 has at least one physical interface 82 so that the device can acquire the waveforms and may have multiple connections, including connections that enable the generation of the signals transmitted in the communication channel. The device has a processor 84 for executing instructions that cause the processor to work on the acquired waveform in the manner described above in order to acquire the S-parameters of a communication channel. The instructions and the acquired waveforms may be stored in a common memory, e.g., 86, or in separate memories. The display 90 will show the waveforms. The incoming waveforms may also be processed by various peripheral circuits, such as an analog-to-digital converter (ADC), a corresponding digital-to-analog converter (DAC), etc.

[0027] Similarly, aspects of disclosure can operate on specially created hardware, firmware, digital signal processors, or a specially programmed general-purpose computer with a processor operating according to programmed instructions. The terms controller or processor used here are intended to encompass microprocessors, microcomputers, application-specific integrated circuits (ASICs), and dedicated hardware controllers.

[0028] One or more aspects of the disclosure may be contained in computer-usable data and computer-executable instructions, for example, in one or more program modules executed by one or more computers (including monitoring modules) or other devices. Generally, program modules comprise routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types when executed by a processor in a computer or other device. The computer-executable instructions may be stored on a non-volatile, computer-readable medium such as a hard disk, optical disk, removable media, solid-state storage, main memory (RAM), or random access memory, etc.As those skilled in the art will understand, the functionality of the program modules can be combined or distributed arbitrarily in various respects. Furthermore, the functionality can be contained wholly or partially in firmware or hardware equivalents such as integrated circuits, FPGAs (Field Programmable Gate Arrays), and the like. Certain data structures can be used to implement one or more aspects of the disclosure more effectively, and such data structures are considered within the context of the computer-executable instructions and computer-usable data described herein.

[0029] The disclosed features may in some cases be implemented in hardware, firmware, software, or a combination thereof. The disclosed features may also be implemented in the form of instructions carried on or stored on one or more non-volatile, computer-readable media that can be read and executed by one or more processors. Such instructions may be referred to as a computer program product. Computer-readable media, as discussed here, are all media that a computer device can access. By way of example, but not as a limitation, computer-readable media can include computer storage media and communication media.

[0030] Computer storage media are defined as any medium that can be used to store computer-readable information. Examples, but not limitations, include RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other storage technologies, compact disc (CD-ROM) storage, digital video disc (DVD) storage or other optical disk storage, magnetic cartridges, magnetic tape, magnetic disk storage or other magnetic storage devices, and any other volatile or non-volatile, removable or non-removable medium implemented in any technology. Computer storage media exclude signals themselves and transitory forms of signal transmission.

[0031] Communication media are defined as all media that can be used to transmit computer-readable information. Examples, but not limitations, include coaxial cables, fiber optic cables, air, or any other medium suitable for transmitting electrical, optical, radio frequency (RF), infrared, acoustic, or other types of signals.

[0032] Additionally, this written description refers to special features. It should be understood that the disclosure in this specification encompasses all possible combinations of these special features. For example, if a particular feature is disclosed in connection with a specific aspect, this feature may, where possible, also be used in connection with other aspects.

[0033] Even if this application refers to a procedure with two or more defined steps or operations, the defined steps or operations can be performed in any order or simultaneously unless the context excludes these possibilities.

[0034] Although certain aspects of the revelation have been presented and described for illustrative purposes, it will be understood that various modifications may be made without deviating from the spirit and scope of the revelation. Accordingly, the revelation should not be limited except by the attached claims. EXAMPLES

[0035] Illustrative examples of the disclosed technologies are given below. An embodiment of the technologies may comprise one or more, and any combination of, the examples described below.

[0036] Example 1 is a device configured to determine an S-parameter of a communication channel, comprising: a physical interface configured to send and receive signals over a communication channel under test.The device includes a processor configured to execute instructions which, when executed, cause the processor to: detect a first waveform corresponding to a first data pattern transmitted by a transmitter over the communication channel at a first data rate, and determine a first impulse response from the detected first waveform; calculate a first transfer function from the first impulse response; detect a second waveform corresponding to a second data pattern transmitted by the transmitter over the communication channel at a second data rate, and determine a second impulse response from the detected second waveform; calculate a second transfer function from the second impulse response; and combine the first and second transfer functions to determine an S-parameter of the communication channel.

[0037] Example 2 is the device of Example 1, wherein the first data rate and the second data rate are chosen such that the first and second data rates do not have overlapping zero values.

[0038] Example 3 is the apparatus of one of Examples 1 and 2, wherein the instruction causing the process to acquire the first waveform and to acquire the second waveform includes an instruction causing the processor to determine a first averaged waveform and a second averaged waveform.

[0039] Example 4 is the apparatus of Example 3, wherein the apparatus comprises a real-time oscilloscope and the instruction which causes the processor to determine a first averaged waveform and a second averaged waveform further causes the processor to perform a clock recovery in order to determine the first averaged waveform and the second averaged waveform.

[0040] Example 5 is the apparatus of Example 3, wherein the apparatus comprises a scanning oscilloscope and the instruction which causes the processor to determine a first averaged waveform and a second averaged waveform further causes the processor to set a capture mode on the scanning oscilloscope in order to determine the first averaged waveform and the second averaged waveform.

[0041] Example 6 is the apparatus of one of Examples 1-5, wherein the instruction causing the processor to compute the first transfer function further causes the processor to: compute a first ideal spectrum of a first ideal pulse, wherein the first ideal pulse width is an inverse of the first data rate; determine a first spectrum of the first impulse response; and use the ratio of the first spectrum to the first ideal spectrum as the first transfer function.

[0042] Example 7 is the apparatus of one of Examples 1-6, wherein the instruction causing the processor to compute the second transfer function further causes the processor to: compute a second ideal spectrum of a second ideal pulse, wherein the second ideal pulse width is an inverse of the second data rate; determine a second spectrum of the second impulse response; and use the ratio of the second spectrum to the second ideal spectrum as the second transfer function.

[0043] Example 8 is the device of one of Examples 1-7, wherein the instruction causing the processor to combine the first transfer function and the second transfer function further causes the processor to align the first and the second transfer function.

[0044] Example 9 is the device of one of Examples 1-8, wherein the instruction causing the processor to align the first and second transfer functions further causes the processor to adjust a phase of the second transfer function in order to align the second transfer function in phase with the first transfer function.

[0045] Example 10 is the apparatus of one of Examples 1-9, wherein the instruction causing the processor to combine the first and second transfer functions further causes the processor to: use data only from one of the first and second transfer functions if the other of the first and second transfer functions has zero data; and average data of the first and second transfer functions using a weighting based on an energy of the ideal spectrum.

[0046] Example 11 is a method for characterizing a communication link with a transmitter and a channel, comprising: transmitting a first data pattern from the transmitter over the channel at a first data rate; capturing a first waveform corresponding to the first data pattern and determining a first impulse response from the captured first waveform; calculating a first transfer function from the first impulse response; transmitting a second data pattern from the transmitter over the channel at a second data rate; capturing a second waveform corresponding to the second data pattern and determining a second impulse response from the captured second waveform; calculating a second transfer function from the second impulse response; and combining the first and second transfer functions to determine an S-parameter of the communication link.

[0047] Example 12 is the procedure of Example 11, wherein the first data rate and the second data rate are chosen such that the first and second data rates do not have any overlapping zero values.

[0048] Example 13 is the method of one of Examples 11 and 12, wherein capturing the first waveform and capturing the second waveform includes determining a first averaged waveform and a second averaged waveform.

[0049] Example 14 is the procedure of Example 13, wherein determining a first averaged waveform and a second averaged waveform includes performing clock recovery on a real-time oscilloscope used to acquire the first waveform and the second waveform.

[0050] Example 15 is the procedure of Example 13, wherein determining a first averaged waveform and a second averaged waveform includes setting a capture mode on a scanning oscilloscope to obtain the first averaged waveform and the second averaged waveform.

[0051] Example 16 is the procedure of one of Examples 11-15, wherein calculating the first transfer function comprises: calculating a first ideal spectrum of a first ideal impulse, where the first ideal impulse width is an inverse of the first data rate; determining a first spectrum of the first impulse response; and using the ratio of the first spectrum to the first ideal spectrum as the first transfer function.

[0052] Example 17 is the procedure of one of Examples 11-16, wherein calculating the second transfer function comprises: calculating a second ideal spectrum of a second ideal impulse, where the second ideal impulse width is an inverse of the second data rate; determining a second spectrum of the first impulse response; and using the ratio of the second spectrum to the second ideal spectrum as the second transfer function.

[0053] Example 18 is the method of one of Examples 11-17, wherein combining the first transfer function and the second transfer function involves aligning the first and second transfer functions.

[0054] Example 19 is the procedure of Example 18, wherein aligning the first and second transfer functions involves adjusting a phase of the second transfer function to align the phase of the second transfer function with the first transfer function.

[0055] Example 20 is the procedure of one of Examples 11-19, wherein combining the first and second transfer functions includes: using data from only one of the first and second transfer functions when the other of the first and second transfer functions has zero data; and averaging data from the first transfer function and the second transfer function using a weighting based on an energy of an ideal spectrum.

[0056] Although certain embodiments have been presented and described for illustrative purposes, it is assumed that various modifications can be made without departing from the spirit and scope of the disclosure. Accordingly, the invention should not be limited except by the appended claims.

Claims

[1] An apparatus configured to determine an S-parameter of a communication channel, comprising: a physical interface configured to send and receive signals over a communication channel under test; and a processor configured to execute instructions that, when executed, cause the processor to: acquire a first waveform corresponding to a first data pattern transmitted from a transmitter over the communication channel at a first data rate and determine a first impulse response from the acquired first waveform; to calculate a first transfer function from the first impulse response; acquire a second waveform corresponding to a second data pattern transmitted from the transmitter over the communication channel at a second data rate and determine a second impulse response from the acquired second waveform; to calculate a second transfer function from the second impulse response; and to combine the first and second transfer functions to determine the S-parameter of the communication channel. [2] The apparatus of claim 1, wherein the first data rate and the second data rate are selected such that the first and second data rates do not have overlapping zero values. [3] The apparatus of claim 1 or 2, wherein the instruction causing the processor to acquire the first waveform and acquire the second waveform comprises an instruction causing the processor to determine a first averaged waveform and a second averaged waveform. [4] The apparatus of claim 3, wherein the apparatus comprises a real-time oscilloscope, and the instruction causing the processor to determine a first averaged waveform and a second averaged waveform further causes the processor to perform clock recovery to determine the first averaged waveform and the second averaged waveform. [5] The apparatus of claim 3 or 4, wherein the apparatus comprises a sampling oscilloscope, and the instruction causing the processor to determine a first averaged waveform and a second averaged waveform further causes the processor to set an acquisition mode on the sampling oscilloscope to determine the first averaged waveform and the second averaged waveform. [6] The apparatus of any one of claims 1 to 5, wherein the instruction causing the processor to calculate the first transfer function further causes the processor to: calculate a first ideal spectrum of a first ideal pulse, wherein the first ideal pulse width is an inverse of the first data rate; to determine a first spectrum of the first impulse response; and to use the ratio of the first spectrum to the first ideal spectrum as the first transfer function. [7] The apparatus of any one of claims 1 to 6, wherein the instruction causing the processor to calculate the second transfer function further causes the processor to: calculate a second ideal spectrum of a second ideal pulse, the second ideal pulse width being an inverse of the second data rate; to determine a second spectrum of the second impulse response; and to use the ratio of the second spectrum to the second ideal spectrum as the second transfer function. [8] The apparatus of any one of claims 1 to 7, wherein the instruction causing the processor to combine the first transfer function and the second transfer function further causes the processor to align the first and second transfer functions. [9] The apparatus of claim 8, wherein the instruction causing the processor to align the first and second transfer functions further causes the processor to adjust a phase of the second transfer function to phase align the second transfer function with the first transfer function. [10] The apparatus of any one of claims 1 to 9, wherein the instruction causing the processor to combine the first and second transfer functions further causes the processor to: to use data only from one of the first and second transfer functions if the other of the first and second transfer functions has zero data; and To average data of the first transfer function and the second transfer function using a weighting based on an energy of the ideal spectrum. [11] A method for characterizing a communication link with a transmitter and a channel, comprising: transmitting a first data pattern from the transmitter over the channel at a first data rate; Acquiring a first waveform corresponding to the first data pattern and determining a first impulse response from the acquired first waveform; Calculating a first transfer function from the first impulse response; transmitting a second data pattern from the transmitter over the channel at a second data rate; Acquiring a second waveform corresponding to the second data pattern and determining a second impulse response from the acquired second waveform; Calculating a second transfer function from the second impulse response; and Combining the first and second transfer functions to determine an S-parameter of the communication link. [12] The method for characterizing a communication link according to claim 11, wherein the first data rate and the second data rate are selected such that the first and second data rates do not have overlapping zero values. [13] The method for characterizing a communication link according to claim 11 or 12, wherein detecting the first waveform and detecting the second waveform comprises determining a first averaged waveform and a second averaged waveform. [14] The method for characterizing a communication link according to claim 13, wherein determining a first averaged waveform and a second averaged waveform comprises performing clock recovery on a real-time oscilloscope used to acquire the first waveform and the second waveform. [15] The method for characterizing a communication link according to claim 13 or 14, wherein determining a first averaged waveform and a second averaged waveform comprises setting an acquisition mode on a sampling oscilloscope to obtain the first averaged waveform and the second averaged waveform. [16] The method for characterizing a communication link according to any one of claims 11 to 15, wherein calculating the first transfer function comprises: Calculating a first ideal spectrum of a first ideal pulse, wherein the first ideal pulse width is an inverse of the first data rate; Determining a first spectrum of the first impulse response; and Using the ratio of the first spectrum to the first ideal spectrum as the first transfer function. [17] The method for characterizing a communication link according to any one of claims 11 to 16, wherein calculating the second transfer function comprises: Calculating a second ideal spectrum of a second ideal pulse, wherein the second ideal pulse width is an inverse of the second data rate; Determining a second spectrum of the first impulse response; and Using the ratio of the second spectrum to the second ideal spectrum as the second transfer function. [18] The method for characterizing a communication link according to any one of claims 11 to 17, wherein combining the first transfer function and the second transfer function comprises aligning the first and second transfer functions. [19] The method for characterizing a communication link according to claim 18, wherein aligning the first and second transfer functions comprises adjusting a phase of the second transfer function to phase align the second transfer function with the first transfer function. [20] The method for characterizing a communication link according to any one of claims 11 to 19, wherein combining the first and second transfer functions comprises: Using data only from one of the first and second transfer functions when the other of the first and second transfer functions has zero data; and Averaging data of the first transfer function and the second transfer function using a weighting based on an energy of an ideal spectrum.

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