Methods for measuring low frequency S parameters

Abstract

The present disclosure relates to systems and methods related to test and measurement systems, and in particular to characterizing the performance of a test and measurement probe for a test and measurement system. The method determines scattering parameters S parameters of a device under test for a first frequency range. The method includes receiving the S parameters of the device under test for a second frequency range, the second frequency range being greater than the first frequency range. In general, the S parameters of the device under test for the second frequency range can be determined using known methods. The method further includes measuring an actual response of the device under test, determining an expected signal of the device under test, and determining the S parameters of the device under test for the first frequency range based on the S parameters for the second frequency range, the actual response of the device under test, and the expected signal of the device under test.

Description

[0001] priority

[0002] This disclosure claims the benefit of U.S. Provisional Application No. 62 / 858,271, filed on June 6, 2019, entitled “LOW FREQUENCY S-PARAMETER MEASUREMENT AND ESTIMATION,” which is incorporated herein by reference in its entirety. Technical Field

[0003] The present disclosure relates to systems and methods related to test and measurement systems, and in particular to characterizing the performance of test and measurement probes for use in test and measurement systems. Background Art

[0004] A set of scattering parameters (S parameters) of a device under test, such as a probe, in the frequency range of f1 to f2 can be measured, for example, by a vector network analyzer (VNA). Typically, the lowest frequency at which a VNA can adequately measure S parameters is 25 MHz. Typically, when measuring S parameters, the probe is attached to a fixture. The S parameters of the fixture can be obtained separately, and then the S parameters of the probe and fixture combination can be obtained. The S parameters of the probe are determined by de-embedding the fixture from the obtained S parameters of the fixture and probe combination. This method works well for most probes in the frequency range of f1 to f2.

[0005] However, with the advent of interposers for double data rate (DDR) memory measurements, the tip resistor of the probe has been moved to the interposer circuit with its own set of S-parameters. The tip in the probe may have a 0.0 Ω resistor, which may result in raw probe S-parameters with large overshoot and long decay time of approximately 150 ns. The impedance of the probe tip may change from 50 kΩ to 50 Ω over a span of direct current (DC) (or zero Hz) to 25 MHz. Therefore, existing fixture de-embedding methods are not adequate to measure probe S-parameters in this frequency span because the resistance of the probe tip changes at these low frequencies.

[0006] Embodiments of the present disclosure address these and other deficiencies of the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Aspects, features and advantages of embodiments of the present disclosure will become apparent from the following description of embodiments with reference to the accompanying drawings, in which:

[0008] Figure 1 is an example of a device under test;

[0009] Figure 2 is connected to the fixture Figure 1 Examples of devices under test;

[0010] Figure 3 is connected to Figure 2 A simplified example of a fixture with a device under test;

[0011] Figure 4 is a block diagram of a test and measurement system according to some embodiments of the present disclosure;

[0012] Figure 5 It can be done by Figure 4 Examples of Smith charts utilized by test and measurement instruments in;

[0013] Figure 6 is an example of the time position of the desired signal and the actual measured signal;

[0014] Figure 7 is a flow chart illustrating example operations for determining scattering parameters of a device under test in a low frequency range according to an embodiment of the present disclosure;

[0015] Figure 8 is a flow chart further illustrating example operations for determining scattering parameters of a device under test in a low frequency range according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0016] Currently, as mentioned above, a vector network analyzer is used to measure the S parameters of a device under test in a frequency range of f1 to f2, where f1 is not equal to zero. A vector network analyzer is typically unable to measure at frequencies as low as DC. For a probe, a typical starting frequency value of f1 is 25 MHz. Embodiments of the present disclosure allow for measurement of the S parameters of a device under test from zero frequency (or direct current (DC)) up to f1.

[0017] Figure 1 An example of a device under test 100 is illustrated, which is shown as a high impedance probe, including three ports 102, 104, and 106. For frequencies between f1 and f2, the S parameters of the device under test 100 are measured using known methods. In some embodiments, for example, the device under test 100 may be a high impedance active probe. However, the embodiments of the present disclosure are not limited to the device under test as a probe, but may be any device under test that requires S parameters to be measured for a lower frequency range.

[0018] like Figure 2As illustrated in , the device under test 100 may be connected to the fixture 200. The S parameters of the fixture 200 from f1 to f2 are measured separately, and then the S parameters of the device under test 100 and the fixture 200 from f1 to f2 are measured together. Since the S parameters of the fixture 200 are known, the S parameters of the device under test 100 from f1 to f2 are obtained by de-embedding the S parameters of the fixture 200 from the measured S parameters of the device under test 100 and the fixture 200. The fixture 200 may have a source impedance input 202 of 50 Ohm.

[0019] However, now with interposers for double data rate (DDR) memory measurements, the tip resistors of the probes have been moved into the interposer circuitry with its own set of S parameters. An interposer is a device that is typically inserted between a memory integrated circuit (IC) chip and a printed circuit board on which the memory IC chip is typically mounted. An interposer is a small printed circuit board or flexible circuit that samples the signals between the memory IC chip and the printed circuit board. Test and measurement instruments such as oscilloscopes can be connected to the interposer through the probe to measure the signals. Because the tip resistors are moved into the interposer circuitry, the tips 102 and 104 in the device under test 100 can have 0.0 Ohm resistors, which can result in an original device under test S parameter set with large overshoot and long decay times (such as 150 nanoseconds). In the span from DC to f1, the impedance of the input tips 102 and 104 varies from 5 kOhm to 50 Ohm. Therefore, existing fixture de-embedding methods cannot adequately measure the S parameters in this frequency span.

[0020] Figure 3 A simplified model of the device under test 100 and the source is illustrated. In the model, ports 102 and 104 are considered as a single first differential port. Port 106 is considered as a single-ended port. As seen from the device under test 100, the impedance of the source 300 is 25 Ohm. It has been determined that in the frequency range of DC to f1, the main influencing factors of the step response of the device under test 100 are the differential sd11 and differential sd21 S parameters. Because other S parameters have very small effects, they can be included in the system transfer function using simple point replication or linear extrapolation in the range of DC to f1. If they are incorporated, each value can be used as part of the known value in the solution together with the S parameters measured in advance from f1 to f2, which is discussed in further detail below.

[0021] like Figure 4, the operation for determining the S parameters of the device under test 100 may include a test and measurement system 400 having a step generator 402 connected to the fixture 200 and the device under test 100, and a test and measurement instrument 404 such as an oscilloscope. The test and measurement instrument 404 may include one or more processors 406 and a memory 408. In some embodiments, the test and measurement instrument 404 may determine the S parameters of the device under test 100 from DC to f1. In other embodiments, a remote processor and other hardware may be used to determine the S parameters of the device under test from DC to f1 based on information received from the test and measurement instrument 404. Thus, although the following embodiments discuss the use of a processor 406 for ease of discussion, embodiments of the present disclosure are not limited to the use of a processor 406 in a test and measurement instrument 404.

[0022] As will be discussed in more detail below, to determine the sd11 and sd21 values ​​for the device under test 100, an initial estimate or guess for sd11 may be generated based on circuit simulation, and then multiple iterations may be performed switching between solving for sd21 and sd11 until a final value for each variable is found.

[0023] For example, Figure 5 As illustrated in , the processor 406 may use a Smith chart to estimate the value of sd11 used in an initial iteration of determining the values ​​of sd11 and sd21. Figure 5 An example of a Smith chart 500 is illustrated. Points 502, 504, 506, and 508 are determined based on S parameters 510 measured from f1 to f2. Points 502, 504, 506, and 508 are determined by extrapolation.

[0024] To begin determining sd11 and sd21 of the device under test 100, equation (1) illustrates the equation for Figure 3 A simplified S-parameter model of the device under test 100 is shown in FIG.

[0025] (1).

[0026] The fixture 200 is terminated with 50 Ohm at each point 202. Thus, as can be seen from the first differential probe tip ( Figure 3 The source impedance seen at the position of the tips 102 and 104 in FIG. 1 is 25 Ohms. This is expressed in equation (1) as a reflection coefficient of -1 / 3. For the differential mode case, this ratio is between 100 and 50 Ohms, so the reflection coefficient of the tip load is still -1 / 3. For example, , where 100 is the reference impedance for the differential case, and the probe tip load on one tip 102 is 25 Ohm, and the probe tip load on the other tip 104 is 25 Ohm, for a total of 50 Ohm.

[0027] To determine the S parameters sd11 and sd21, one can generate Figure 6 FIG. 6 shows an ideal step response D of the differential desired signal 600. The ideal step response D is the waveform at the tip of the device under test if the device under test 100 is removed from the circuit. The ideal step response D is Figure 6 The actual signal 602 is shown in FIG. 6 and is compared with the acquired step response X through the device under test 100 .

[0028] To mathematically obtain the actual signal X, the transfer function H from equation (1) is applied to the ideal signal D, as shown in equation (2):

[0029] (2)

[0030] Substituting equation (1) into equation (2) results in the system equation (3):

[0031] (3).

[0032] Equation (3) can be rearranged from its nonlinear form into a linear form as shown in equation (4). Equation (4) can then be used in a least mean square (LMS) calculation process, which will be described in more detail below. In equation (4), D is generated based on what the ideal step response of the probe should be and is used by the test and measurement instrument 404 Figure 4 The actual signal X is obtained by using the test and measurement system 400 shown in FIG.

[0033] (4).

[0034] The zero phase reference of the S parameters is at the beginning of the time domain record, such as Figure 6 . The desired step signal 600 is temporally positioned at the beginning of the time record, which is the zero phase reference position of the tip of the device under test. Due to the probe delay 604, the acquired actual step signal 602 can be shifted in time before solving equation (4) so ​​that its group delay is equal to the group delay of the differential sd21 of the probe. These group delays are accurately positioned within the sub-sample positions because any small error will cause the final filter created from the final probe S-parameters to exhibit a tilt in the step response.

[0035] The two data sets of the desired signal D 600 and the actual signal X 602 can be resampled to have the same length and frequency spacing as the measured S parameters of the device under test from f1 to f2. The signals D and X can be transformed into the frequency domain by taking derivatives and performing a Fast Fourier Transform (FFT). The frequency domain is the original domain of equation (4) as a starting point. In the following equations (5) and (6), x(t) and d(t) are the resampled step responses in the time domain:

[0036] (5)

[0037] (6).

[0038] Equation (4) above is the system equation that will be used as a starting point to solve for the unknown points of sd11 and sd21 in the frequency span from DC to f1. However, the solution to the LMS problem requires transforming the expression in terms of time domain samples. The Inverse Fast Fourier Transform (IFFT) cannot be used for this because it requires all samples to be known in the frequency domain. Therefore, a solution to the equation can be obtained by expressing it in terms of an Inverse Discrete Fourier Transform (IDFT), where the solution is decomposed into known values ​​relative to the unknown values ​​to be solved.

[0039] As mentioned above, the point from f1 to f2 is measured using known methods and may be stored in memory 408. Figure 5 The equivalent model circuit shown in Figure 1 is used to estimate the points of sd11 in the range from DC to f1. The expected signal and actual signal values ​​are obtained by calculating their derivatives and then calculating the fast Fourier transform. Therefore, the only unknown quantity to be solved in the initial equation (4) is the value of sd21 from DC to f1.

[0040] The IDFT definition is shown in equation (7):

[0041]

[0042] (7).

[0043] As is common, the exponential equation can be represented by W variables, which are often called twiddle factors. It is defined according to equation (8):

[0044] (8).

[0045] In practice, the length N of X, D, sd21, and sd11 will be equal to several thousand points. In order to simplify and understand the organization of the solution, an eight-sample example matrix setting configuration will be used to represent the IDFT performed on known and unknown sample points. Therefore, for ease of discussion below, N=8. However, as will be appreciated by those skilled in the art, in practice, N will typically be equal to several thousand points.

[0046] For the sample case, assume that the first two points of C are unknown, but the rest are known. In addition, the complex conjugate point of C(N) is also unknown. It is the complex conjugate of C(1).

[0047] The vector C of the system transfer function in the frequency domain is the right column vector in equation (9). Multiply C by the rotation matrix representing the IDFT to obtain the time domain samples of the solution. The time domain representation is still equal to zero, as shown in (9):

[0048] (9).

[0049] Substituting the variable C into the system equations, we obtain equation (10):

[0050] (10).

[0051] The frequency domain values ​​of the system equations are presented in the column of C values, and W is equal to the matrix of rotation values ​​required for the IDFT to transform to the time domain.

[0052] M is equal to the number of unknown points to be solved. In this example, M is equal to 2 for sd11 and sd21.

[0053] m := M … N – M.

[0054] Equation (10) can be reconstructed so that the unknown terms are on the left side of the equation and the known terms are on the right side of the equation, as shown in equation (11). In equation (11), C7 is equal to the conjugate of C1:

[0055] (11).

[0056] Let Y be equal to the known part of the IDFT vector on the right side of equation (11), and we get .

[0057] In equation (11), the conjugate of the unknown variables C(0) and C(1) are not independent. Therefore, to solve for C(0) and C(1), a P matrix can be created to separate the real and imaginary parts of each. Remember, the variable C is a system equation written in terms of sd21 and sd11 along with the desired step response D and the actual step response X. Once the value of C is solved, the desired sd21 or sd11 will be calculated based on the value of C.

[0058]

[0059] (12).

[0060] P is the transformation matrix that converts the array of C values ​​into arrays of equal length for the real and imaginary parts of the unknown values ​​to be solved.

[0061] make:

[0062] (13)

[0063] Substituting (13) into (12):

[0064] (14)

[0065] The LMS solution of (14) is:

[0066] (15)

[0067] (16).

[0068] The vector L in equation (16) contains the real and imaginary parts of the unknown values ​​of C being solved for.

[0069] The next step is to reassemble the real and imaginary parts of L back into the position of C and extract the unknown value. For the first iteration, an estimate of sd11 is used so that the value of sd21 can be extracted from L. Once sd21 is extracted, those values ​​are used to extract sd11 during the next iteration. That is, sd21 is extracted during odd-numbered passes, and sd11 is extracted during even-numbered passes, which will be discussed in more detail below.

[0070] To extract sd21 during odd-numbered rounds, equation (17) is used:

[0071] (17).

[0072] For even-numbered rounds, sd11 can be extracted using equation (18):

[0073] (18).

[0074] From f1 to f2, the original measurement points of the probe's sd11 and sd21 never change during the iteration. However, from DC to f1, after each round, the value of sd11 or sd21 is updated.

[0075] Once the final sd11 and sd21 values ​​are determined, the values ​​can be converted back to their single-ended values ​​of s32 and s31 for the three-port device under test. Equation (19) shows the mixed-mode derivative Sm in terms of single-ended S parameters:

[0076] (19).

[0077] At low frequencies, such as DC to f1, the S parameters s31 and s32 of the device under test 100 are well matched, resulting in s32 being equal to negative s31, as shown in equation (20):

[0078] (20).

[0079] According to the matrix in equation (19) above:

[0080] (twenty one)

[0081] Substituting equation (20) into equation (21) and solving for s31 and s32:

[0082] (twenty two)

[0083] (twenty three).

[0084] The values ​​of s12 and s21 of the impedance terms on the upper left side of equation (19) can be considered to be equal to zero.

[0085] Now we can find the values ​​of s11 single ended and s22 single ended. Also, assume that s12 and s21 single ended are zero:

[0086] (twenty four)

[0087] (25).

[0088] According to the mixed mode matrix in equation (19):

[0089] (26).

[0090] Equation (24) can be substituted into equation (26) to solve for s11 and s22 single-ended given sd11.

[0091] (27)

[0092] (28).

[0093] The determined S-parameter values ​​s11 , s22 , s32 , and s31 may then be saved in a memory of the device under test 100 for use during operation of the device under test 100 .

[0094] Figure 7 A flow chart for determining S parameters of a device under test for a low frequency range according to an embodiment of the present disclosure is illustrated. In operation 700, S parameters within a frequency range of f1 to f2 (where f1 is greater than zero) are determined or otherwise received using known methods.

[0095] In operation 702, initial estimates of s11 and s22 may be generated or determined based on an equivalent circuit model and a Smith chart to create an initial estimate of the probe tip s11. As mentioned above in equations 27 and 28, both s11 and s22 are equal to sd11. Therefore, these initial values ​​of s11 and s22 may be used as initial starting values ​​for sd11.

[0096] In operation 704, the actual signal may be acquired. This may be done using Figure 4 The test and measurement system 400 in FIG. 4 is accomplished by performing a large amount of averaging on an oscilloscope. A differential step generator 402 can be connected to two input ports 102 and 104 of the device under test 100 through a fixture 200. The device under test 100 can operate in a differential mode, and a differential waveform x(t) is acquired by the test and measurement instrument 404.

[0097] In operation 706, an expected step response signal d(t) is generated to represent the waveform at the tip of the device under test 100. The expected step response signal may be generated assuming that the device under test 100 has been de-embedded or may include all fixture effects. However, in some embodiments, since the waveform frequency points at low frequencies are relatively close to ideal at the device under test location, an ideal expected response may be used.

[0098] In operation 708, the desired step response d(t) and the actual step response x(t) may be resampled to match the record length and sampling rate represented by the S-parameters measured in operation 700 and may be transformed to the frequency domain D(f) and X(f) using equations (6) and (7) above.

[0099] In operation 710, the group delay of the converted actual signal X(f) and the converted desired signal D(f) are adjusted to match the group delay relative to the S-parameters of the device under test 100. To do this, the group delay of each variable is first calculated by taking the negative derivative of the phase of each variable expansion. The group delay of D(f) is adjusted to zero. This is because at the beginning of the time record, the S-parameter reference point of the device under test is at zero time. Therefore, the desired signal step must be at this time position relative to the S-parameter data of the device under test. The group delay of X(f) is adjusted to be equal to the group delay of the differential sd21 of the device under test 100.

[0100] In operation 712, a processor such as processor 406 or another remote processor may generate a system transfer function to solve for the differential sd21 and sd11, such as the transfer function of problem (4). However, embodiments of the present disclosure are not limited to the transfer function illustrated in equation (4). More complex transfer functions may be implemented that include more S parameters of the device under test and / or may include more details of the effects of the test fixture 200.

[0101] In operation 714, the S parameter values ​​of sd21 and sd11 are iteratively determined and then converted to single-ended values ​​using equations (19)-(28). The single-ended values ​​may then be stored in a memory of the device under test 100 for use during device operation.

[0102] Figure 8 Operation 714 according to some embodiments of the present disclosure is further illustrated in detail. The S parameters sd21 and sd11 are iteratively determined until a predetermined number of rounds (eg, Figure 8 ), or until the transfer function in equation (4) is within a predetermined tolerance of zero.

[0103] In operation 800, the number of rounds is set. Figure 8 In operation 802, the number of rounds is set to four, but any number of rounds may be used. The number of rounds may be set by a user or may be predetermined. In operation 802, it is determined whether the round is even or odd. If the round is odd, then in operation 804, sd21 is determined using equation (17) to solve for the value of sd21 from DC to f1. During the first round, the value of sd11 is the initial estimate from operation 502. In subsequent rounds, the value of sd11 is the value determined in operation 806 during the previous round.

[0104] If the round number is even, then in operation 806, sd11 from DC to f1 is determined using the last determined value of sd21 in operation 804 and equation (18). In operation 808, the system determines whether the round number is less than the total round number set for the system in operation 800. If so, in operation 810, the round value is incremented by 1, and the system returns to operation 802.

[0105] If the number of rounds is equal to the total number of rounds, then in operation 812, the determined values ​​of sd21 and sd11 are converted into single-ended values ​​of s32, s31, s11, and s22 for the S parameter model of the device under test 100 from DC to f1. These values ​​can be stored in the memory of the device under test 100 along with the S parameters measured from f1 to f2 to be used to perform accurate measurements during operation of the device under test 100.

[0106] Aspects of the present disclosure may operate on specially created hardware, firmware, digital signal processors, or on specially programmed computers including processors operating according to programming instructions. The terms "controller" or "processor" as used herein are intended to include microprocessors, microcomputers, application specific integrated circuits (ASICs), and dedicated hardware controllers. One or more aspects of the present disclosure may be embodied in computer-usable data and computer-executable instructions, such as embodied in one or more program modules executed by one or more computers (including monitoring modules) or other devices. In general, program modules include routines, programs, objects, components, data structures, etc., which perform specific tasks or implement specific abstract data types when executed by a processor in a computer or other device. Computer executable instructions may be stored on a computer-readable storage medium, such as a hard disk, an optical disk, a removable storage medium, a solid-state memory, a random access memory (RAM), etc. As will be appreciated by those skilled in the art, the functions of the program modules may be combined or distributed as desired in various aspects. In addition, the functions may be embodied in firmware or hardware equivalents such as integrated circuits, FPGAs, etc., in whole or in part. Certain data structures may be used to more efficiently implement one or more aspects of the present disclosure, and such data structures are contemplated within the scope of the computer-executable instructions and computer-usable data described herein.

[0107] In some cases, the disclosed aspects may be implemented in hardware, firmware, software, or any combination thereof. The disclosed aspects may also be implemented as instructions carried by or stored on one or more computer-readable storage media, which may be read and executed by one or more processors. Such instructions may be referred to as computer program products. As discussed herein, computer-readable media refers to any medium that can be accessed by a computing device. By way of example and not limitation, computer-readable media may include computer storage media and communication media.

[0108] Computer storage media refers to any medium that can be used to store computer-readable information. By way of example and not limitation, computer storage media may include RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital video disk (DVD) or other optical disk storage, cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, and any other volatile or non-volatile, removable or non-removable media implemented in any technology. Computer storage media excludes the signal itself and the temporary form of signal transmission.

[0109] Communication media refers to any medium that can be used for communication of computer-readable information. By way of example and not limitation, communication media may include coaxial cables, fiber optic cables, air, or any other medium suitable for communication of electrical, optical, radio frequency (RF), infrared, acoustic or other types of signals.

[0110] Example

[0111] Illustrative examples of the techniques disclosed herein are provided below. Implementations of the techniques may include any one or more of the examples described below and any combination of these examples.

[0112] Example 1 is a method for determining scattering parameters S parameters of a device under test for a first frequency range, comprising receiving the S parameters of the device under test for a second frequency range, the second frequency range being greater than the first frequency range; measuring an actual signal of the device under test; determining an expected signal of the device under test; and determining the S parameters of the device under test for the first frequency range based on the S parameters for the second frequency range, the actual signal of the device under test, and the expected signal of the device under test.

[0113] Example 2 is the method of Example 1, further comprising determining a starting value of a first S parameter for the first frequency range based on the received S parameter for the second frequency range; and determining the S parameter of the device under test for the first frequency range based on the starting value.

[0114] Example 3 is the method of Example 2, wherein determining S parameters of the device under test for the first frequency range includes iteratively determining first S parameters and second S parameters for the first frequency range within a plurality of rounds until a predetermined number of rounds are completed.

[0115] Example 4 is the method of Example 3, wherein during a first round, a second S parameter is determined using a starting value of the first S parameter, during each subsequent even-numbered round, the first S parameter is determined using an updated second S parameter determined during a previous odd-numbered round, and during each subsequent odd-numbered round, the second S parameter is determined using the updated first S parameter determined during a previous even-numbered round.

[0116] Example 5 is the method of any one of Examples 1 to 4, wherein determining S parameters of the device under test for the first frequency range includes determining differential S parameters of the device under test for the first frequency range and converting the differential S parameters to single-ended S parameters.

[0117] Example 6 is the method of any one of Examples 1 to 5, further comprising resampling each of the actual signal and the desired signal to match a record length; and converting the resampled actual signal and the resampled desired signal to the frequency domain.

[0118] Example 7 is the method of Example 6, further comprising adjusting a group delay of the converted resampled actual signal and the converted resampled desired signal to match a group delay of a device under test.

[0119] Example 8 is the method of any of Examples 1 to 7, further comprising storing S parameters of the device under test for the first frequency range in a memory of the device under test.

[0120] Example 9 is the method of any of Examples 1 to 8, wherein the first frequency range is between zero hertz and 25 megahertz.

[0121] Example 10 is a test and measurement system comprising: a step generator configured to generate a step signal; a test and measurement instrument configured to measure an actual response of a device under test based on the step signal; and one or more processors configured to determine an expected signal of the device under test, and determine scattering parameters S parameters of the device under test for the first frequency range based on the received S parameters of the device under test for a second frequency range greater than the first frequency range, the actual response of the device under test, and the expected signal of the device under test.

[0122] Example 11 is a test and measurement system of Example 10, wherein the one or more processors are further configured to determine a starting value of a first S parameter for a first frequency range based on the received S parameter for a second frequency range; and determine the S parameter of the device under test for the first frequency range based on the starting value.

[0123] Example 12 is the test and measurement system of Example 11, wherein determining S parameters of the device under test for the first frequency range includes iteratively determining first S parameters and second S parameters for the first frequency range until a predetermined threshold is met.

[0124] Example 13 is the test and measurement system of Example 12, wherein during a first iteration, the second S parameter is determined using a starting value of the first S parameter, during each subsequent even-numbered iteration, the first S parameter is determined using an updated second S parameter determined during a previous odd-numbered iteration, and during each subsequent odd-numbered iteration, the second S parameter is determined using the updated first S parameter determined during a previous even-numbered iteration.

[0125] Example 14 is the test and measurement system of Examples 10 to 13, wherein determining S parameters of the device under test for the first frequency range includes determining differential S parameters of the device under test for the first frequency range and converting the differential S parameters to single-ended S parameters.

[0126] Example 15 is the test and measurement system of any one of Examples 10 to 14, wherein the one or more processors are further configured to resample each of the actual response and the expected signal to match the record length; and convert the resampled actual response and the resampled expected signal to the frequency domain.

[0127] Example 16 is the test and measurement system of Example 15, further comprising adjusting a group delay of the converted resampled actual response and the converted resampled desired signal to match a group delay of a device under test.

[0128] Example 17 is the test and measurement system of any of Examples 10 to 16, wherein the device under test is a high impedance active probe.

[0129] Example 18 is the test and measurement system of any of Examples 10 to 17, wherein the first frequency range is between zero Hertz and 25 Megahertz.

[0130] Example 19 is one or more computer-readable storage media comprising instructions, which, when executed by one or more processors of a test and measurement instrument, cause the test and measurement instrument to measure an actual step response signal of a device under test; determine an expected step response signal of the device under test; and determine scattering parameter S parameters of the device under test for a first frequency range based on the received S parameters of the device under test for a second frequency range, the actual step response signal of the device under test, and the expected step response signal of the device under test, wherein the second frequency range is greater than the first frequency range.

[0131] Example 20 is one or more computer-readable storage media of Example 19, wherein the instructions further cause the test and measurement instrument to determine a starting value of a first S parameter for a first frequency range based on the received S parameter for a second frequency range; and determine the S parameter of the device under test for the first frequency range based on the starting value.

[0132] The previously described versions of the disclosed subject matter have many advantages that are described or should be apparent to those of ordinary skill. Even so, not all versions of the disclosed apparatus, system or method require these advantages or features.

[0133] Additionally, this written description mentions specific features. It is to be understood that the disclosure in this specification includes all possible combinations of those specific features. Where a specific feature is disclosed in the context of a particular aspect or example, the feature may also be used in the context of other aspects and examples to the extent possible.

[0134] Furthermore, when a method having two or more defined steps or operations is referred to in the present application, the defined steps or operations may be performed in any order or simultaneously, unless the context excludes those possibilities.

[0135] Although specific examples of the present invention have been illustrated and described for purposes of illustration, it will be appreciated that various modifications may be made without departing from the spirit and scope of the present invention. Accordingly, the present invention should not be limited except by the appended claims.

Claims

1. A method for determining scattering parameters S parameters of a device under test for a first frequency range, comprising: receiving S parameters of the device under test for a second frequency range, wherein the second frequency range is from a frequency f1 to a frequency f2, wherein f1 is greater than zero, and the first frequency range is from a frequency greater than or equal to a zero frequency DC to a frequency f1; measuring an actual signal of the device under test; Determining an expected signal of the device under test; as well as Based on the S parameters for the second frequency range, the actual signal of the device under test, and the expected signal of the device under test, the S parameters of the device under test for the first frequency range are determined.

2. The method according to claim 1, further comprising: determining a starting value of a first S parameter for the first frequency range based on the received S parameter for the second frequency range; as well as An S parameter of the device under test for the first frequency range is determined based on the starting value. 3 . The method of claim 2 , wherein determining the S parameters of the device under test for the first frequency range comprises iteratively determining the first S parameters and the second S parameters for the first frequency range in a plurality of rounds until a predetermined number of rounds are completed.

4. The method of claim 3 , wherein during a first round, the second S parameter is determined using a starting value of the first S parameter, during each subsequent even-numbered round, the first S parameter is determined using an updated second S parameter determined during a previous odd-numbered round, and during each subsequent odd-numbered round, the second S parameter is determined using the updated first S parameter determined during a previous even-numbered round. 5 . The method of claim 1 , wherein determining the S parameters of the device under test for the first frequency range comprises determining differential S parameters of the device under test for the first frequency range and converting the differential S parameters into single-ended S parameters.

6. The method according to claim 1, further comprising: resampling each of the actual signal and the desired signal to match the record length; as well as Convert the resampled actual signal and the resampled desired signal to the frequency domain.

7. The method of claim 6, further comprising adjusting a group delay of the converted resampled actual signal and the converted resampled desired signal to match a group delay of a device under test. 8 . The method of claim 1 , further comprising storing S-parameters of the device under test for the first frequency range in a memory of the device under test.

9. The method of claim 1, wherein the frequency f1 is 25 MHz and the first frequency range is between zero Hz and 25 MHz.

10. A test and measurement system comprising: a step generator configured to generate a step signal as an input to a device under test; a test and measurement instrument configured to measure an actual response of a device under test based on the step signal; and One or more processors configured to: receiving an actual response of the device under test from the test and measurement instrument, Determine the expected signal from the device under test, and Based on the received S parameters of the device under test for the second frequency range, the actual response of the device under test and the expected signal of the device under test, scattering parameters S parameters of the device under test for the first frequency range are determined, wherein the second frequency range is from frequency f1 to frequency f2, wherein f1 is greater than zero, and the first frequency range is from a frequency greater than or equal to zero frequency DC to frequency f1.

11. The test and measurement system of claim 10, wherein the one or more processors are further configured to: determining a starting value of a first S parameter for the first frequency range based on the received scattering parameters for the second frequency range; and S parameters of the device under test for a first frequency range are determined based on the starting values. 12 . The test and measurement system of claim 11 , wherein determining S parameters of the device under test for the first frequency range comprises iteratively determining first S parameters and second S parameters for the first frequency range until a predetermined threshold is met.

13. The test and measurement system of claim 12 , wherein during a first iteration, the second S parameter is determined using a starting value of the first S parameter, during each subsequent even-numbered iteration, the first S parameter is determined using an updated second S parameter determined during a previous odd-numbered iteration, and during each subsequent odd-numbered iteration, the second S parameter is determined using the updated first S parameter determined during a previous even-numbered iteration.

14. The test and measurement system of claim 10, wherein determining S parameters of a device under test for a first frequency range comprises determining differential S parameters of the device under test for the first frequency range and converting the differential S parameters to single-ended S parameters.

15. The test and measurement system of claim 10, wherein the one or more processors are further configured to: resampling each of the actual response and the desired signal to match the record length; and Convert the resampled actual response and the resampled desired signal to the frequency domain.

16. The test and measurement system of claim 15, further comprising adjusting a group delay of the converted resampled actual response and the converted resampled desired signal to match a group delay of a device under test.

17. The test and measurement system of claim 10, wherein the device under test is a high impedance active probe.

18. The test and measurement system of claim 10, wherein the frequency f1 is 25 MHz and the first frequency range is between zero Hz and 25 MHz.

19. One or more computer-readable storage media comprising instructions that, when executed by one or more processors of a test and measurement instrument, cause the test and measurement instrument to: Measure the actual step response signal of the device under test; Determining an expected step response signal of the device under test; as well as Based on the received S parameters of the device under test for a second frequency range, the actual step response signal of the device under test, and the expected step response signal of the device under test, scattering parameter S parameters of the device under test for a first frequency range are determined, wherein the second frequency range is from frequency f1 to frequency f2, wherein f1 is greater than zero, and the first frequency range is from a frequency greater than or equal to zero frequency DC to frequency f1.

20. The one or more computer-readable storage media of claim 19, wherein the instructions further cause the test and measurement instrument to: determining a starting value of a first S parameter for the first frequency range based on the received S parameter for the second frequency range; and An S parameter of the device under test for the first frequency range is determined based on the starting value.

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