S-parameter measurements of time domain reflectometry and transmission-EEWORLD

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S-parameter measurements of time domain reflectometry and transmission

Among the three basic electrical characteristic test and measurement instruments in the frequency domain, time domain, and impedance domain, the impedance domain test and measurement instruments have the most complex circuit structure, the most time-consuming test operation, and the highest price as a set. Currently, there are only a few companies that can supply GHz-level impedance domain test and measurement instruments, especially vector network analyzers (VNA), which are only produced by Agilent, Anritsu, Rohde & Schwarz, etc. The maximum bandwidth of VNA reaches 65GHz, and the use of a frequency converter at the front end can expand the bandwidth to 120GHz. The price of a set is more than US$200,000.

We know that any electronic component can be characterized by a two-terminal or four-terminal network, and the parameters used are Z (impedance), Y (conductance), H (mixing) and S (scattering). Since the measurement of Z, Y and H parameters involves open circuit and short circuit conditions, which are not easy to achieve in the GHz frequency band, VNA measures S parameters under impedance matching conditions. Ten years ago, some test and measurement experts tried to start with the measurement of time domain-frequency domain characteristics, and transformed the amplitude-time characteristics into discrete amplitude-frequency characteristics through fast Fourier function transformation, and derived S parameters on this basis. The entire test process and measurement conditions are the same as those for directly measuring S parameters, except that the excitation source is changed from a sweep generator to a step pulse generator, and S parameters are derived from time domain reflection (TDR) and time domain transmission (TRT) parameters.

The simplest two-port S scattering matrix of a physical coaxial line connection point is shown in expression (1), which is defined by the four Sij parameters of the incident wave and the reflected wave at the input port and the output port. The voltage V and current I of each port are composed of the incident wave V+, I+ and the reflected wave V-, I-, respectively, that is, V=V++V- and I=I++I-. From expression (1) and Figure 1a, it can be seen that S11 is the input port voltage reflection coefficient, S12 is the reverse voltage gain, S21 is the forward voltage gain, and S22 is the output port voltage reflection coefficient. All S parameters are obtained under the condition of matching the input and output impedance of the coaxial line.

1a Two-port network

1b Four-port network

Figure 1 S parameter array

In the case of four ports in Figure 1b, the S scattering matrix is much more complicated. It is expanded from a two-port matrix and is defined by four groups of 16 Sij parameters, see expression (2).

Transformation and inverse transformation between time domain and frequency domain

Computing technology and digital processing have promoted the application of Fourier transform. Fast Fourier transform (FFT) and inverse Fourier transform (IFFT) enable the time-frequency domain transformation of digital sampling oscilloscopes to complete complex calculations of 1024 samples within 1ms. The discrete time-frequency domain relationship is shown in Figure 2. The left side of the figure is a step pulse, which is sampled by an extremely short pulse △t, and the time window is equal to N△t. The right side of the figure is the frequency component after FTT operation, and the corresponding frequency increment is equal to △f=1/N△t, where N is the number of sampling points. Figure 2 is also the basis of digital sampling oscilloscopes, which sequentially sample fast pulse transients with extremely short unit pulses △t, and then reconstruct fast pulse waveforms in a lower time domain. At present, the △t of digital sampling oscilloscopes is less than 10ps and the equivalent bandwidth reaches 100GHz. Its bandwidth exceeds the 65GHz of vector network analyzers, making it the highest bandwidth measurement instrument.

Figure 2 Principle of time domain-frequency domain transformation

Digital sampling oscilloscopes are mainly used to measure basic pulse parameters of fast transients, such as rise, fall, overshoot, jitter time, etc. They also use the time domain reflection (TDR) and time domain transmission (TDT) characteristics of coaxial lines, cables, microstrip lines, coaxial components and connectors. Its resolution can reach 1mm to measure the reflection coefficient, transmission coefficient and impedance from short circuit to open circuit. Ten years ago, test and measurement experts have confirmed that it is feasible to derive S parameters through TDR/TDT measurement with the help of FFT transformation and inverse transformation. At that time, the equivalent bandwidth of the digital sampling oscilloscope was not high enough, the computer operation time of FFT transformation was not fast enough, and the coaxial calibration components were not accurate enough. Only laboratory measurement results were obtained, and the equivalent bandwidth was about 10GHz. Now the measurement conditions have been greatly improved, and the S parameter measurement based on TDR/TDT has changed from laboratory results to practical results.

Figure 3 Analogy between time domain reflection/transmission parameters and S parameters

The sampled data of the S parameter measurement based on TDR/TDT is first obtained from the digital oscilloscope, and then the sampled data is transformed into the S parameters in the frequency domain using a calculation program. For example, the four TDR/TDT values of the two ports are equivalent to four S parameters, namely forward TDR→S11, forward TDT→S21, reverse TDR→S22, and reverse TDT→S12, as shown in Figure 3. The simplest measurement configuration is a digital sampling oscilloscope with a TDR/TDT plug-in, a fast step pulse generator, a coaxial line calibration tool, and a time domain-frequency domain conversion program, as shown in Figure 4. The standard configuration of RF instruments is coaxial line and coaxial connector output, that is, single-ended output with the shell grounded, rather than differential double-ended output. In order to measure parallel microstrip structures or differential signals, a TDR/TDT plug-in with differential output is required. The calibration tool usually uses the short-circuit-open-load-through (SOLT) calibration technology, and a kit is provided according to the coaxial line model. The purpose is to establish a calibration plane to eliminate the error introduced by the measurement system and improve the accuracy of the measurement results. The calibration plane is actually the time reference zero point between the measurement fixture and the components under test. The output impedance of the measurement system in front of the calibration plane should be in a completely matched state, as shown in Figure 5.

Figure 4 Composition of the time domain reflectometry system

Figure 5 Matching of the time domain reflectometry system

Several S-parameter measurement devices based on TDR/TDT

Currently, there are three test and measurement instrument companies that supply a complete set of S-parameter measurement equipment based on TDR/TDT. They are Agilent's 86100C series digital sampling oscilloscopes and TDR modules, Tektronix's DSA8200 digital serial analyzer and 80E10 and other TDR plug-ins, and LeCroy's WaveExpert sampling oscilloscope and ST-20 TDR module. The following briefly introduces their characteristics.

Agilent's DCA86100 digital communication analyzer consists of an 86100C mainframe and two 54754A differential TDR modules, with a built-in tunnel diode step pulse generator and a rise time of <25ps. With the support of 86100C Option 202 (enhanced impedance and S parameter measurement) software, the DCA86100 has an 18GHz bandwidth, can measure 32 S parameters, and display 6 S parameters at the same time. It has a wide range of calibration and measurement functions and a dynamic range of more than 45dB. The S parameter measurement results based on TDR/TDT are compared with the measurement data of Agilent's PNA series four-port 20GHz precise vector network analyzer. The two results are highly matched within the frequency range of 10GHz. Figure 6 is a comparison curve of the input port differential loss SDD11. The red curve is measured by the VNA method and the blue curve is measured by the TDR/TDT method, which proves that the S parameter measurement technology based on TDR/TDT has a high degree of credibility.

The DCA86100 host can also be equipped with the 86118A single-ended dual-channel module, which has a bandwidth of up to 70GHz, and uses a remote probe to shorten the distance between the TDR/TDT reference plane and the measured component. However, the rise time of the 86118A step pulse generator is about 25ps. In order to fully utilize the S parameter measurement capability of 70GHz bandwidth, a step pulse generator with a rise time of <10ps is required. The 4020 pulse enhancement module of the third-party PSPL (Picosecond Laboratory) provided by Agilent can generate a step pulse signal of <9ps. The TDR/TDT-based S parameter measurement equipment equipped with the 86118A/4020 module represents the highest level currently achieved.

Tektronix's DSA8200 digital serial analyzer is mainly used to measure various high-speed serial link network characteristics, including time domain reflection, S parameters, signal reliability and noise. Currently, the DSA8200 has the lowest noise and time jitter in the industry, and provides a variety of plug-ins, from bandwidth options of 10GHz to 70GHz, and the rise time of the step pulse generator is 12ps. For example, the DSA8200 with the 80E10 sampling plug-in has a bandwidth of 70GHz and a dynamic range of 70dB. Up to 8 80E10 plug-ins can be installed to achieve 8-channel input, which facilitates the measurement of multi-port S parameters. Tektronix also provides differential TDR/TDT sampling plug-ins.

The software used by DSA8200 for S parameter measurement based on TDR/TDT is IConnect, which has a sampling point of 1M points, simplifies the calibration process, improves measurement accuracy, and shortens measurement time. DSA8200 uses differential TDR/TDT measurement to obtain the following S parameter bandwidths:

In the above figures, the incident wave rise time is the rise time of the step pulse generator. For 80E10, a rise time of 12ps can obtain a 50GHz bandwidth for S parameter measurement. At this time, the S parameters of the 1mm discontinuity point of the short-distance coaxial line and the 100m long cable combination can be measured. In this measurement environment, S parameter measurement based on TDR/TDT is more convenient and accurate than VNA technology, and provides more information.

Figure 6: Comparison of S parameters obtained by two measurement methods

LeCroy's WaveExpert digital sampling oscilloscope, combined with the ST-20TDR module, can achieve single-ended and differential S-parameter measurements based on TDR/TDT. The sampling oscilloscope has a bandwidth of up to 100GHz. It uses a sampling head provided by PSPL, which is currently the highest level sampling component in the industry. The bandwidth of the ST-20 module is 20GHz, the step pulse time is 20ps, and the sampling point acquisition length is 100,000 points. Obviously, the S-parameter measurement bandwidth of the ST-20 module still has the potential to be improved, and LeCroy will launch better S-parameter measurement equipment based on TDR/TDT.

PSPL mentioned above is a supplier of picosecond pulse measurement instruments. Its products include general and special pulse generators and step pulse generators, sampling oscilloscope modules and sampling gates, etc. If users need to expand the characteristics of the S parameter measurement equipment of the above three companies or build S parameter measurement equipment by themselves, they can consider using the company's products as the preferred components.

Misunderstandings of S-parameter Measurement Based on TDR/TDT

In order to correctly use the S-parameter measurement method based on TRD/TRT, it is necessary to avoid some misconceptions, mainly as follows:

First, it completely replaces VNA. VNA can measure active and passive components and is the most comprehensive and accurate device in the impedance domain measurement instrument. Currently, S parameter measurement based on TRD/TRT can only solve the passive S parameter measurement of coaxial lines, cables, etc., and VNA is used as the standard for measurement comparison.

Second, choose a digital storage oscilloscope with a high sampling rate. The bandwidth of a digital storage oscilloscope depends on the increase in sampling rate, but the bandwidth of S-parameter measurement based on TRD/TRT has nothing to do with the sampling rate, but depends on the rise time of the step pulse. Therefore, for measurement based on TRD/TRT, there is no need to use the most comprehensive digital storage oscilloscope with the highest sampling rate among time domain measurement instruments. You only need to use a digital sampling oscilloscope.

Third, VNA has the lowest background noise. VNA uses bandpass filters and digital filters, which have very low background noise. Similarly, digital sampling oscilloscopes use multiple averaging operations, which can also significantly improve the signal-to-noise ratio. The low frequency of VNA starts from 100KHz or 1MHz, while the low frequency of TRD/TRT extends to DC, and the latter has better low-frequency characteristics.

Fourth, the dynamic range of TDR/TDT-based measurements is low. In the early days, the dynamic range of TDR/TDT measurements was only 40dB. In recent years, progress has been made, and the dynamic range has been expanded to 70dB when the bandwidth is above 20GHz. In addition, the dynamic range has been further improved by using data multiple averaging noise reduction technology, providing sufficient dynamic range for S parameter measurements of coaxial cables, microstrips, and cables.

Conclusion

S parameter measurement based on TDR/TDT is a successful measurement technology. In the past, the two domains were connected through time domain-frequency domain transformation and inverse transformation. Now, the three domains of time, frequency and impedance are connected through time domain-frequency domain transformation-S parameter calculation. The prospect of inter-domain intercommunication measurement technology is even broader.

VNA is the most advanced and expensive equipment among test and measurement instruments. Generally, laboratories do not have the means to measure the S parameters of RF/microwave, while digital sampling oscilloscopes are easier to have. It has been proven that the TDR/TDT, which is built on the basis of digital sampling oscilloscopes, is an S parameter measurement device, and the cost is less than half of VNA. If we consider that the price of a single VNA is 200,000 to 300,000 US dollars, saving 100,000 to 150,000 US dollars is a considerable expense. In addition, VNA requires skilled engineering and technical personnel to operate, and the measurement time is more than half an hour. The operation of S parameter measurement based on TDR/TDT is relatively simple, and the measurement time only takes a few minutes. It is indeed a measurement method that saves money, effort, and time.

Reference address：S-parameter measurements of time domain reflectometry and transmission

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