distance-to-fault is spelled tdr or vna

Distance-to-Fault Is Spelled TDR or VNA


Written by Tom Lecklider, Senior Technical Editor

Time-domain reflectometry (TDR) is a very simple concept. A voltage pulse or step is applied to the end of a cable, and the reflections are measured and analyzed. As with most simple concepts, the detailed implementation determines how well practice conforms to theory.

Anritsu MS202xC/MS203xC VNA Master

Because electrical signals typically propagate at about two-thirds the speed of light (C), the transit time for a voltage step can be very short. The speed of light is approximately 3E8 m/s, 2E8 m/s for an electrical sig-nal, so it takes a voltage step 5 ns to travel 1 meter. TDR measurements are based on reflections, which means that twice the distance must be tra-versed. For a TDR, a 10-ns period is roughly equivalent to 1 meter or 40 -inches.

To determine details of faults within a 1-m length of cable requires a sampling rate significantly faster than 100 MS/s—the rate corresponding to a 10-ns period. For this reason, many TDRs are based on sampling scope techniques that use equivalent time sampling (ETS). Interleaved random sampling is a faster form of ETS found in some high-bandwidth DSOs. And, LeCroy has developed a coherent interleaved sampling technique that also is a form of fast ETS.

In these techniques, a repetitive signal is required. All types of ETS recon-struct a representative waveform from samples taken on successive repe-titions of the signal. The basic sampling scope approach acquires only one point from each repetition but successively delays the sampling instant slightly more from one to the next. This technique is limited by jitter in the trigger circuitry and uncertainty in the delay between the trigger and sampling instant. Nevertheless, 50-GHz bandwidth and equivalent sampling rates of hundreds of gigasamples/second are available.

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As an example of a TDR instrument that uses this technique, Mohr and As-sociates claims 0.003-in. horizontal resolution in the Model CT100. The datasheet lists the time-base resolution as 760 fs. Solving the equation

gives X = 0.003 in. The 0.003-in. resolution is claimed for any length cable up to the maximum 30,000-ft range. This implies that the trigger-to-sample delay setting has a resolution of 760 fs although it is called time-base resolution.

The CT100 datasheet also quotes a 250-kS/s maximum sampling rate that can generate up to 500 complete TDR frames per second. For cables shorter than 100 meters, the total step transit time is less than 1 µs. The time between 250-kS/s samples is 4 µs. This means that for relatively short cables the instrument can launch steps and acquire reflections at a 250-kS/s rate, developing complete 500-point TDR displays at a 500-Hz rate.

Such a high update rate allows real-time applications to be addressed, as described by Brandt Mohr, the company’s chief technology officer. “We have several customers who routinely use our equipment to characterize dynamic switch and button impedance down to 2-ms intervals.”

This is only practical if each reflected signal is nearly identical during the time required to build a frame. Otherwise, the ETS image will not corres-pond to the actual device characteristics. The total transit time for very long cables limits the TDR frame rate that can be achieved.

Vertical resolution is equally important and another advantage of ETS. Be-cause the rate at which the ADC actually is running is low, very high-resol-ution devices can be used—14-bit and 16-bit being common. High-speed direct-sampling DSOs are limited to 8-bit resolution and may not be cap-able of distinguishing very small perturbations in a reflected signal. When DSOs are used in TDR applications, averaging can improve vertical resolu-tion at the expense of greater acquisition and processing time.

Because S parameters are defined as ratios of incident and reflected waves, they can be determined by a TDR. Alternatively, you could use a vector network analyzer (VNA). There is some truth to the observation that engineers accustomed to working with scopes in the time domain prefer TDRs while RF and microwave engineers are more comfortable with VNAs. However, there are fundamental instrument differences as well as user preferences.

Agilent Technologies supports both conventional TDR- and VNA-based dis-tance-to-fault (DTF) measurement. Robert Sleigh, product marketing en-gineer, digital test division—scopes, explained, “Modeling and simulation are most accurate when using S-parameters that have frequency content that spans from DC to the bandwidth of the system. TDR-based measure-


ments have an advantage because they yield S-parameters that include lower frequency content than typical VNA solutions.

“On the other hand,” he continued, “TDR instruments use wide-bandwidth receivers that do not have the dynamic range of the tuned narrow-band-width receiver used in a VNA. As a result, high-frequency amplitude and phase information suffer when measuring devices having high loss or crosstalk. For this reason, signal-integrity engineers often combine S-para-meter measurements from TDRs and VNAs to yield a single high-quality S-parameter file covering low and high frequencies with excellent amplitude/phase fidelity.”


Under the TDR Hood

The shape and speed of the step edge are critical in a TDR. Distortion ahead of or following the rising edge causes reflections that appear to come from nonexistent faults in the wrong places. The speed of the edge determines the spatial resolution. The closest two faults can be in time and still remain distinguishable is

A 200-ps edge corresponds to a 100-ps separation or about 10 cm.

It is possible to work with rise times as short as 10 ps, but the faster the edge, the more important the cabling and connectors become to the over-all system performance. As a guide, a rising edge contains frequencies as high as 70% of the inverse of the rise time. As a result, you are cabling 70-GHz components when applying a 10-ps edge. Obviously, poor-quality cables or connectors will degrade the edge rate and perhaps cause aberra-tions as well.

Dr. Alan Blankman, technical product marketing manager, signal integrity at LeCroy, commented on the shape of the pulse used in the company’s SPARQ Signal Integrity Network Expert instrument, “The TDR pulse has a frequency content that is different from that used by other TDR instru-ments and rises toward 40 GHz rather than being flat. This rising fre-quency response plays an important role in achieving the 50-dB dynamic range, giving us about a 12-dB improvement over a flat pulse shape. A typical TDR pulse has frequency content that is falling, which causes prob-lems for achieving high dynamic range.”

A Tektronix application note explains that you may not want to examine your PCB traces or cabling using the fastest possible TDR edge. Impedance variations no doubt will exist and cause aberrations in the reflected pulse, but the real signals carried by the traces or cables may not be affected by them. For example, anomalies extending over a cable length equivalent to a few hundred picoseconds won’t have much effect on the 1-ns rise time typical of an ECL logic gate output.1

Conversely, an Agilent application note examines the spatial resolution im-provement possible when a Picosecond Pulse Labs Model 4015C Pulse Generator is used to develop a 15-ps rise-time TDR pulse. The results are contrasted with those obtained using Agilent’s standard 40-ps rise-time pulse generator built into the Model 86100A Infiniium Digital Communica-tions Analyzer (DCA). For this exercise, the DCA is used as a general-pur-pose 50-GHz sampling scope.2

At these speeds, the effect of the 50-GHz bandwidth sampling head cannot be ignored because its 9-ps rise time significantly interacts with the 15-ps edge. Agilent deconvolves the measured result to remove this effect as


well as imperfections in the actual test pulse. Deconvolution includes di-gital filtering that allows test pulses to be simulated with faster or slower rise times than the real 15-ps pulse.

Equally as important as the post-processing, the 4015C Generator is about the size of a coaxial attenuator and can be operated remotely, connected directly to the DUT. This eliminates cabling and connections that otherwise would slow down the edge speed. The Picosceond Pulse Labs Model 4005 is a current product that also uses remote pulse heads and provides an 11-ps edge rate.

Chris Loberg, senior technical marketing manager at Tektronix, discussed the importance of remote sampling heads used with the company’s mul-tichannel TDRs based on the DSA8200 Series Mainframe: “The remote 80E10 sampling heads enable location of the TDR’s sampler as near as possible to the measurement plane being observed while ensuring the best signal fidelity. The intelligent TDR modules characterize crosstalk by using TDR steps to drive one line while monitoring a second line with the other channel.”

Inside the VNA-Based IFFT

VNAs perform frequency-domain reflectometry (FDR) by successively ap-plying a series of increasing frequency sine waves to the DUT and measur-ing the reflections. Because the VNA’s receiver is narrowband and tuned to the same frequency being applied, a high dynamic range results.

The frequency-domain data is transformed by an inverse FFT (IFFT) to yield a time-domain DTF result comparable to a TDR waveform. For an IFFT, the time span is the reciprocal of the frequency resolution, and the time resolution is equal to 1/(2F) where F is the highest frequency.

As an example, consider testing a coaxial cable with propagation speed of 0.66 C from DC to 2.5-GHz maximum frequency. The corresponding time interval is 200 ps or 2 cm. If 500 frequency steps of 5 MHz each are used, the total time span is 200 ns or 20 m. For both the time span and resolu-tion, a factor of 2 has been included to account for the sum of the incident and reflected distance. Increasing the size of each step as well as the max-imum frequency improves resolution but shortens the alias-free range.

According to Mohr and Associates’ Brandt Mohr, “Aliasing is inherent in the IFFT and exhibited as a repetition of the time-domain waveform after a dis-tance proportional to the inverse of the frequency step size—the alias-free range. Although newer VNAs can acquire many data points to increase the alias-free range, this weakness still hinders the use of VNA or FDR tech-niques, especially for cable testing.”

National Instruments’ (NI’s) David Broadbent, product marketing manager RF and wireless test at the company, elaborated on the use of a VNA for time-domain testing. “With a VNA, you have three different modes of oper-ation for a time-domain measurement: band-pass, low-pass step, and low-


pass impulse,” he said. “The low-pass step mimics a TDR measurement and requires a DC path. The low-pass impulse mode features high resolu-tion and is used for in-depth examination of effects caused by closely spaced components. Finally, the band-pass mode has unlimited frequency span.”

A good example of the band-pass technique was included in a paper de-livered at the 2010 International Wire and Cable Symposium (IWCS).3

A frequency band from DC to 200 MHz is used for one test, and a separate configuration with the same 200-MHz band but positioned between 1,700 and 1,900 MHz is used for a contrasting test. The IFFT performed on both sets of data has an 8-µs maximum alias-free time corresponding to a 125-kHz frequency increment. A total of 1,600 frequency measurements is re-quired.

For the baseband case, the time interval is equal to 1/(2 x 200) µs or 2.5 ns, and the resulting time-domain waveform is shown as the blue trace in Figure 1. The pass-band configuration has a highest frequency of 1,900 MHz, which corresponds to a time interval of 1/(2 x 1,900) µs or 263 ps. If the frequency increment remains at 125 kHz, the time span still is 8 µs, but 15,200 frequency points now are needed.

Figure 1. Comparison of Baseband and Pass-Band VNA-Based DTF Measurement © 2010 IWCS

For an IFFT based on VNA frequency measurements made in the band-pass mode, the highest frequency still sets the time interval. But, all fre-quencies below the lower frequency and down to DC can be thought of as being zero-padded. That is, the IFFT is computed as though the frequency samples existed at the prescribed frequency spacing all the way from DC to the highest frequency. But, because of the zero padding, complex sinus-oids only exist between the lowest and highest frequencies. These will be added together to reconstruct the time-domain waveform as shown by the red trace in Figure 1.4

According to the IWCS paper, “...system output is the cable reflection re-sponse convolved with... [the] input functions. [The higher frequency test]...is capable of resolving smaller point defects while [the lower fre-quency test] sees further into the cable due to the lower frequency con-tent where the medium has lower loss.”3


Finally, a paper written by Yuenie Lau of Anritsu discusses possible inac-curacies in VNA-derived DTF measurements: “The side lobes from any peak reflection [are] the result of the IFFT mathematics conversion from return loss in frequency to return loss in distance.... There will be interac-tion between side lobes from different peaks if those peaks are in close proximity to each other. Windowing can help to minimize the side lobes, but there are pitfalls associated with different types of windowing.”5

The paper describes the effects of the types of windowing built into the Site Master Series of hand-held cable and antenna analyzers. Similar con-siderations apply to the recently introduced VNA Master™ and LMR Mas-ter™. “By displaying the narrowest peak, the rectangular windowing is able to display more details for a given distance resolution, but it also dis-plays the most side lobes for any given peak. The [nominal-, low-, and minimum-side lobe] windowing filters out some or all of the side lobes but at the expense of widening the peak’s width....”5

Trade-Offs and Applications

NI’s Mr. Broadbent described a customer’s application that required open and short identification on-board an airplane. Portable instruments didn’t have the desired performance. NI’s PXIe-5630 6-GHz 2-port VNA occupies only two chassis slots and has a dynamic range greater than 100 dB. This type of solution allowed the customer to retain the advantages of a VNA for his purposes but within tight space constraints.

In a separate application, an Agilent TDR helped NASA locate the faulty feedthrough connector to the external fuel tank that grounded the space shuttle in December 2007. The TDR was used to pulse a twisted pair wire that was more than 170 ft long with multiple connectors. The TDR isolated the problem to an open in the feedthrough connector that was approxim-ately 140 ft away from the TDR output.

Mike Resso, signal integrity applications scientist at Agilent, highlighted some of the pros and cons associated with TDRs and VNAs. TDRs are easier to use and calibrate and generally cost less. The wide bandwidth re-ceiver inherently has a higher noise floor. Also, when the time-domain data is processed by the FFT to produce S-parameters, many details of the FFT implementation and parameter assumptions come into play. It be-comes particularly difficult to correlate answers when multiple FFT al-gorithms have been used. In contrast, a VNA has a greater dynamic range and well-established error-correction techniques such as short-open-load-through (SOLT), through reflect line, and automatic fixture removal.

Pico Technology’s Jeff Bronks discussed Redmere Technology’s use of the PicoScope 9211A TDR/TDT to test 3.4-Gb/s and 6-Gb/s active cable equal-izers. The USB-connected instrument has a built-in step generator and al-lowed the company to characterize cables in the field instead of having to ship them back to the lab. Mr. Bronks concluded, “A VNA may still be used at the design stage to give the most accurate possible results but is too


slow and expensive for the production line. TDR/TDT is the most econom-ical way to test mass-produced components.”

It’s helpful to remember that neither a TDR nor a VNA actually determines distance to a fault but can only measure time. The accuracy with which a cable’s propagation speed is known determines how well time can be re-lated to distance.

Strengths and Weaknesses

Agilent has developed separate application notes, one favorable to TDRs2

and another to VNAs6, each no doubt written by the relevant company di-vision. Tektronix favors TDRs while acknowledging that electronic calibra-tion removes most of the time-consuming setup required for a VNA. But, the company’s DSA8200 Series Mainframe can accommodate up to eight TDR channels while automated VNA calibration typically is limited to four.

Dr. Andrew Dawson, sales manager, business development at Gage Ap-plied Technologies, highlighted the importance of bandwidth in a TDR. “Of-ten overlooked but almost as important as a digitizer’s sampling rate is its analog bandwidth. If the bandwidth is significantly lower than half the di-gitizer’s sampling rate—the Nyquist frequency—then the reflected signals will be smoothed over several sample points. Users should ensure that both the bandwidth and sampling rate of a reflectometer system are suffi-cient to fulfill their spatial resolution requirements.”

There is general agreement that a VNA is more accurate than a TDR and that a TDR is better suited to lower frequencies and a VNA to higher ones. Nevertheless, even within these areas there can be complicating implica-tions.

Anritsu’s David Witkowski, product manager microwave measurement di-vision, explained, “A TDR’s pulse energy is largely contained near DC and at lower frequencies. To achieve reasonable dynamic range, the TDR has to emit a stronger pulse to get the same result as achieved by using FDR. Because of this, there are cases in which a TDR can’t be used because it will damage active devices in the DUT.”

Of course, TDR manufacturers can make counterclaims based on features such as the internal calibration systems on the Mohr and Associates CT100 TDR claimed to ensure 1% accuracy over the 0°C to +50°C operating range. Similarly, LeCroy’s Dr. Blankman cited SPARQ’s wavelet denoising algorithm that helps achieve the instrument’s 50-dB dynamic range at 40 GHz. SPARQ also includes an internally connected SOLT calibration kit that supports automatic calibration.


Figure 2. Comparison of TDR-Based and VNA-Based Insertion Loss Measurement Data Courtesy of Samtec7

In addition to discussing the differences between TDR and VNA cable test-ing, it’s helpful to emphasize the importance of having multiple ways of determining S-parameters and time-domain behavior. The results can be nearly the same for each method as shown in Figure 2. Each type of in-strument has its strengths and weaknesses, so there is no clear-cut winner in every situation.


References

1. TDR Impedance Measurements: A Foundation for Signal Integrity, Tek-tronix, Application Note, 2008.

2. Faster Risetime for TDR Measurements, Agilent Technologies, Applica-tion Note 5988-3424EN, 2001.

3. Hayes, T. and Cook, C., “A Comparison of Time and Frequency Domain Reflection Measurement Methods on Metallic Transmission Lines,” Pro-ceedings of the 59th IWCSD/IICIT, 2010, pp. 59-68.

4. Gaberson, H. A., “Applying the Inverse FFT for Filtering, Transient De-tails, and Resampling,” Sound and Vibration, August 2005, pp. 18-23.

5. Lau, Y., “Understanding the Distance-to-Fault Measurement Data,” http://www.rfmarketing.com/rfm/aw/ref/dtf-yl.pdf.

6. Comparison of Measurement Performance between Vector Network Ana-lyzer and TDR Oscilloscope, Agilent Technologies, White Paper, 5990-5446EN, 2010.

7. Comparison of Vector Network Analyzer and TDA Systems IConnect® Generated S-Parameters, Samtec Technical Note, 2004, p. 2.

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distance-to-fault is spelled tdr or vna

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