The sharp increase in the use of high-speed digital signals in electronic designs makes it necessary to characterize high-frequency interconnections, since, if they do not, there can be many design changes and delays when launching the products to the market. The time domain reflectometer (TDR) or a digital analyzer has evolved a lot since its inception, when it was used to identify cable faults. If your designs use signals with rise times of less than one nanosecond, the properties of the transmission line of the interconnections are important. The TDR is a versatile and intuitive tool that allows you to observe the performance of your interconnections in order to quickly and routinely solve the three important questions: does the specifications fulfill my interconnection? Will it work in my application ?, and where do I look to improve its performance? The TDR is not just a simple radar station for transmission lines that sends pulses along the line and observes the reflections of impedance discontinuities. It is also an instrument capable of directly providing first order topology models and behavior models of the S parameters. We will analyze the five most important applications of the TDR of a port, from the most common to the most advanced.
Measurement of the characteristic impedance and uniformity of a transmission line
To achieve an ideal transmission line without losses, there are only two parameters that completely characterize the interconnection: its characteristic impedance and its time delay. This is the simplest and most common application of TDR. The TDR sends a calibrated pitch edge of approximately 200 mV to the device under test (DUT). All the changes in the instantaneous impedance that the flank finds in its path will cause the signal to be reflected backwards, depending on the change seen in the impedance. The constant incident voltage of 200 mV, plus any reflected voltage, is what is shown on the TDR screen. Figure 1 shows the response of the TDR of a microstrip transmission line and an open reference. The DUT is a two-section microstrip transmission line with a characteristic impedance of 50 Ω and 40 Ω, and with the far end open. The blue trace shows the TDR response when the cable is not connected to the DUT and defines the start of the cable. The yellow trace of the TDR shows the small voltage reflected from the launch of the SMA launch connector, followed by the 50 Ω section, the small voltage drop of the 40 Ω section (with a lower impedance) and the open end of the trace . From the TDR response, we can obtain the instantaneous impedance of each segment using trace markers or by converting the vertical stress scale into an impedance scale. This method allows us to evaluate the uniformity of the impedance of the line. The blue trace shows the TDR response when the cable is not connected to the DUT and defines the start of the cable. The yellow trace of the TDR shows the small voltage reflected from the launch of the SMA launch connector, followed by the 50 Ω section, the small voltage drop of the 40 Ω section (with a lower impedance) and the open end of the trace . From the TDR response, we can obtain the instantaneous impedance of each segment using trace markers or by converting the vertical stress scale into an impedance scale. This method allows us to evaluate the uniformity of the impedance of the line. The blue trace shows the TDR response when the cable is not connected to the DUT and defines the start of the cable. The yellow trace of the TDR shows the small voltage reflected from the launch of the SMA launch connector, followed by the 50 Ω section, the small voltage drop of the 40 Ω section (with a lower impedance) and the open end of the trace . From the TDR response, we can obtain the instantaneous impedance of each segment using trace markers or by converting the vertical stress scale into an impedance scale. This method allows us to evaluate the uniformity of the impedance of the line. followed by the 50 Ω section, the small voltage drop of the 40 Ω section (with a lower impedance) and the open end of the trace. From the TDR response, we can obtain the instantaneous impedance of each segment using trace markers or by converting the vertical stress scale into an impedance scale. This method allows us to evaluate the uniformity of the impedance of the line. followed by the 50 Ω section, the small voltage drop of the 40 Ω section (with a lower impedance) and the open end of the trace. From the TDR response, we can obtain the instantaneous impedance of each segment using trace markers or by converting the vertical stress scale into an impedance scale. This method allows us to evaluate the uniformity of the impedance of the line. One drawback is that we are assuming that all the measured voltage that comes from the TDR is due to reflections of discontinuities of the impedance. It is a good guess when there are only small impedance discontinuities up to the place of the marker. In Figure 2, we can see the response of the measured TDR of a uniform transmission line from the nominal point of view, on an enlarged vertical scale of 2 Ω / div. The impedance of the center of the screen is set to 50 Ω. The big peak seen at the beginning of the line is the inductive discontinuity of the SMA launch connector, which, with this high-resolution scale, seems huge. At this scale, the uniform transmission line does not seem so uniform. Is this variation real or some kind of artifact? There are two important artifacts capable of causing this behavior. It may not be perfectly flat, like an ideal Gaussian sidewall. After all, the reflected signal shown in the TDR is actually the reflection of the incident signal. If the incident signal has a long tail, we will see that long tail in the TDR response and it can be misinterpreted as a variation of the impedance profile. One method to solve this problem is to use the calibrated response function of the TDR DCA 86100D sampling oscilloscope from Keysight, as we do in this case. Another source of artifacts are the typical losses of the line. The trace could present resistance in distributed series or distributed shunt conductance. The series resistance will cause the reflected voltage to increase as we move along the line, while the shunt conductance will reduce the response of the reflected TDR as we go along the line, as in this case. One way to evaluate whether an impedance profile actually shows a variation in the instantaneous impedance of the transmission line or an artifact is to measure the response of the TDR of the line at both ends. If it is real, we should see how the slope of the response changes depending on the end of the line from where we make the launch. If it is one of the two artifacts, the response will have the same appearance on the screen regardless of the endpoint from which we launch, as shown in Figure 3. One way to evaluate whether an impedance profile actually shows a variation in the instantaneous impedance of the transmission line or an artifact is to measure the response of the TDR of the line at both ends. If it is real, we should see how the slope of the response changes depending on the end of the line from where we make the launch. If it is one of the two artifacts, the response will have the same appearance on the screen regardless of the endpoint from which we launch, as shown in Figure 3. One way to evaluate whether an impedance profile actually shows a variation in the instantaneous impedance of the transmission line or an artifact is to measure the response of the TDR of the line at both ends. If it is real, we should see how the slope of the response changes depending on the end of the line from where we make the launch. If it is one of the two artifacts, the response will have the same appearance on the screen regardless of the endpoint from which we launch, as shown in Figure 3.
Measuring the time delay of a transmission line
The time delay of a transmission line from one end to the other can be measured directly from the TDR screen using markers. In Figure 4 we can see TDR responses for an open cable and when the DUT is connected. To increase the accuracy, the time of the central point between the two open responses is used. The time interval from the beginning of the reflection of the open end of the cable to the reflection of the farthest open end of the DUT is the total round trip time. The time delay is half that value. To ensure the integrity of the measurement of the assembly artifacts such as the launch connector, a test line can be included to aid in the characterization of the circuit board and each layer. For example,
Accurate measurement of the signal speed in a transmission line
With the end-to-end method to measure the time delay, we can obtain an accurate measurement of the speed of the signal that travels the transmission line, regardless of the type of launch connector. This is achieved by dividing the physical distance separating the two reference patches between the time delay obtained. Figure 5 shows two negative drops of the reference patches with a known separation distance. The time difference between these two negative drops is the round trip time between the patches.
Extraction of the crude dielectric constant of the laminate
The signal speed of the transmission line is directly proportional to the dielectric constant Dk that sees the signal. In the case of a stripline transmission line, the effective dielectric constant can be extracted using the simple relationship shown below: Dk = (0.3 / v) 2 where 0.3 is the speed of light in m / ns However, In a microstrip, some of the electric field lines are in the raw laminate and some are in the air. The signal sees a composite of these two materials, which creates an effective dielectric constant, Dkeff. This value is the one that affects the speed of the signal and can be extracted from the measured speed of the signal.
Creating a model of a discontinuity or interconnection
The incorporation of structures such as test patches, component terminals, corners and gaps in the return path will create discontinuities. The discontinuities can be characterized as capacitive, inductive and resistive. These structures are not uniform and, to calculate them, a 3D field solver may be necessary. Sometimes, the fastest way to evaluate your impedance is to create a structure and measure it. From the measured response, we can empirically evaluate the impact of the signal if we match the rise time of the TDR with the application's rise time. We can measure directly from the TDR screen the amount of reflected voltage that we could see in the system. Another method would be to use the TDR to extract a simple first-order model for the structure and use that model in a simulation at the system level to evaluate the impact of the discontinuity. For example, the TDR allows us to observe that the corners (or 90 degree flexes) have a response similar to that of a condenser with localized constants. Using the TDR measurement, we can obtain the capacitance value for the condenser model with localized constants and use that model in a simulation of the system to evaluate if a corner can be a potential problem or if it can be ignored. For the same impedance trace, the amount of capacitance in a corner will increase with the width of the line. It is interesting to remember that the capacitance of a corner is around 1 fF by 0, 025 mm line width for a 50 Ω line. Therefore, in lines of 1.524 mm and 0.127 mm in width, the capacitance of a corner will be around 60 fF and 5 fF, respectively. Finally, if we need more precision or a model with a greater bandwidth than we can obtain directly from the screen, we can use the measured data of the TDR and transfer them to a modeling or simulation tool, such as SPICE or ADS, to establish a more accurate model.