*This article appeared in Microwave and RF** and has been published here with permission.*

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**What you will learn:**

- The basic concepts underlying time domain reflectometry.
- Difference between frequency and time analysis.
- Some applications of TDR measurements.

Time Domain Reflectometry (TDR) is a technique that measures and displays the impedance of a network (cable, filter, etc.) over time. Traditionally, this is done with a device that generates very fast pulses, injects them into the network, and measures the time and amplitude of the reflected pulses.

The TDR provides impedance information as a function of the time it takes for a pulse to reflect or pass through the medium. And, because signals travel with (almost) the speed of light, time can be translated into distance over a cable or network.

The same kind of measurement can be done using a vector network analyzer (VNA), but in a roundabout way. A VNA measures impedance (reflected) over frequency. We can use a Fourier transform to convert this to a series of impedances over time, much like that produced by a TDR instrument.

This article describes frequency and TDR measurements of coaxial networks and the analysis of PCB trace impedances on a test PCB, which are some of the applications of TDR analysis. The measurements were performed with a MegiQ VNA-0460e 6 GHz vector network analyzer.

### A simple TDR measurement

The following graphs show a measurement of a short terminated piece of 50 Ω coaxial cable. *Figure 1* shows the configuration of this measurement.

The graphics in *Figure 2* are all different representations of the same S11 metric on that network.

At the top of *Figure 2* are three graphs of impedance over frequency:

- In the Smith chart, the impedance travels in circles around the perimeter. It is an open impedance with an increasing phase on the frequency.
- The return loss is almost 0 dB because all the energy is reflected back from the short circuit at the end.
- In the impedance graph, the impedance varies wildly because the signal reflected from the short termination adds or subtracts at different frequencies.

It is difficult to fully discern the geometry of the network from these frequency graphs.

At the bottom of *Figure 2* are two TDR graphs that show return loss and impedance over time:

- The return loss TDR chart at the top illustrates the return loss at different times.
- The impedance graph below which shows how the impedance itself develops over time.

At T=0, the signal leaves the VNA port. At T=1 ns (marker 2), the signal reflected from the short circuit returns to the VNA port. The signal first passes through the 50 Ω cable and the impedance then drops to (almost) zero at the short circuit. In coaxial cable, time is distance since the signal travels at nearly the speed of light.

The second horizontal axis (bottom) of the TDR graphs converts time to distance in the cable. The signal travels down the cable at the speed of light multiplied by a “speed factor” which depends on the type of cable. This speed factor is normally of the order of 60% to 90% of the speed of light; this parameter can be modified for the cable used.

For return measurements, the distance scale accounts for the round trip of the signal from the port to the far end and back to the port. So the distance scale is the actual distance between the port and the impedance drop. Of course, the VNA cannot look beyond the end of the cable. Generally, however, the graph tilts towards the termination impedance.

The TDR transformation shows the actual impedance at different positions in the network. A TDR signal has no phase information. It looks like the characteristic impedance of a coaxial cable, which is also a real number. For this reason, there is no Smith-chart representation of a TDR signal.

### Several impedance jumps

With a little creativity we can create a more interesting network *(Fig.3)*. The signal travels through a length of 50 Ω cable, then through two parallel 50 Ω cables (forming a 25 Ω line) and back to a single cable, “terminated” with an opening.

*Figure 4* shows the measurements of this network. Again, the frequency graphs look spectacular, but they don’t tell us much about the structure of the network. In the TDR graphs at the bottom, impedances and jumps are clearly visible. It goes from 50 Ω to the 25 Ω of the two parallel cables, back to 50 Ω, then to high impedance at the end.

### Two-port measurements over a long cable

Next, let’s connect a long 50 Ω coaxial cable to the top-hop network and perform a two-port measurement. The hopping network is made even more interesting with an extra length of coaxial cable in one arm of the split network *(Fig.5)*. There are now two unequal signal paths. The “far end” of the network is connected to port 2 of the VNA; therefore, it ends in 50 Ω. For port 2, this is “near end”.

The measurement of this network is shown in *Figure 6*. At the top are the frequency graphs and at the bottom are the TDR graphs. The S11 Smith chart in the upper part of the figure looks like before. Smith’s diagram S22 seems to have better impedance because the offset is located at the end of the long coax, which dampens reflections. The gains (S12 and S21) also vary wildly due to all the impedance jumps in the network. Note that the forward and reverse gain (loss) are the same, as there is no directivity in the network.

In the TDR graphs of the S11 and S22 impedances we see that the jumps are close to port 1 and away from port 2. Adding an extra delay in one arm of the split part gives extra short jumps in the impedance TDR (marker 1).

Gain TDR graphs show that the signal arrives at the other port after the network delay. The “Gain-TDR-Step” graph reveals that the signal arrives in two steps. This arrival in two stages is clearer with the pulsed mode of the TDR transform. There are clearly two peaks in the signal arrival at the other end. Double peaks are caused by the unequal length of the two arms of the split grating part.

### Fault distance detection

As the previous examples show, the impedance over a length of cable is clearly visible. This is the basis of Distance to Fault (DTF) detection, which helps locate damage in (long) coaxial cable.

In the TDR graph, it is easy to see if there are any impedance jumps, such as a short or open in the cable, and how far they are from the VNA. When a coaxial cable has minor damage (crushed or bent), it may exhibit a slight or large variation in impedance along its length. The advantage of TDR for fault detection is that the cable does not need to be terminated with a specific impedance, so it can be applied on long cables without immediate end point checking.

### Time Gating

With the TDR functionality it is possible to “filter” the gain-frequency graph with a time filter. In effect, VNA software can perform a TDR transformation of the frequency measurement, remove signal components outside (or within) a certain time range, and then transform the signal into a frequency graph. . This is called time-gating.

*Picture 7* shows the definition of such a time gate on the signal transformed into TDR. Markers 1 and 2 define a time range and the filter is displayed in black.

*Figure 8* represents the result of several time gates. At the top is the original gain graph, and below is the gain with a time gate around the two peaks. It shows the gain with the spurious (reflection) peaks removed. The third from the top shows the gain with a time gate around the first peak, while the fourth graph is the gain with a time gate around the second peak.

### PCB trace analysis

TDR measurements can also be used to analyze PCB trace impedances and connector launch footprints. To measure these small features, the VNA has an enhanced TDR mode that uses oversampling and extrapolation of measurement data.

We designed a PCB with different ground-coplanar waveguide (CPWG) traces and SMA connector launches to study the impedances of these geometries. PCB *(Fig.9)* is a four-layer PCB with an upper and lower core made of 254µm Isola I-Tera material.

Circuits 2, 3, 6 and 7 are traces of different widths and a ground clearance of 200 µm. They terminate in 50 Ω (2 × 100 Ω) near the center of the PCB. The SMA connector is a solderless type that we have moved to different positions. The connector has been removed from the measurements to only display the impedances of the traces.

The graphics in *Picture 10* show the impedance of traces with widths of 430, 450, 470, and 500 µm, respectively. Impedance decreases with wider track widths. The 450 µm track shows the best match of 50 Ω. The impedance drop at the end of the trace is due to the termination network layout with a larger footprint that accommodates two resistors.

### The effect of vias

We have planned circuit 4 (with the connector) to study the effect of the vias. It has a trace width of 470 µm with two vias to jump to the bottom layer and back up again. The graphics in *Picture 11* show the impedance of the normal 470 µm trace (left) next to the impedance of the same trace with two vias. The impedance is very similar to normal, with a slight drop due to the vias. This suggests that the vias have a similar impedance to the 470 µm trace.

### conclusion

Where regular VNA graphs of network measurements can be confusing or complicated, TDR analysis of these measurements can provide greater insight into the physical geometry of a network. Time domain reflectometry is also useful to better understand the local impedance effects of networks. Additionally, time-triggering can be used to isolate certain areas of a network for frequency representation.