TDRs are one of the most valuable tools an SI engineer uses to characterize an interconnect or debug a problem in a high-speed channel, but they are often expensive and not always available. This paper demonstrates how a practical TDR can be built in just a few minutes using commonly available lab components, including the ability to plot the impedance profile of a transmission line.

TDR Principles

A TDR (Time-Domain Reflectometer) analyses reflections caused by impedance discontinuities in a device under test (DUT) to plot its impedance profile. By leveraging the finite propagation speed of the signal, it also provides spatial information about where these discontinuities occur.

A TDR instrument, illustrated in Figure 1, includes two important components: a fast step-edge generator and a scope to measure the voltage near the signal launch. This voltage includes the incident signal to the DUT and the reflected signal from the DUT.

Figure 1. TDR block diagram. 

The signal generator sends a short rise-time signal step edge toward the DUT. When the step edge encounters an impedance discontinuity, such as at the interface of the launch and the DUT,  a portion of the signal edge is reflected. This reflected wave is captured by the scope. From the source impedance, the reflected signal, and the incident signal, the impedance change the signal encounters can be calculated. 

As the pulse continues through the DUT, it reflects at every impedance change, all the way to the far end. By analyzing the timing and magnitude of these reflections, the TDR provides a time-resolved impedance profile of the DUT.

Roll Your Own TDR Setup

The roll-your-own TDR consists of a square wave generator, an oscilloscope, and a 3-port power splitter, as shown in Figure 2. The role of each of these components is detailed below. 

Figure 2. Roll-your-own TDR setup.

Short Rise Time Source

In principle, any square wave generator can be used, with two constraints. In order to match to the power splitter, its output impedance needs to be smaller than 50 Ω. If it is lower than 50 Ω, a series resistor can be added to match it to 50 Ω. But, if its impedance is higher than 50 Ω, it is more difficult to match this to 50 Ω.

The rise time of the sources sets the fundamental limit on the spatial resolution of the TDR. This is the closest spacing two discontinuities can have and still be distinguished as two structures. To first order, the spatial resolution is the speed of the signal x the rise time. 

A 1-nsec rise time source would provide a resolution between discontinuities that can be distinguished as separate structures of about 6 in. A shorter rise time would also make the TDR more sensitive to smaller capacitive or inductive discontinuities.

Three common signal sources were explored in this early study. The list below includes their output impedance and their 10-90 rise times:

Power Splitter

A power splitter is a three-terminal device. It divides an incoming voltage signal at port 1 equally between ports 2 and 3. An input signal of 1 V entering port 1, leaves port 2 and port 3 as a 0.5 V signal into 50 Ω loads.  

It works by adding 17 Ω resistors in series with the transmission line connections to each port. If the terminations to each port are 50 Ω, then the input impedance looking into each port is 50 Ω. This means there are no reflections from any port coming from a 50 Ω source. 

In this study, we used a very simple, low-cost power splitter available on Amazon for $5. An example is shown in Figure 3. Its bandwidth is in excess of 3 GHz, well above the measurement range for this study.

Figure 3. The resistive power splitter used. 

The power splitter splits the signal from the square wave source into a component that is measured by the scope and a component that is sent into the DUT. 

The reflected signal from the DUT is further divided into a component that goes back to the source and into the scope, delayed by the round-trip delay from the discontinuity. The scope measures the incident signal into the DUT and half the reflected voltage. The other half of the reflected voltage is absorbed by the 50 Ω of the source. This bounce diagram is illustrated in Figure 4. 

Figure 4. Bounce diagram depicting the voltage transitions in the TDR setup.

The Oscilloscope

Any scope can be used as a TDR as long as its input can be set to 50 Ω, or at least a 50 Ω terminating resistor added to its 1 meg input. If its bandwidth is higher than the bandwidth of the signal, the signal source sets the limit to the resolution of the TDR. If its bandwidth is lower than the signal source, the scope’s bandwidth sets the limit to the TDR resolution. 

A scope with a 200 MHz bandwidth will have a shortest rise time it can measure of about 0.35/0.2 GHz = 1.7 nsec. This results in a spatial resolution between discontinuities of about 1.7 nsec x 6 in./nsec = 10 in. Higher bandwidth scopes would enable a shorter spatial resolution. 

In our approach, any scope can be turned into a TDR as long as its limitations are acceptable in the application. 

In this example study, a Keysight InfiniiVision DSOX4024A, with a bandwidth of 200 MHz was used. Additionally, when measuring the time delay of a DUT in our TDR , the timing uncertainty is +/-0.2 nsec due to the scope’s sampling rate of 5 Gbps.

Turning a Scope into a TDR

Combining these three elements into a TDR is simple. The signal source drives port 1 of the power splitter. The scope input connects to port 2 and the DUT connects to port 3. One configuration with a long coax cable as the DUT is shown in Figure 5.

Figure 5. The final setup with everything put together. 

The initial edge of the square wave is measured by the scope. Some time later, reflections from any impedance discontinuities in the DUT are also measured by the scope. At any instant, the scope is measuring both the incident signal into the DUT and the reflected signal. The actual scope measured incident and half reflected signal from a 24 ft long RG58 coax cable, using a function generator source, is shown in Figure 6.

Figure 6. The scope waveform of the incident and reflected signal from a long coax cable.

Plotting the Impedance Profile

To extract an accurate TDR measurement from the scope, a simple calibration measurement is first performed. The DUT is replaced by a 50 Ω resistor. This way, the voltage waveform measured by the scope is only the incident signal to the DUT, V(t)_incident. This waveform is recorded.

Then the 50 Ω resistor is replaced with the DUT. The voltage waveform measured by the scope, V(t)_measured, is the combination of the incident waveform and the reflected waveform, V(t)_reflected:

V(t)_measured = V(t)_incident + ½ V(t)_reflected

The waveform math to convert the two measured waveforms into the impedance profile can be done with many different external tools, such as excel or SPICE. In this study, Keysight’s ADS was used. The analysis is:

V(t)_reflected = 2 (V(t)_measured - V(t)_incident)

The reflection coefficient can be turned into an instantaneous impedance profile using:

An example of the calculated TDR profile of this long coax cable is shown in Figure 7.

Figure 7. Impedance plot for four segments of RG58 coax cables connected in series.

The upward slope in the impedance profile is from the distributed series resistance of this 24 ft RG58 cable. 

Effect of Source Rise Time

The bandwidth of the scope used in this study was 200 MHz. This means the shortest rise time that can be resolved is about 1.7 nsec. The three different sources, with rise times of 7.2 nsec, 3.6 nsec, and 1.4 nsec, were used to measure the same 4-segment coax cable. This cable is illustrated in Figure 8, featuring three BNC connectors between the segments. 

Figure 8. DUT made up of four 6 ft cables with BNC barrels connecting them.

The resulting TDR response of this same DUT using the three different sources, with different rise times and spatial resolution is shown in Figure 9. The impedance profiles are identical. The shorter rise time signal sources enable seeing more clearly the small inductive discontinuity of the barrel connectors. 

Figure 9. Impedance plot with all three pulse sources.

Verifying the Accuracy of the TDR

The impedance plotted by the TDR is the instantaneous impedance of the attached DUT. When the DUT is a resistor, calculating the reflection coefficient is straightforward. A collection of ¼ watt resistors was soldered to the end of SMA connectors and their resistance measured with a DMM to 1 percent accuracy. These were then measured by the TDR. The measurement configuration is shown in Figure 10.

Figure 10. TDR measurement of resistors on the ends of SMA connectors.

The measured TDR response from three of these resistors, a 68 Ω, 50 Ω, and 22 Ω resistor, as measured by the DMM, are shown in Figure 11.

Figure 11. TDR plot of the resistors.

The TDR measured resistances were within the 1 percent of the DMM measured resistances. 

Conclusion

This paper presented a simple yet effective method to roll your own TDR using any square wave source, any scope, and a $5 power splitter. By extracting voltage waveforms from the oscilloscope and processing them with free or open source tools, we were able to successfully plot the impedance profile of a DUT. This low-cost approach offers a practical and accessible solution for characterizing transmission lines in educational or resource-constrained lab environments. While any scope and any function generator can be used, the resolution of the roll-your-own TDR can be significantly enhanced by using shorter rise-time sources and higher-bandwidth oscilloscopes. 

REFERENCES

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