Background A TDR measures the reflections that result from a signal traveling through a transmission environment of some kind - a circuit board trace, a cable, a connector, and so on. In the past, a TDR was often a large, expensive instrument that included a high-speed edge pulse and a sampling oscilloscope. A TDR is a great tool that can be used to qualify vendor stack-ups, such as identifying the dielectric constant (Dk) variation of impedance. Some examples of information that can be provided by a TDR are shown in Figures 1 and 2.Â
Figure 1 demonstrates how impedance discontinuities can be measured on a PCB trace. Figure 2 is an example of TDR data computed from measured S-parameters, along with labels on the various features. In this case, the individual elements such as vias, traces, and connectors are clearly visible in the TDR trace [2].
A TDR is particularly useful for verifying connector and cable continuity. However, the spatial resolution of the TDR measurement setup ultimately depends on the total system rise time. Where the spatial resolution defines how well our measurement setup can delineate between these structures such as vias, traces, connectors, etc.
Figure 1 - TDR Waveform Reveals Trace Discontinuities [1].
Figure 2 - SiSoft Article Example TDR Derived from Measured S-parameter Data [2].
Per IPC-TM-650 Test Methods Manual [3], the TDR resolution limit is defined as
  Resolution Limit =(0.5)(tr_sys)(Vp)                        (1)
Where:
tr_sys = the TDR system rise time or fall time, 10% to 90%
Vp = the signal propagation velocity, same as Vf
The total system rise time (tr_sys) includes all components from the DUT to the scope, in other words, the TDR, scope, and probes. The tr_sys is shown by EQ(2). It should be noted that the rise time from 10% to 90% is arbitrary, in other words, 20% to 80% could also be used for each component in the tr_sys calculation. It only matters that the rise time values are consistent across all components.
   tr_sys=sqrt[(tr_TDR)^2+(tr_scope)^2+(tr_probe)^2]                                      (2)
Where:
tr_TDRÂ = the TDR rise time or fall time, 10% to 90%
tr_scope = the oscilloscope rise time or fall time, 10% to 90%
tr_probe = the probe rise time or fall time, 10% to 90%
From the tr_sys the total system equivalent bandwidth can be found by EQ(3).
BW_sys=(0.35)/(tr_sys)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (3)
Where:
BW_sys = the total system equivalent bandwidth
A simple example of adequate and inadequate resolution is shown by Figure 2.
Figure 2 - Resolution and Electrical Length of Transmission Line [3].
EXAMPLE 1 - TDR RESOLUTION LIMIT EXAMPLE WITH P2104A 1-PORT PDN PROBE
As an example of how to calculate the resolution limit, if the transmission line Dk = 3.5, then by EQ(4) and EQ(5), Vf = 6.33 in/ns.
Vf = c/sqrt(Dk)                                                                             (4)
Vf =(11.86 in/ns)/sqrt(3.5)=6.33 in/ns                                                                (5)
The P2104A 1-port probe has a bandwidth of 6.43 GHz. From EQ(3), we can calculate the probe’s rise time as
P2104A tr_probe=(0.35)/(6.43 GHz)=54.4 ps                             (6)
For the J2154A TDR, tr_TDR = 34ps. For the Tektronix MSO68B, tr_scope = 40 ps. For the P2104A 1-port probe, tr_Probe = 54.4 ps. Thus, by EQ(2), tr_sys is
(7)
BW_sys=(0.35)/(75.6 ps)=4.63 GHz                              (8)
With reference to EQ(1) and the results from EQ(5) and EQ(7), the resolution limit for the J2154A TDR with MSO68B, using the P2104A 1-port probe, with Dk = 3.5 is calculated to be
Resolution Limit =(0.5)(75.6 ps)(6.33 in/ns)=0.239 in = 239 mils              (9)
EXAMPLE 2 - TDR RESOLUTION LIMIT EXAMPLE WITH P2105A TDR PROBE
As an example of how to calculate the resolution limit, if the transmission line Dk = 3.5, then by EQ(4) and EQ(5), Vf = 6.33 in/ns. The Picotest P2105A TDR probe has a bandwidth of 16 GHz. From EQ(3), we can calculate the probe’s rise time as
P2105A tr_probe=(0.35)/(16 GHz)=21.88 ps                             (10)
For the J2154A TDR, tr_TDR = 34ps. For the Tek MSO68B, tr_scope = 40 ps. For the P2105A TDR probe, tr_Probe = 21.88 ps. Thus by EQ(2), tr_sys is
  tr_sys=sqrt[(34ps)^2 + (40 ps^2 + (21.88 ps)^2]=56.9 ps                      (11)
BW_sys=(0.35)/(56.9ps)=6.15 GHz                                                             (12)
With reference to EQ(1) and the results from EQ(5) and EQ(11), the resolution limit for the J2154A TDR with the Tektronix MSO68B, using the P2105A TDR probe, with Dk = 3.5 is calculated to be
Resolution Limit =(0.5)(56.9 ps)(6.33 in/ns)=0.180 in = 180 mils                (13)
This means that a TDR setup with the MSO68B, J2154A, and P2105A can delineate a spatial resolution between structures as small as 180 mils. If we want a smaller spatial resolution, we would need to decrease our system risetime, which is a function of what is calculated as shown by EQ(2).
When looking at the resolution limits between EXAMPLE 1 and EXAMPLE 2, it becomes clear as to the impact that having a higher bandwidth probe such as the P2105A in comparison to the lower bandwidth option has on the TDR during measurement. Mathematically, it is shown we are able to measure structures (or artifacts) almost 60 mils closer together just by having the higher bandwidth (16GHz) P2105A TDR probe vs. the lower bandwidth (6.43GHz) P2104A 1-port probe. Lastly, by comparing results from EQ(9) and EQ(13), we can see the system bandwidth impacts on the system.
Figure 3 - TDR Measurement Setup with J2154A, P2105A, MSO68B.
If you want to learn more about how to do TDR measurements or you are interested in purchasing a TDR or even probes for your oscilloscope, then check out the links to our store below.
References
TDR Impedance Measurement: A Foundation for Signal Integrity - https://download.tek.com/document/55W_14601_2.pdf
SISoft: TDR: Reading the Tea Leaves
IPC-TM-650 Test Methods Manual - https://www.ipc.org/sites/default/files/test_methods_docs/2-5-5-7a.pdf
Measuring the Bulk Dielectric Constant (Dk) on a Microstrip with a TDR