Reflectometry
A step that returns 303 ns later says that the cable has a fault at 30 m. The shape of the step says whether it is an open, a short or a badly assembled connector.
01A radar for cables
Time-domain reflectometry (TDR) injects a fast step into a transmission line and observes the voltage at the input. While the step travels along a uniform line, the input sees the characteristic impedance and the voltage stays at a fixed value. When the wavefront meets a discontinuity, part of it comes back, and the voltage at the input changes after the round-trip time. The theory of reflections was covered in transmission lines, in Transmission Media.
02How to read a trace
| Discontinuity | What is seen |
|---|---|
| Open circuit | The voltage doubles: Γ = +1 |
| Short circuit | The voltage drops to zero: Γ = −1 |
| Resistance greater than Z0 | A step upward, proportional to Γ |
| Resistance less than Z0 | A step downward |
| Capacitance | First it drops, like a short circuit, and rises as it charges |
| Inductance | First it rises, like an open, and falls as the current builds up |
The time constant of the capacitive response is \( Z_0 C \) and that of the inductive one, \( L/Z_0 \): the value is deduced from the shape of the trace. A loose connector, a crushed cable, a splice or a via on a printed circuit show up as small discontinuities at their position.
A 50 Ω TDR with an ideal 1 V step on a 50 Ω cable terminated in the chosen load. The trace is the voltage at the cable input as a function of time.
03Resolution and range
Two discontinuities can be told apart if they are separated by more than the wavefront travels during its rise time: with a 35 ps rise time and a velocity factor of 0.66, about 3.5 mm of separation, enough to see vias and connectors on a board. TDRs for installation cables use slower, more powerful pulses, which reach kilometers but resolve meters. In optical fiber, the equivalent is the OTDR, which measures the backscattered light and shows splices, connectors and breaks along the link, as seen in optical fibers.
04In the laboratory
With a fast pulse generator and an oscilloscope in parallel with the input of a coaxial cable, measure the length of the cable with the far end open and shorted. Calculate the velocity factor.
Terminate the cable with 25 Ω, 50 Ω, 100 Ω, a capacitor and an inductor, and compare the traces with those of the lab.
Crush a point on a cable and locate the discontinuity with the TDR.
05Common mistakes
- Forgetting to divide by two. The measured time is a round trip.
- Using the wrong velocity factor. A 20% error in the factor is a 20% error in the distance.
- Reading a distant reflection without considering losses. The cable’s attenuation shrinks the far-end steps.
- Confusing a capacitance with a short circuit. You have to look at the trace for a long time: the capacitance charges.
06Self-assessment
A TDR sees a change 500 ns after the step on a cable with a factor of 0.66. How far away is it?
\( 0.66 \cdot 3\cdot10^8 \cdot 500\cdot10^{-9}/2 \approx 49.5 \) m.
What level does the trace show with a 75 Ω load on a 50 Ω line?
Γ = 0.2: 60% of the step.
What time constant does the response of a 100 pF capacitor at the end of a 50 Ω line have?
5 ns.
Which instrument performs the function of the TDR in optical fiber?
The optical time-domain reflectometer, OTDR.
07Further reading
- Eric Bogatin. Signal and Power Integrity — Simplified. 3rd ed., Prentice Hall, 2018. TDR as a tool for seeing the discontinuities of a board.
- Keysight Technologies. Time Domain Reflectometry Theory. Application Note 1304-2, Keysight. Reading TDR traces with resistive, capacitive and inductive loads.
- Howard Johnson and Martin Graham. High-Speed Digital Design: A Handbook of Black Magic. Prentice Hall, 1993. Reflections in fast digital signals and how to measure them.