EMC Question of the Week: April 8, 2024

A 1-Gbps clock driver transmits a signal on a 50-Ω coaxial cable to the 50-Ω input of a 4-GHz digital oscilloscope.  The sampling rate of the oscilloscope is 20 GSa/sec. If the actual transition time of the signal is 20 ps, what would the expected transition time of the measured signal be?  

1. 20 ps
2. 25 ps
3. 90 ps
4. 250 ps

Answer

The best answer is “c.” The measured value of the transition time is limited by the bandwidth of the oscilloscope. A signal with a very fast transition time, on the order of a few picoseconds, input to a 1-GHz oscilloscope would exhibit a measured transition time of approximately,

${\text{t}}_{\text{r-scope}}\approx \frac{\text{0}\text{.35}}{{\text{BW}}_{\text{scope}}}\text{=}\frac{\text{0}\text{.35}}{{\text{4x10}}^{\text{9}}\text{Hz}}\text{=}\text{88}\text{ps}\text{.}$

If the actual transition time is 20 ps, then we would expect to measure a transition time of approximately,

${\text{t}}_{\text{r-measured}}\approx \sqrt{{\left({\text{t}}_{\text{r-signal}}\right)}^{\text{2}}\text{+}{\left({\text{t}}_{\text{r-scope}}\right)}^{\text{2}}}\text{=}\sqrt{{\left(\text{(20}\text{ps)}\right)}^{\text{2}}\text{+}{\left(\text{(88}\text{ps)}\right)}^{\text{2}}}\approx \text{90}\text{ps}\text{.}$

Note that the sampling rate (presuming it is at least about 2.5 times the bandwidth) does not affect the measured transition time.

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