This tool computes the minimum Rise Time of a signal from its Bandwidth.
It’s useful if you want to find the fastest rise time that can be measured with an oscilloscope having a certain bandwidth specification.
Formula
Trise = 0.35 / BW
where
- Trise is the Rise Time in Nanoseconds (ns)
- BW is the Bandwidth in Gigahertz (GHz)
Background
As the bandwidth of the oscilloscope increases, the signal rise time that can be measured with it decreases. The rise time is associated with the 10-90% amplitude.
Calculation Example
What is the rise time associated with a 50 MHz bandwidth?
The calculator is used to find Trise = 0.35 / 0.05 = 7 nanoseconds.
What is the rise time associated with a 250 MHz bandwidth?
Once again the calculator is used to find Trise = 0.35 / 0.25 = 1.4 nanoseconds.
As the bandwidth of the instrument increases, the rise time measurement capability is increases. In other words, with increasing bandwidth an oscilloscope can measure faster rise times.
What is Bandwidth?
Within the context of an oscilloscope, bandwidth is the highest frequency of a sine wave that can be measured with at most a 3 dB error. In linear terms, the signal amplitude drops no more than 70.7% of its actual value as shown in the picture below. (Use -3 dB in the dB to linear calculator)
Example Application
The calculator can be used to find the minimum rise time that can be measured by an oscilloscope considering its bandwidth specification.
The DS1202Z-E oscilloscope has a bandwidth of 200 MHz. The minimum rise time is therefore 1.75 ns. The oscilloscope will not be able to measure a rise time of 1 ns for example.
While this specification sheet confirms the 1.75 ns number, there are many oscilloscope vendors that might not include this spec – specially the cheaper ones. The calculator is useful in that case.
Related Calculators
References
[1] Bandwidth of a signal from its rise time: Rule of Thumb #1. In this post the author derives the relationship between rise time and bandwidth empirically.
[2] How do I determine what bandwidth of scope I require for my application? An application note that estimates a 2% measurement error when the five times rule is used.