# Rise Time Calculator (with examples)

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.

ðŸ”„ Rise Time to Bandwidth

## 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.

## 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.