In this post we compute the bandwidth requirements for a scope considering the rise time of the waveform it is to measure.
Enter the rise time in the calculator below with the appropriate units and it will provide the bandwidth requirement.
Formula
BW = 0.35 / Trise
where
- Trise is the Rise Time in Nanoseconds (ns)
- BW is the Bandwidth in Gigahertz (GHz)
Example Application
A scope bandwidth of at least 350 MHz is required to measure a rise time of 1 nanosecond. The most economical oscilloscope by Rigol has a rise time of 7 nano seconds which is equivalent to 50 MHz.
In general, the smaller the rise time, the higher the bandwidth.
Background
What is rise time?
It is the amount of time it takes a signal to go from 10% to 90% of its peak value.
What is Oscilloscope Bandwidth?
Oscilloscope bandwidth is a key specification of the instrument. It represents the highest input signal frequency that can be measured without error.
This video below does an excellent job of articulating what Oscilloscope bandwidth means and how its different from sampling rate.
When you select a scope, the bandwidth really depends on what types of signals you are trying to measure. A good rule of thumb for digital signals such as square waves is that the bandwidth should be 5 times the fundamental frequency of the sine wave. However the rise time of the waveform plays an important role and should be considered in bandwidth selection.
As an example, an Arduino Uno toggles a signal at 1 kHz. Based on that, we might be tempted to state the bandwidth requirements for a scope that measures the activity should be 5 kHz.
For an accurate characterization and measurement of square waves however, the rise time has to be taken into account.
It can (as is shown in the video above) result in a larger scope bandwidth requirement.
Even though the Arduino has a relatively slow clock rate, the CMOS circuits create signals that have fast edges and a scope bandwidth of 100 to 500 MHz is required to accurately characterize activity.
Related Calculators
- Square Wave Harmonics – provides insight into the harmonics of a square wave and respective amplitudes of each harmonic. The fifth harmonic for instance is 25% the value of the fundamental. As the harmonic multiple increases, the amplitude drops.
- Oscilloscope and Probe Bandwidth Calculator – the frequency response of a probe can be a limiting factor in your measurement. This tool allows you to calculate the effect of both the probe and the oscilloscope on the overall system or measurement bandwidth.