Learning Library · Signals and oscilloscopes · 3
Bandwidth and rise time
An oscilloscope's front end is a low-pass filter. Its bandwidth sets how fast an edge it can follow, and an edge faster than the scope gets slowed down on screen. The question is how much, and how much bandwidth is enough.
Yellow: the real edge at the probe tip. Blue: what the scope draws. Dashed lines mark 10 % and 90 %, where rise time is measured.
The rule of thumb
The 0.35 comes from a single-pole or Gaussian response, which many scopes up to about 1 GHz approximate. Scopes with a flatter, sharper roll-off use a factor nearer 0.4 to 0.45. A 100 MHz scope therefore has a rise time of about 3.5 ns.
The two rise times add as a root sum of squares. When the scope is five times faster than the signal, the displayed rise time is only 2 % slow. When they are equal, it reads 41 % slow.
Bandwidth is about edges, not just frequency
A 10 MHz square wave is not a 10 MHz problem. Its sharp edges are built from harmonics far above 10 MHz, and the scope needs enough bandwidth to pass the ones that shape the edge. A useful estimate of the highest significant frequency in an edge is its knee frequency, about 0.5 ÷ rise time.
| Scope bandwidth | Scope rise time (0.35) | Fastest edge for a 2 % error |
|---|---|---|
| 100 MHz | 3.5 ns | 17.5 ns |
| 350 MHz | 1.0 ns | 5.0 ns |
| 1 GHz | 350 ps | 1.75 ns |
| 8 GHz | 44 ps | 219 ps |
Try this
- Set a 5 ns edge and a 100 MHz scope. The scope's own 3.5 ns rise time stretches the display to about 6.1 ns, a 22 % error.
- Raise the bandwidth to 350 MHz. The error falls to about 2 %.
- Slow the edge to 50 ns. Now even a 100 MHz scope reads within 0.3 %: bandwidth only matters relative to the edge.
The probe is part of the system. A 100 MHz probe on a 1 GHz scope makes a slower system than either alone, and the same root-sum-of-squares rule applies to it. The probes explainer covers the other half of that system.
Match the bandwidth to your fastest edge. Oscilloscopes from tens of megahertz to gigahertz bandwidth.
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