# Electronic – How is rise time related to bandwidth of the signal

bandwidthrise timetransmission line

Say, I want to limit the rise time of my digital signal edges to avoid dealing with transmission line effects.

How do I determine the maximum frequency of harmonics in my signal knowing that my rise time is, say 5ns?

How do I determine corner frequency of my low pass filter knowing that hold time on the receiver chip is, say 10ns?

In wikipedia I've found the formula

$$BW=\frac{0.34}{t_{rise}}$$

does it apply in this case?

Edit

I failed to make myself clear, so I'll try to explain my line of thought.

Say, I have a 30HMz signal and my trace length is well below 1/10 of the wavelength. So I don't have to deal with transmission line effects in respect to that. But my edges are steep – 5ns. This adds some high frequency components into my signal that potentially will suffer from transmission line effects.

My idea is that I slow down edge transitions up to a point where I don't have to deal with transmission line phenomena. The question is twofold:

• how do I calculate fastest rise/fall time that with the given trace length would enable me to traeat my circuit as "lumped"?
• how do I slow down the rise/fall time?

Rise/fall time is time for voltage to change from 10% to 90% of max value. I know how to calculate the approximate speed of signal on FR4 board.

There is no one to one relationship between rise time and bandwidth. A slew rate limiter is a non-linear filter, so can't directly be characterized as a low pass filter with some obvious rolloff frequency. Think of it in the time domain, and you can see that a slew rate limit effects signals proportional to amplitude. A 5 Vpp signal limited to 5 V/µs can't have a period shorter than 2 µs, at which point it degenerates to a 500 kHz triangle wave. However, if the amplitude only needed to be 1 Vpp, then the limit is a 2.5 MHz triangle wave. Since the concept of bandwidth get less clear when a non-linear filter is envolved, you can at best talk about it approximately.

Your answer can also vary greatly depending on what exactly "rise time" is. This is a term that should never be used without some qualification. Even a simple R-C filter has ambiguous rise time. Its step response is a exponential with no place being a clear "end". It's rise time is therefore infinite. Without a threshold of how close to the end you need to be to considered to have risen, the term "rise time" is meaningless. This is why you need to either talk about rise time to a specific fraction of the final value, or slew rate.

The equation you site is therefore just plain wrong, at least without a set of qualifications. Perhaps those are found on the page you got it from, but quoting it out of contect makes it wrong. Your question is unaswerable in its current form.