Bandwidth of the oscilloscope Digital applications
Experience tells us that the bandwidth of an oscilloscope should be at least five times higher than the fastest digital clock rate of the system under test. If we select an oscilloscope that meets this criterion, then the oscilloscope will be able to capture the 5th harmonic of the signal under test with minimal signal attenuation. The 5th harmonic of the signal is important in determining the overall shape of the digital signal. However, this simple formula does not take into account the actual high-frequency components contained in the fast rising and falling edges if accurate measurements of high-speed edges are required.
Formula: fBW ≥ 5xfclk
A more accurate way of determining the bandwidth of an oscilloscope is based on the highest frequency present in the digital signal, rather than the maximum clock rate. The highest frequency of the digital signal depends on what the fastest edge speed in the design is. Therefore, we first need to determine the rise and fall times of the fastest signals in the design. This information can usually be obtained from the published specifications of the devices used in the design.
The maximum "real" frequency component of the signal is calculated using a simple formula, and Dr Howard W. Johnson has written a book on this topic, High Speed Digital Design. In this book, he refers to this frequency component as the "fknee" frequency. The spectrum of all fast edges contains an infinite number of frequency components, but there is a point of inflection (or "knee") above which the frequency components are irrelevant in determining the shape of the signal. Step 2: Calculate fknee
fknee=0.5/RT(10%-90%) fknee=0.4/RT(20%-80%)
For signals with rise time characteristics defined by the 10% to 90% threshold, the inflection frequency fknee is equal to 0.5 divided by the rise time of the signal. For signals with rise time characteristics defined according to the 20% to 80% threshold (which is the usual definition in today's device specifications), fknee is equal to 0.4 divided by the rise time of the signal. But be careful not to confuse the signal rise time here with the oscilloscope's rise time specification; what we are talking about here is the actual signal edge speed. The third step is to determine the oscilloscope bandwidth required to measure the signal based on the level of accuracy required to measure the rise and fall times. Table 1 gives the oscilloscope bandwidth needed versus fknee for various accuracy requirements for oscilloscopes with Gaussian frequency response or maximum flat frequency response. It should be remembered, however, that most oscilloscopes with bandwidth specifications of 1 GHz and below are usually Gaussian, while those with bandwidths greater than 1 GHz are usually of the maximum flat frequency response type. Table 1: Coefficients for calculating the required bandwidth of an oscilloscope based on the accuracy required and the type of frequency response of the oscilloscope Step 3: Calculate the oscilloscope bandwidth
Let's walk through a simple example:
Determine the minimum bandwidth required for an oscilloscope that has a correct Gaussian frequency response when measuring 500ps rise time (10-90%); if the signal has a rise/fall time of approximately 500ps (defined by the 10% to 90% criterion), then the maximum real frequency component of the signal, fknee = (0.5/500ps) = 1GHz
If a timing error of 20% is allowed when making measurements of rise time and fall time parameters, then an oscilloscope with a bandwidth of 1GHz would be adequate for this digital measurement application. However, if the timing accuracy is required to be within 3%, then an oscilloscope with a bandwidth of 2GHz would be better.
20% timing accuracy: oscilloscope bandwidth = 1.0x1GHz = 1.0GHz
3% timing accuracy: oscilloscope bandwidth = 1.9x1GHz = 1.9GHz
