# Choosing an Oscilloscope with the Right Bandwidth

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Bandwidth is the specification that most engineers consider first when they select an oscilloscope. This article provides some guidance on how to select an oscilloscope with the appropriate bandwidth for digital and analog applications. Before getting started, however, it's first necessary to define oscilloscope bandwidth.

**Oscilloscope Bandwidth**

All oscilloscopes exhibit a low-pass frequency response that rolls-off at higher frequencies, as shown in **Figure 1**. Most scopes with bandwidth specifications of 1GHz and below typically have what is called a Gaussian response, which exhibits a slow roll-off characteristic beginning at approximately one-third the -3dB frequency. Oscilloscopes with bandwidth specifications greater than 1GHz typically have a maximally-flat frequency response, as shown in **Figure 2**. This type of response usually exhibits a flatter in-band response with a sharper roll-off characteristic near the -3dB frequency.

There are advantages and disadvantages to each of these types of oscilloscope frequency responses. For instance, oscilloscopes with a maximally-flat response attenuate in-band signals less than scopes with a Gaussian response, meaning that scopes with maximally-flat responses are able to make more accurate measurements on in-band signals. However, a scope with a Gaussian response attenuates out-of-band signals less than a scope with maximally-flat response, meaning that scopes with Gaussian responses typically have a faster rise time than scopes with maximally-flat response, given the same bandwidth specification. But, sometimes it is advantageous to attenuate out-of-band signals to a higher degree in order to help eliminate higher-frequency components that can contribute to aliasing in order to satisfy Nyquist criteria (f_{MAX}< f_{S}).^{1}

Whether your scope has a Gaussian response, maximally-flat response, or somewhere in between, the lowest frequency at which the input signal is attenuated by 3dB is considered the scope's bandwidth. Oscilloscope bandwidth and frequency response can be tested with a swept frequency using a sine wave signal generator. Signal attenuation at the -3dB frequency translates into approximately -30% amplitude error. So you cannot expect to make accurate measurements on signals that have significant frequencies near your scope's bandwidth.

Closely related to an oscilloscope's bandwidth specification is its rise time specification. Scopes with a Gaussian-type response will have an approximate rise time of 0.35/f_{BW} based on a 10- to 90-percent criterion. Scopes with a maximally-flat response typically have rise time specifications in the range of 0.4/f_{BW}, depending on the sharpness of the frequency roll-off characteristic. But it is important to remember that a scope's rise time is not the fastest edge speed that the oscilloscope can accurately measure. It is the fastest edge speed the scope can possibly produce if the input signal has a theoretical infinitely fast rise time (0 ps). Although this theoretical specification is impossible to test (since pulse generators don't have infinitely fast edges) from a practical perspective, you can test your oscilloscope's rise time by inputting a pulse that has edge speeds that are 3 to 5 times faster than the scope's rise time specification.

**Digital Applications**

As a rule of thumb, your scope's bandwidth should be at least five times higher than the fastest digital clock rate in your system under test. If your scope meets this criterion, it will capture up to the fifth harmonic with minimum signal attenuation. This component of the signal is very important in determining the overall shape of your digital signals. But if you need to make accurate measurements on high-speed edges, this simple formula does not take into account the actual highest-frequency components embedded in fast rising and falling edges.

Rule of thumb: f_{BW}≤5 x f_{clk}

A more accurate method to determine required oscilloscope bandwidth is to ascertain the maximum frequency present in your digital signals, which is *not* the maximum clock rate. The maximum frequency will be based on the fastest edge speeds in your designs. So, the first step is to determine the rise and fall times of your fastest signals. You can usually obtain this information from published specifications for devices used in your designs.

You can then use a simple formula to compute the maximum "practical" frequency component. Dr. Howard W. Johnson refers to this frequency component as the "knee" frequency (f_{knee}).^{2} All fast edges have an infinite spectrum of frequency components. However, there is an inflection (or "knee") in the frequency spectrum of fast edges where frequency components higher than f_{knee} are insignificant in determining the shape of the signal. To calculate f_{knee}:

*f _{knee}=0.5/RT (10-90 percent)
f_{knee}=0.4/RT (20-80 percent)*