Service Manuals, User Guides, Schematic Diagrams or docs for : Agilent 5989-5732EN English _ 2014-08-04 _ PDF 7.28 MB c20140812 [18]

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Keysight Technologies
Evaluating Oscilloscope Sample
Rates vs. Sampling Fidelity

Application Note
Introduction

How to Make the Most Accurate Digital Measurements
Digital storage oscilloscopes (DSO) are the primary tools used today by digital designers to perform
signal integrity measurements such as setup/hold times, eye margin, and rise/fall times. The two
key banner specifications than affect an oscilloscope's signal integrity measurement accuracy are
bandwidth and sample rate. Most engineers have a good idea of how much bandwidth they need for
their digital measurements. However, there is often a lot confusion about required sample rates--and
engineers often assume that scopes with the highest sample rates produce the most accurate digital
measurements. But is this true?

When you select an oscilloscope for accurate, high-speed digital measurements, sampling fidelity
can often be more important than maximum sample rate. Using side-by-side measurements on
oscilloscopes with various bandwidths and sample rates, this application note demonstrates a
counterintuitive concept: scopes with higher sample rates can exhibit poorer signal fidelity because
of poorly aligned interleaved analog-to-digital converters (ADCs). This application note also will show
how to easily characterize and compare scope ADC sampling fidelity using both time-domain and
frequencydomain analysis techniques.

Let's begin with a discussion of minimum required sample rate and a
review of Nyquist's sampling theorem.

Table of Contents
Introduction ............................................. 2
Nyquist's Sampling Theorem ................. 3
Interleaved Real-Time Sampling ........... 7
Testing for Interleave Distortion ............ 9
Effective number of bits analysis ......... 9
Visual sine wave comparison tests ...... 10
Spectrum analysis comparison tests .. 13
Summary .................................................. 16
Related Keysight Literature .................... 16
Glossary .................................................... 17
03 | Keysight | Evaluating Oscilloscope Sample Rates vs. Sampling Fidelity - Application Note

Nyquist's Sampling Theorem
How much sample rate do you need for What Nyquist calls f MAX is what
your digital measurement applications? Nyquist Sampling Theorem we usually refer to as the Nyquist
Some engineers have total trust For a limited bandwidth signal with frequency (f N), which is not the same
in Nyquist and claim that just 2X a maximum frequency fMAX, the as oscilloscope bandwidth (f BW ). If an
sampling over the scope's bandwidth is equally-spaced sampling frequency oscilloscope's bandwidth is specified
sufficient. Other engineers don't trust fS must be greater than twice the exactly at the Nyquist frequency (f N),
digital filtering techniques based on maximum frequency fMAX, in order this implies that the oscilloscope has
Nyquist criteria and prefer that their to have the signal be uniquely an ideal brick-wall response that falls
scopes sample at rates that are 10X reconstructed without aliasing. off exactly at this same frequency,
to 20X over the scope's bandwidth as shown in Figure 2. Frequency
specification. The truth actually lies components below the Nyquist
somewhere in between. To understand Nyquist's sampling theorem can be frequency are perfectly passed (gain
why, you must have an understanding summarized into two simple =1), and frequency components above
of the Nyquist theorem and how rules--but perhaps not-so-simple for the Nyquist frequency are perfectly
it relates to a scope's frequency DSO technology. eliminated. Unfortunately, this type of
response. Dr. Harry Nyquist (Figure 1) frequency response filter is impossible
postulated: 1. The highest frequency component to implement in hardware.
sampled must be less than half the
sampling frequency.
2. The second rule, which is often
forgotten, is that samples must
be equally spaced.
Attenuation

Figure 1: Dr. Harry Nyquist, 1889-1976,
articulated his sampling theorem in 1928

Frequency

Figure 2: Theoretical brick-wall frequency response
04 | Keysight | Evaluating Oscilloscope Sample Rates vs. Sampling Fidelity - Application Note

Nyquist's Sampling Theorem (continued)
Most oscilloscopes with bandwidth
specifications of 1 GHz and below
have what is known as a Gaussian
frequency response. As signal input
frequencies approach the scope's
specified bandwidth, measured

Attenuation
amplitudes slowly decrease. Signals
can be attenuated by as much as 3 dB
(~30%) at the bandwidth frequency.
If a scope's bandwidth is specified
exactly at the Nyquist frequency (f N),
as shown in Figure 3, input signal
frequency components above this
frequency

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