Getting answers from a digital scope
BY MIKE LAUTERBACH
LeCroy Corp.
Chestnut Ridge, NY
The ability of a digital storage oscilloscope (DSO) to provide valid and useful
data measurement depends not only on the quality of the data, but also on the
scope's ability to process the data. A variety of capabilities is available for
capturing, viewing, measuring, analyzing, and documenting signals. All these
capabilities depend on one key factor: the amount of processing power built
into the scope.
This article describes how to obtain best- and worst-case circuit performance
measurements from a DSO, how to get more analysis power from a fast Fourier
transform (FFT), and how to perform complex analysis tasks faster. Measuring
the instantaneous power and total power in an electrostatic discharge is
examined as an example of a complex analysis task made easy.
Best- and worst-case analysis
When testing circuits or components, it is often vital to know the boundaries
of performance parameters. In debugging a circuit, the crucial measurement
might be the maximum jitter of a data bit (worst case). In testing a laser
diode, it might be the total power output of the largest pulse in the safe
operating range (best case). And if the job includes testing the frequency
stability of a communications signal, it may be necessary to measure the
lowest, highest, and average frequency (worst-case low, worst-case high, and
average).
The good news is that most DSOs can perform automatic measurements of a wide
variety of signal parameters, such as the time between two signal edges, the
area inside a pulse, and the frequency of a signal. A DSO with a reasonably
powerful processor can update the values of multiple signal parameters every
time the scope triggers. The bad news is that DSOs erase the old values on the
screen every time they write the new values, so unless the scope user is a
speed reader with perfect memory retention, there is no way to remember the
highest and lowest values.
Back to the good news. Some DSOs can help solve this dilemma. They store the
high and low values of each parameter in memory, and then display these values
on screen. The values are updated any time a new measurement extends them to a
new boundary.
For example, in Fig. 1 a data bit is analyzed for amplitude, positive
overshoot, rise time, and jitter (the delay between the leading edge of the bit
and a reference signal used as the trigger). In this case, the scope has
triggered 9,639 times. All the data bits have tightly packed amplitudes,
ranging from 3.94 to 4.00 V; positive overshoot, ranging from 0% to 3%; and
rise times, ranging from 36.2 to 40.3 ns. But the scope user notes a problem on
the fourth parameter. This data bit should arrive at the same time as the “data
latch” signal, which would store the bit into memory. But on at least one
occasion, the bit came -18.6 ns earlier than the “data latch” signal, which is
being used as a trigger for the scope. If the scope user was trying to debug a
problem caused by the failure to latch the leading edge of this data bit, the
user now knows the problem is not the amplitude, overshoot, or rise time of the
edge. The problem is timing jitter.
Calculating pulse parameters and saving the high, low, or average values in a
buffer may seem like a fairly easy application of processing power. But some of
the calculations are quite complex. For example, to measure the rise time of an
edge, the scope generates an internal histogram of voltage levels in a signal
(to find the level of the baseline and top of the signal). The scope then finds
the points on the signal corresponding to the desired rise time (10% to 90%,
20% to 80% or even a rise time between two absolute voltages) and then measures
the time between these points. If there are 50 pulses on the screen, the scope
may calculate all 50 of the rise times and perform a sort for high/low and
compute average/standard deviation. To handle this type of processing while
still maintaining a fast trigger rate requires a fast processor, numeric
coprocessor, and fast RAM.
An alternative to using a scope that can keep track of best- and worst-case
circuit performance is to have a computer program that will trigger the scope,
read data, perform the calculations, and re-arm the scope for the next trigger.
But a measurement that can be made in a few minutes using internal scope
processing may take an hour under program control.
Suppose the scope user spots a problem by measuring worst-case performance of
signal parameters. The next step would be to analyze the source of the problem.
Assume the problem is in a communications circuit and that it has been narrowed
down to instability in the carrier frequency. The persistence display mode of a
scope might show the top trace in Fig. 2. The scope is triggering near the left
side of the screen so all the sine waves are aligned. But by the time the
signal reaches the right side of the screen there are considerable differences.
Short-term changes in signal frequency may be hard to see on a spectrum
analyzer, but show up clearly on an oscilloscope.
Figure 2 also shows a histogram of the signal. Note that the lower scale is 0.5
kHz per horizontal division. The histogram shows two frequency peaks that are
approximately 2 kHz apart. In this case, a phase-locked loop is not operating
properly, causing the oscillator to run in a bistable mode.
In some testing modes, particularly when producing ISO 9000 performance
documentation, a visual picture of the raw signal may not be useful, but
multiple numerical bar charts documenting component performance may be ideal.
For example, Fig. 3 shows a scope that has triggered eight times on a string of
pulses. The top histogram summarizes all the pulse widths while the bottom one
shows pulse amplitudes. Up to four histograms can be displayed simultaneously.
They can be saved as paper copy or onto floppy disk, portable hard disk, or
PCMCIA memory card internal to the scope.
Better performance data from FFTs
The FFT is one of the most common analysis packages for use with DSOs. While
the most common way to view a signal on a scope is to look at its voltage as a
function of time, this time function F(t) can be transformed from the time
domain to the frequency domain by an FFT and viewed as a function of
frequencies, F(w).
There is an unique, one-to-one correspondence between F(t) and F(w). Both
functions are equally valid pictures of the same signal–one view from the time
domain and one from the frequency domain. But each view shows different facets
of the signal. The FFT provides the scope user with a fast, easy, and
inexpensive way of getting a second viewpoint into the behavior of a signal. It
can be used for anything from characterizing the rolloff of a filter to
identifying noise sources by the frequency “fingerprints.”
Spectrum analyzers still provide superior performance in spotting very small
frequency components against a background of stronger frequencies. A spectrum
analyzer will often have more than 100 dB of dynamic range. By comparison, a
typical DSO can achieve 60 to 70 dB of dynamic range. But there are some
advantages to the DSO approach. Although some scopes limit the FFT analysis to
the first 10 Kpoints of acquired data, others allow the user to select any
portion(s) of the data for FFT analysis. This means the user can compare the
spectral content of various portions of the signal. Up to four different
segments of the data can be simultaneously analyzed in this fashion.
A typical application of this is the examination of bursts of data from a
transmitter. Several bursts can be captured by a DSO, and each one can be
individually analyzed for frequency content. In this way, problems that would
disrupt adjacent or alternate channels can be spotted.
A scope user can employ signal averaging on multiple acquisitions to evaluate
the basic components of a signal and eliminate high-frequency noise. If the
trigger of the oscilloscope is unrelated to the high-frequency noise source,
the high-frequency components of the FFT will be reduced. On the other hand, if
the high-frequency noise is the component of interest, but more dynamic range
is needed than can be acquired by a single trigger, the scope can do its
averaging in the frequency domain. For example, assume the high-frequency noise
is only affecting one section of the signal. The user selects individual parts
of the signal and can do separate FFTs on each part for comparison. By
subtracting the two FFTs, the user can get a frequency spectrum of the noise.
A DSO acquires a discrete set of points in the time domain (the data samples
from the A/D converter). So when these points are transformed to the frequency
domain, the data set is also a discrete set of points. In the time domain, the
most accurate picture of a signal is obtained when the spacing between sample
points,
maximum amount of detail in the signal and make the most accurate measurement
of time between two signal edges.
Similarly, in the frequency domain, the user wants the smallest possible
in the frequency content and the best measurement of the difference in
frequency between two peaks. The data set in the frequency domain for positive
frequencies will have one half the number of time domain points input to the
FFT algorithm. The frequency span of those points covers the range from dc to
the Nyquist frequency.
The Nyquist frequency is the fastest frequency that can be measured and is
equal to one half the sampling rate. For example, if the data input to an FFT
algorithm is a set of points whose spacing is 2 ns (sampling rate of 500
Msamples) then the highest-frequency component of the FFT will have a period of
4 ns (frequency of 250 MHz). The calculation of
sampling rate of data input to FFT
number of sample points input to FFT
An alternative would be simply to analyze the first 10,000 acquired points.
This preserves the ability to measure high-frequency components, but loses all
information in the last 90% of the signal. It also makes the frequency
resolution,
equation above has been reduced from 100,000 to 10,000. An example contrasting
a 10,000-point FFT and a 1-million-point FFT is shown in Fig. 4. Notice that
Why would a vendor produce a scope that can capture 100,000 data samples in the
time domain but only process 10,000 samples in the FFT? Obviously, this is a
disadvantage to the user. A typical FFT algorithm requires 10 bytes of
processing RAM for each time domain data point in the sample set. So analyzing
a 10,000 point record only requires 100 Kbytes of RAM. Analyzing 1 million data
points requires 10 Mbytes of RAM. In addition to the RAM, analyzing such large
data sets requires a powerful high-speed processor and coprocessor.
The answers for the user have 100 times better resolution, but the tradeoff is
data quality versus manufacturing costs. The highest-resolution FFTs currently
available in DSOs are obtained by processing 6 million data points using 64
Mbytes of RAM.
There are two ways in which a DSO can acquire a long set of data samples in the
time domain at a fast sampling rate and still yield poor FFT measurements. Both
ways are due to insufficient processing power and are easy to spot if the scope
user knows what to look for. For example, assume 100,000 points of data are
captured at a 2-ns sampling rate in the time domain, but the FFT algorithm can
only handle 10,000 points.
It's possible that the DSO vendor could have chosen the first data point, the
11th, 21st, and so on, and by choosing only one tenth of the points, the scope
can analyze the frequency content of the signal from beginning to end. In this
case, however, the sampling rate of the data that has input to the FFT
algorithm is now 20 ns between points and the fastest signal period (Nyquist
frequency) that can be measured is 40 ns.
Making complex analysis easier
In the previous example, a scope user acquired data, performed FFTs on two
different sections of the data, then continued to acquire more data and perform
averaging in the frequency domain of the FFTs. After acquiring all the data,
the two FFTs were subtracted to observe differences.
Actually, this was an example of performing “math on math.” The scope acquired
the raw data set, performed the first math operation (FFT), stored the result
in RAM, acquired more data, performed another FFT, added the two results,
continued n times, and then divided each point of the FFT waveform by n to
obtain an average result. The FFT data sets were then subtracted and the result
was also stored to RAM. Obviously, this test scheme is much easier, faster, and
cheaper than trying to use two gated spectrum analyzers, dumping their data to
a computer, and writing a program to subtract the two data sets.
Another common analysis task involves looking at the instantaneous power and
total power in a pulse. The pulse under observation might be from a laser or
from an electrostatic discharge (see Fig. 5). Electrostatic discharge
resistance is now tested on devices ranging from semiconductor chips to
higher-level assemblies like keyboards and automobile dashboards.
The top trace (channel 1) in Fig. 5 shows the voltage versus time curve of the
electrostatic discharge. This trace can be used to document the test pulse as
meeting the requirements of a particular testing standard, such as IEC 804.1.
The second trace (math function A) shows V
square of the top trace. The third trace (math function B) shows V
It is obtained from Trace A by applying a scaling function. The scaling
function allows both a multiplicative constant (such as 1/R) and also a scaling
constant (to adjust offset if necessary). Waveform B shows the instantaneous
power of the electrostatic discharge at each point in time. Trace C is the
integral of trace B. The integral waveform shows how much total energy has been
discharged at each point in time. The final value of trace C measures the total
power in the pulse. Some scopes can perform these operations “live” each time
the scope triggers.
Other scopes can multiply, divide, and integrate, but can only perform these
operations on the raw data–they cannot integrate the square of a waveform.
Some scopes can perform one operation “live,” but require the scope to be
stopped to store the result of squaring. Then the user can manually recall the
squared waveform from a math reference memory to integrate it.
These kinds of complex analysis tasks abound in today's engineering and test
departments. Performing the tests quickly and documenting the results in a
single screen dump can significantly reduce the time it takes to get a new
product to market or to move inventory through the test department to finished
goods while satisfying ISO 9000 test documentation requirements.
Analysis results can be saved as hard copies, to floppy disks, or even to
portable hard drives. The bottom line is that digital scopes are moving to
longer memory lengths for data acquisition, but the user only gets the benefit
of having more data if the scope boosts its processing power to display, zoom,
measure, and analyze long waveforms.
CAPTIONS:
Fig. 1. A stream of 9,639 captured and analyzed data bits shows worst-case
amplitude, positive overshoot, rise time, and jitter (delay relative to a
reference).
Fig. 2. The oscillographic trace shows a persistence display of a sine wave
whose frequency is unstable, while the histogram of frequencies shows two major
components in the frequency distribution.
Fig. 3. Histograms can show the amplitudes and widths of the bits in a data
stream.
Fig. 4. Because of its much better resolution than the waveform in (a), the
waveform in (b) clearly shows that the waveform on the far left in (b) is
actually two closely spaced peaks.
Fig. 5. Analyzing the instantaneous and total power is another common task of
“smart” DSOs.
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