It can be difficult for you, as a design engineer, to measure the high-speed signals of microprocessor systems, especially those using bus architectures such as DDR II and RapidIO. The same can be said for high-speed serial data buses such as Fibre Channel, SONET, Gigabit Ethernet, and InfiniBand.
Making accurate delta-time measurements is especially difficult—and those involving jitter are the hardest—because engineers must see all the high-speed signal components. Determining the accuracy of this measurement type is no trivial task, especially given how highly interdependent it is on the signal under test.
To assure accurate measurements, you should thoroughly understand the different types of delta-time measurements and the various sources of errors that affect the ability to make precise measurements.
Sources of measurement inaccuracy come from the digital oscilloscope and its connection to the test component.
Delta-Time Measurements
Back to top
When making delta-time measurements, it's important to remember that there are two basic types: direct and derived.
Direct measurements determine the elapsed time between two events as defined by the crossings of a specific voltage level. Essentially, they are elapsed-time measurements, that is, how much time elapsed between events A and B. Direct measurements include period, pulse width, delay time, skew, rise time, and fall time.
Derived measurements are calculated from one or more direct measurements. This means that smaller errors in the direct measurements can, in some cases, be compounded and at other times minimized. Derived measurements include frequency, time-interval error, cycle-to-cycle jitter, and N-cycle jitter. Because derived measurements are calculated, they're affected more by a digitizing oscilloscope.
Reducing Error Sources
Back to top
There are several potential sources of error that can affect the delta-time accuracy of a digital oscilloscope. Some of these are due to the connection to the design-under-test. Others are caused by the oscilloscope itself.
To minimize errors resulting from signal connections, use the highest bandwidth, lowest noise probes available. Then follow standard techniques for acquiring high-quality signals. Also, take any necessary precautions to eliminate any degradation of the signal as it moves from the device-under-test to your scope.
Of course, you have to determine whether your digital oscilloscope is adequate to make the measurement, and you have to know its sources of error (within it) to minimize those effects. Such errors are significant threats to delta-time accuracy and are, unfortunately, extremely difficult to determine and minimize.
Many of the errors depend on the measurements being made, and on the type of signal under examination, including its frequency and period.
Six Primary Sources
Back to top
There are six primary sources of error inherent in the digital oscilloscopes used for delta-timing measurements. These sources include timebase center frequency accuracy, timing instability, vertical noise, bandwidth effects, interleaving or calibration error, and interpolation (aliasing) error. Let's discuss each in more detail.
Center Frequency Accuracy
Back to top
Let's look at the timebase center frequency accuracy first. Often quoted in parts per million (ppm), it represents the average frequency error of the instrument's reference clock. The timebase center frequency accuracy generally has minimal impact on the accuracy of most delta-time measurements.
For example, should an engineer examine 100 ps of jitter on a clock using a digital oscilloscope with a 10 ppm timebase center frequency accuracy, this error would introduce only 1 fs (femtosecond) of inaccuracy. This level of inaccuracy is generally of concern only when making extremely long duration measurements. As such, the timebase center frequency accuracy is usually the least significant of the error sources.
Timing Instability
Back to top
Next let's consider timing instability. Instability in the time base of an oscilloscope indicates a combination of phase noise in the instrument clock and aperture jitter in the samplers.
This inaccuracy is often a significant in today's oscilloscope designs, but is not a dominant source of timing error.
Bandwidth Effects
Back to top
Now let's examine bandwidth effects. Oscilloscope bandwidth has a larger effect on certain parametric measurements, such as rise time and certain skew measurements, than on other measurements, such as period.
For example, the period of a 500 MHz clock with a 50 ps rise time can be measured with a 500 MHz oscilloscope. However, the bandwidth of the oscilloscope acts as a harmonic limiter to the higher frequency components. This means that any transient and edge information contained in the original signal is removed.
To avoid this, the oscilloscope you choose should have adequate bandwidth to acquire the higher order harmonics of the signal. The Fibre Channel standard, for example, recommends an oscilloscope bandwidth of three to five times the frequency of the data signal being measured.
It's also important to consider that both the rise time of an oscilloscope and the rise time of the probe or interconnect cabling affect your final rise-time measurement.
You can apply this formula to make small corrections to a measurement when the rise times of the oscilloscope and probe are smaller than that of the signal. If the rise times of the oscilloscope and probe are close to, or larger than, that of signal, you may get incorrect results if you use this equation to adjust a measurement.
Also, with current digital oscilloscope technology, the rise time may not fit a Gaussian distribution, thereby making any use of this technique unreliable.
Vertical Noise
Back to top
Let's turn our attention now to vertical noise. Noise is inherent in any oscilloscope's vertical system. The amount of inherent vertical noise is a measure of the quality of the oscilloscope design. Vertical noise can also result from improper probing and acquisition techniques, bad connections, or environmental noise.
Vertical noise is important because it's often the dominant error in timing measurements, especially for signals with relatively low slew-rates. Because this is such an important source of error, you should use oscilloscopes that have vertical systems with the lowest noise.
To minimize sources of vertical noise outside the scope, also follow good basic probing techniques. Make a secure connection and keep your ground leads as short as possible.
Try to control the test environment as much as possible, too. Eliminate any stray interference that could inadvertently affect your design's signal quality. In digital-sampling oscilloscopes, maximizing the amplitude of a signal applied to the acquisition system will improve the signal-to-noise ratio, and will minimize the vertical quantization error within the system.
Interleaving Errors
Back to top
Now consider interleaving or calibration error. Today's high-speed digital oscilloscopes use multiple digitizers, which are interleaved in a predetermined order to achieve high digitizing rates. Typically, these digitizers are interleaved in powers of two, with the predominant numbers being eight and sixteen.
Interleaving errors result from mismatches in performance characteristics between these digitizers. All modern digitizers have calibration adjustments or self-calibrating routines. In order to get the optimum accuracy, you need to be sure that your instrument is properly calibrated (or self-calibrated) before beginning a measurement. Finally, digitizing errors will be different at different frequencies.
Aliasing
Back to top
Now consider interpolation error (also known as aliasing). This source of error also poses a major threat to delta-time accuracy. Since the sampling techniques used in digitizers sample the signal at a point in time determined by the system clock, the sample may not fall at the exact crossing level set for the measurement.
To alleviate this problem, the system uses an interpolation algorithm to calculate where in time the signal crossed the level set between the digitized points. As a result, the accuracy of the measurement is dependent on the accuracy and consistency of this interpolation algorithm.
Moreover, for the interpolation algorithm to be effective, there must be a sufficient number of sample points with respect to the frequency content of the signal and the bandwidth of the instrument. Both are needed to supply the necessary performance.
Good, Bad, and Worst
Back to top
The most effective way to demonstrate the delta-time measurement accuracy of an instrument is to use what is referred to as the good, the bad, and the worst cases. As the three displays below show, an engineer in the real world may have a signal that's designed to operate in the "good" category of the digital oscilloscope (a 100 MHz clock signal, for example).
But all real-world signals have jitter. If this signal has a peak jitter of 100 ps, it will operate in the bad or even worst-case category for some amount of time. Therefore, even if the design engineer's input signal happens to nominally match the digital oscilloscope's best conditions (with respect to delta-time accuracy), the worst-case measurement inaccuracy should still be assumed.
With all these different sources of error affecting the accuracy of the instrument—especially errors due to vertical noise, interleaving, and interpolation—there is no easy way to specify a simple delta-time accuracy for an arbitrary real-world signal. Instead, the only safe assumption is to determine the worst-case scenario for an actual signal.
The Good. This waveform benchmarks the overall system's ability to measure the standard deviation, which is equivalent to the RMS jitter on a square wave with a period of 800 ps. This results in an impressive 822.11 fs delta-time measurement accuracy.
The Bad. This waveform demonstrates the effect of accuracy when the error from digitizer interleaving is introduced, by changing the input signal to a square wave with a period of 850 ps. This results in RMS jitter of 1.2031 ps.
The Worst Case. This waveform presents the worst-case scenario when the errors from both digitizer interleaving and interpolation occur at an input square-wave signal with a period of 875 ps. With a rise time of 100 ps, there are only two to three sample points on each edge at a sampling interval of 50 ps/point. This results in RMS jitter of 1.9183 ps.
Even in those situations where the signal is thought to fit the best case, the worst should be assumed, because in the real world a signal could easily change, resulting in an erroneous measurement.
The easiest way for you to ensure that your measurements are accurate is to use the highest quality instrument available, for example, an oscilloscope with a noise jitter floor of 700 fs rms and a delta-time accuracy of 3 ps rms. Once you remove the oscilloscope as a factor for errors, then you only have to focus on understanding where you might potentially introduce other errors into the measurement (probing, interconnection cables, external noise sources). You can then do your best to minimize these effects in order to ensure the best measurement accuracy possible.
About The Author
Back to top
Tim Margesan is a Product Marketing Manager in the Oscilloscope Solutions Segment of Tektronix' Instrument Business. He is responsible for defining, marketing, and supporting jitter and timing measurement approaches for the firm's oscilloscope product lines. Margesan has been with Tektronix for 18 of the 28 years he has worked in the test and measurement industry. He has an engineering background in design, manufacturing, and test phases of product development. He has developed systems ranging from electrometers to precision time-domain reflectometry systems.
