Harmonics occur at every 0.5 times the bit rate. For example, a 4-Gbit/s signal would have significant harmonics at 2, 4, 6, 8, 10 GHz, going to infinity. In a perfect square wave with an instrument that has infinite dynamic range, getting the fifth harmonic requires an oscilloscope with at least 10 GHz of bandwidth. However, perfect square waves don’t exist in real life, especially in today’s high-speed digital signals. A number of factors erode the strength of the harmonics and can spread out the harmonic content. The most important factor is the signal’s rise time.
An ideal square wave has a rise time of near 0 ps. In real-world applications under the best designs, however, rise times at the receiver very rarely exceed 30 ps. Rise times are slowed by PCB material, connectors, traces, and distance. FR-4 material, popular due to its low cost, is one of the most common materials used in PCB material. FR-4 has an absolute maximum rise time of 45 ps; however, it will typically see maximum rise times of only 50 to 60 ps (80/20).
Consider the SATA 6G HFTP signal spectrum analysis with a rise time of 45 ps (Fig. 2). It has a bit rate of 6 Gbits/s (fifth harmonic at 15 GHz). However, the fifth harmonic has an amplitude that’s 45 dB less than the first harmonic. For an oscilloscope to display any of its content in the time domain, the oscilloscope must have a dynamic range of at least 45 dB. RT oscilloscopes have real-world dynamic ranges of 44 dB or less, meaning even RT scopes with 15 GHz or more of bandwidth will miss the fifth harmonic.
For the fifth harmonic to significantly influence the measurement of an RT scope (about 35 dB below the carrier frequency), the rise time must be faster than 30 ps. Such fast rise times don’t occur frequently in real-life signals. On the other hand, an ET oscilloscope has the dynamic range to capture the entire fifth harmonic of a SATA 6G signal. At this point, a designer must decide between using an RT oscilloscope that can capture through the third harmonic or an ET oscilloscope that can capture harmonic content equivalent to its bandwidth.
Another example to consider is PCI Express Gen 2. The Gen 2 signal has a data rate of 5 Gbits/s. This data rate would require an oscilloscope of at least 12.5 GHz to capture the fifth harmonic. However, the signal will typically have rise times from between 50 and 70 ps at the receiver. The result is that the fifth harmonic is 48 dB down from the zero crossing, meaning that a 12.5-GHz RT scope (dynamic range of 35 to 45 dB) won’t capture any of the fifth-harmonic content.
Incredibly, 8- and 12.5-GHz RT oscilloscopes will capture the same harmonic content of the PCI Express Gen II signal. For this signal to capture the fifth-harmonic content, it’s necessary to use an ET oscilloscope with its higher dynamic range. It should be noted that the PCI Express Sig currently requires at least 12.5 GHz for PCI Express Gen 2 testing. This is evident by the two real-time eyes shown in (Figs. 3a and 3b). Note that despite the extra bandwidth, the real-time eyes look identical at 60-ps rise times.
TRADEOFFS
If the third harmonic is enough harmonic content, RT oscilloscopes offer a number of features not available with ET oscilloscopes. The most significant of these is that an RT scope will offer a sampling rate and memory depth significantly higher than an ET scope. An RT scope also doesn’t require an external trigger, because it will trigger itself. An ET scope, on the other hand, requires an outside trigger and takes multiple single-point acquisitions to display the data.
RT oscilloscopes tend to have more automated compliance software applications, adding convenience and speed to measurements. For PCI Express Gen 2, Agilent, LeCroy, and Tektronix RT scopes have automated software for measuring a number of key specifications. In contrast, ET scopes have more bandwidth and less noise. In addition to bandwidth, ET scopes provide a module that will allow for TDR measurements.
CONCLUSION
Choosing the right oscilloscope for your application is, of course, very important. A general rule of thumb has been to use the fifth harmonic as a measure for how much bandwidth to purchase. However, for rise times slower than 30 ps, RT oscilloscopes won’t capture a significant amount of harmonic content from the fifth harmonic.
In fact, at high data rates (6 Gbits/s and faster) at the receiver in most cases, RT scopes won’t capture the fifth harmonic at all regardless of bandwidth. This is because the fifth harmonic’s content is below the dynamic range of an RT scope. To capture the fifth harmonic, it’s necessary to use an ET oscilloscope. RT scopes offer features such as deeper memory and sampling rate.
This all means that an oscilloscope purchaser must decide between capturing up to the third harmonic and getting the features of an RT scope or capturing the fifth harmonic with an ET scope. It should be noted that as rise times decrease below 30 ps, the fifth-harmonic content will become much more prevalent. As a result, in the future, RT scopes will also be able to capture the fifth harmonic.
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