What's the difference between a GHz and a GS?

One of the most confusing things for real-time oscilloscope buyers is the difference between sample rate and bandwidth. I remember when I started with Tektronix, I heard people tell me they owned a "20GHz Agilent oscilloscope". At the time, Tektronix was the only one making a 20GHz oscilloscope. Agilent made nothing more than 13GHz. What they were telling me was impossible. However, the lower bandwidth Agilent oscilloscopes did have 20GS/s sample rate, which was the source of their confusion.

So what is the difference between a GHz and a GS?
In short, gigahertz (GHz) is a measure of the frequency content that the scope can see, and gigasamples per second (GS/s) is a measure of the digitizing rate of the scope.

On the GS side, the bandwidth of the oscilloscope is determined by the Nyquist bandwidth, or the requirement that the oscilloscope must digitize at least 2x higher than the highest frequency content in the signal. Typically, oscilloscope vendors use the 2.5x rule of thumb for specifying sample rate.  Some optical and RF applications are okay with 2x, and some high speed serial applications require more than 2.5x.  But 2.5x is a pretty good industry standard.  So if you have a 2GHz oscilloscope, then it requires 5GS/s of sampling rate.

So why does the Tektronix DPO73304D with 100GS/s not have a 50GHz bandwidth?  Why does a Tektronix MSO4104B with 5GS/s not have 2.5GHz of bandwidth?

In the following example, you can see a generic 2GHz oscilloscope with a 5GS/s sampling rate.  This is a generic example and not matched to anything in the market today.  The first piece of the oscilloscope that determines the bandwidth is actually the variable gain front-end amplifier.  This is the part that the volts/division knob adjusts when you change vertical scale.  It also acts like a low pass filter, passing only the specified signal through at the specified amplification to fill the digitizer input.

Now suppose I only had a 1GS/s digitizer.  The 2.5x Nyquist rule tells me I can only digitize a 1GS/2.5 or 400MHz signal with this digitizer.  The solution is to use a track-and-hold as a decelerator.  In the above case, the track-and-hold reduces my 2GHz signal by a factor of 5, delivering it to five slower digitizers.  The effective sampling rate of my system is 5GS/s, and the bandwidth is determined by the front-end and track-and-hold combination.

If I wanted a 4GHz oscilloscope, I could use the exact same digitizers as above.  I would just need a higher-bandwidth front-end with a higher speed track-and-hold.

In this example, the same base digitizer now yields a 10GS/s system, with a 4GHz bandwidth.  In both examples, I actually use the same speed digitizer.  But the track-and-hold means my system digitizing rate is twice as high in the second example.

Now if I were to put this same track-and-hold on the 2GHz front end (10GS with 2GHz), my system would still only be 2GHz.  I may get some advantage to oversampling in noise reduction or effective number of bits improvement, but I do not get extra bandwidth.  The lowest bandwidth piece of the link determines my eventual system bandwidth.

There is a cool trick to determine the base rate of any digitizer system.  FFT the trace and apply averaging to remove random noise.  In both cases above, you would see spikes every 1GHz, indicating that despite being 5GS or 10GS systems, there is interleaving being performed.  The spikes are called interleave errors, and while major oscilloscope vendors work hard to reduce them, they will always be present.  Even femtoseconds of error will appear in an FFT since they are consistent and repeated.

In the past year, both major oscilloscope manufacturers announced high-bandwidth oscilloscopes.  Agilent introduced their oscilloscope based on Indium Phosphide (InP) technology, a 32GHz, 80GS/s oscilloscope, the DSOX93204A.  Tektronix introduced an oscilloscope based on 8HP Silicon Germanium (SiGe), a 33GHz, 100GS/s oscilloscope.  That oscilloscope is the Tektronix DPO73304D.

Tektronix DPO73304D - 33GHz and 100GS/s Real-Time Oscilloscope

Reading press releases from both companies, they stress that the new chipset replaces the front-end and track-and-hold, but neither makes any claim as to new digitizers.  As you can see above, the bandwidth is determined by the front-end and track-and-hold, not the digitizer.  In fact, a simple FFT on the Agilent DSOX93204A reveals they are still using their 250MS/s CMOS digitizer, and Tektronix is using the same 3.125GS digitizers in their DPO73304D.  Now there are distinct advantages to using a higher base-rate digitizer, including less digitizer distortion and better spurious response.  But the base-rate of the digitizer does not determine the overall system bandwidth.

Tektronix SiGe 8HP - 100GS Track-and-Hold (center) with two 33GHz front-ends (sides)

In the above photo, you can see there are 100GHz SMPM connectors directly on the package of the ASIC that contains both the track-and-hold and the front-end.  In fact, there are 2 front-ends on the same multi-chip module, so the 100GS/s track-and-hold can supply 100GS to a single channel or 50GS to two channels.  The connectors are on the package itself because the signal is high bandwidth until it hits the track-and-hold, so the desire is to preserve every bit of signal strength as long as possible.  Once it passes by the track-and-hold, it is decelerated and can be sent over the PCB to be digitized.

The track and hold itself is an 8-way track and hold, so it can split a single 100GS signal 8-ways or two 50GS signals 4-ways (you can see those traces above and below the package).  This feeds the 12.5GS digitizer module, which also has a slower track-and-hold on-board that gets down to the 3.125GS base-rate.

For more on the acquisition technology, watch this video: How the Tektronix DPO73304D acquisition system operates.

The other reason it is important to understand sample rate is that both the Tektronix and Agilent oscilloscopes divide sample rate.  On the Tektronix DPO73304D, it is 100GS/s on 2 channels.  Pure Nyquist rules would indicate effective bandwidth of 40-50GHz, but the front-end limits it to 33GHz.  The extra oversampling serves to reduce noise and improve effective bits.  When going to 4 channels, the oscilloscope provides 50GS/s, which is 20-25GHz depending on the oversampling needed for a given application. 

On the Agilent DSOX93204A, it is only 80GS/s on 2 channels, which is sufficient at 2.5x for a 32GHz system, but does not give you any extra oversampling.  On 4 channels, it is 40GS/s, which at 2.5x Nyquist yields 16GHz of bandwidth.

There is a way to get the full 33GHz on all 4 channels of the Tektronix DPO73304D, and that is to use equivalent time sampling.  I will discuss exactly what this means in a later post, but the DPO73304D can achieve 10TS/s so long as a signal is repetitive and there is a trigger.  Now 10TS/s does not provide 4THz of bandwidth, because the front-end will still limit the system to 33GHz.  But it does provide plenty of bandwidth to ensure 33GHz on all 4 channels simultaneously.