By MIKE MARTIN
Senior Marketing Engineer
Tektronix, www.tek.com
Over the past decade, serial data communication rates have increased more than tenfold. This has driven the need for ever-higher-bandwidth (BW) real-time oscilloscopes to verify and debug high-speed system designs. In an effort to meet these communications test requirements, test manufacturers have responded with interleaving techniques to extend the BW performance of real-time oscilloscopes beyond the physical capabilities of today’s analog-to-digital converter (ADC) technology. But with 100/400G data communications heading for deployment, and optical communications researchers targeting speeds as fast at 1 Tbit/s, even faster real-time oscilloscopes will be needed in the future.
One possible solution is called “asynchronous time interleaving” (ATI), which has the potential to extend real-time oscilloscope performance into the 70-GHz range and beyond, while maintaining excellent signal fidelity. In this article, we first review the techniques currently in use to extend the BW performance of real-time oscilloscopes and then contrast these current techniques against ATI to provide a deeper understanding of the potential provided by this new technology.
The conventional ADC channel
A conventional real-time digital oscilloscope channel typically employs an analog front-end consisting of a preamp and/or attenuation for signal conditioning, and a track-and-hold for locking the signal amplitude during the sampling period. An ADC is used to convert the sequential voltage levels coming from the track-and-hold into a stream of numeric values. Assuming the analog front-end supports the full BW requirements of the channel, the sample rate of the ADC represents the primary constraint to the channel’s BW potential.
The Nyquist Theorem states that in order to reproduce an accurate representation of all signal content within the desired BW, the sample rate must be greater than two times greater than BW. For example, a 25-GHz channel BW will require a sample rate above 50 Gsamples/s. As the BW requirements continue to increase, finding ADCs that meet the Nyquist requirement becomes a significant challenge.
A key consideration for any oscilloscope is channel noise (Fig. 1 ). Because random noise by definition contains all frequencies, the power spectral density is spread equally across the Nyquist BW of the instrument. In the case of a 50-Gsample/s channel, the Nyquist BW is 25 GHz. There is some noise rejection that occurs in Fig. 1 because the oscilloscope BW limit filter (also called an anti-alias filter) rejects noise in the spectral region between the cutoff of the BW limit filter and the Nyquist BW of the channel.
Fig. 1: Random-noise power spectral density (PSD) is shown here relative to frequency.
Time-interleaved channels
Time interleaving is a common technique used to extend sample rate performance beyond the capability of available ADC components. With this approach, the analog front-end is designed to pass the entire BW of interest, and two ADCs are used in parallel. Each ADC must provide a sample rate greater than half the total sample rate required to meet the Nyquist requirement.
For example, if the analog front-end can support up to 50 GHz, two 50-Gsample/s ADCs can be interleaved to provide 100-Gsample/s conversion. In this case, the two ADCs are clocked 180º out of phase. Data is stored in the memory behind each ADC. Following a successful acquisition, the complete 100-Gsamples/s representation of the waveform is reconstructed by de-interleaving the data (sometimes called demuxing).
There is no theoretical limitation to how many ADCs can be interleaved. In practice, however, it becomes difficult to carefully control the time alignment of interleaved devices as the ADC count goes up. This type of time-interleave technique has been used by all the major oscilloscope manufacturers to push performance into the GHz range.
On the noise front, as sample rate increases, random noise is spread evenly across the new Nyquist BW. In the example shown in Fig. 2 , the sample rate is increased from 50 to 100 Gsamples/s, so the Nyquist BW is now extended from 25 to 50 GHz. If the noise performance of each of the time-interleaved channels is equal, the noise power spectral density is now about half the power, spread evenly across the new Nyquist BW. The main goal for time-interleave is to extend the BW of the system by providing a higher-BW analog front-end, and a higher sample rate, but if the BW is kept to the same value as described initially (using the same BW limit filter), the net effect is to reject a larger amount of the noise signal. Implementations of this approach have demonstrated noise reduction in the range of 15% to 20%.
Fig. 2: The Nyquist BW is extended as a result of time interleaving.
Frequency interleaving with downconverters
Downconverters have been used for well over a century in radio receivers and other RF applications. The concept is simple: mix two frequencies, and the result will be a sum and a difference in frequencies (also called hetrodynes). If you can carefully select one of the two frequencies (e.g., a local oscillator) in relationship to the other, you have the ability to move the different frequencies to a more convenient range (typically lower) within which to work.
In oscilloscopes, this mixer-based technique is called frequency interleaving (Fig. 3 ). In the early days, the downconverter was an external unit, and the integration and calibration of the downconverter with the oscilloscope was the user’s responsibility. Eventually, work was done to incorporate the downconverter into the instrument. In the case of an oscilloscope channel, setting the local oscillator frequency to equal the mid-band of the analog front-end BW makes it possible to acquire the upper half of the scope passband with one ADC, and the lower half of the passband with another ADC. The total waveform is then reconstructed by “stitching” together the upper and lower spectral halves, a task for digital signal processors (DSP).
Fig. 3: A frequency-interleaved acquisition channel can be created using downconverters.
The key advantage of frequency interleaving for the oscilloscope designer is that each ADC needs only to have a sample rate that is greater than the total BW, making it possible to produce oscilloscopes with more than 60-GHz BW. However, there are challenges in this design approach. Once the acquisition has completed, and the data is in waveform memory, it is necessary to upconvert the upper band back to its original frequency range using digital signal processing techniques.
Recovering the two spectral “halves” and reconstructing the waveform is complicated and prone to errors. Because the paths are not identical, it is necessary to compensate for these differences in the calibration that is part of the DSP. Furthermore, due to the sharp bandpass filters used on the two spectral halves, recovering the exact center of the spectrum is problematic. Issues can include flatness at the recombination zone, and phase linearity shifts at that point.
In addition, channel noise takes on greater significance when using the frequency interleaving technique. As mentioned previously, the noise PSD is evenly spread across the Nyquist BW (half the sample rate) of an acquisition channel. Because each ADC is acquiring half of the entire frequency span, there is no potential opportunity for noise reduction when going from time-interleaved to frequency-interleaved configurations (while keeping the BW constant). In fact, there is generally a noise increase when using frequency interleaving (Fig. 4 ).
Fig. 4: With frequency interleaving, the noise PSD across Nyquist BW generally increases, as compared to Fig. 1.
Asynchronous time interleaving
Although frequency interleaving offers increased BW, its practical application is degraded by unavoidable technical issues and challenges that compromise signal integrity. While offering similar performance gains, asynchronous time interleaving (ATI) avoids these problems through the use of a pre-sampler as a harmonic mixer (Fig. 5 ).
Fig. 5: The circuit shown here is used to create asynchronous time interleaving.
An important element of this design is that the paths are symmetrical. As a result, there are no significant differences in propagation delay or phase shift between the two sides of the acquisition channel. This simplifies the post-acquisition process of DSP re-mixing, or “reconstruction,” and thus minimizes the amount of error at the mid-band crossover. With ATI, the entire BW of the signal is applied to both ADCs. In this way, the PSD of the noise is evenly spread across the total sample rate, which is twice the sample rate of the individual ADCs. The result is that the overall noise in the passband is lower than it would be in the comparable frequency-interleaved architecture.
Because harmonic mixing and time sampling are really the same thing, it is possible to accomplish the mixing shown in the ATI circuit diagram using a pre-sampler. This design utilizes the pre-sampler to intentionally sub-sample the input signal, thereby aliasing or folding back the upper half of the spectral content back into the Nyquist BW of the ADC (Fig. 6 ). For example, a 70GHz system could be achieved by running the asynchronous sample clock at 75 GHz. This would result in the upper half of the 70GHz signal being aliased back into the range of DC to 37.5 GHz. The resulting data from the pre-sampler could then be sampled by the ADC at a rate independent from the pre-sampler, such as 100 Gsamples/s. Note that the pre-sampler would run asynchronously from the ADC sample clock. represents the signal on each leg of the ATI channel.
Fig. 6: Presampling places the signal on each leg of the ATI channel in the ADC’s bandwidth .
A more complete representation of the block diagram for an ATI channel is shown in Fig. 7 , with an indication of the spectral content of the signal at key points in the acquisition channel. In this configuration, the entire spectrum is applied to the preamp, and passes through the splitter to each pre-sampler. The output of the pre-sampler is a spectrum that contains a difference spectrum of the upper band folded back onto the lower band range, as well as the sum spectrum of the lower band overlaid on the upper band range.
Fig. 7: In this more complete representation of an ATI channel block diagram, spectral content is indicated at key points in the channel.
This complex spectrum is then passed through a low-pass filter that removes the upper band range, but passes the lower band (including the folded back upper band content) intact. This filtered signal is then passed to the track and hold, and captured by the ADC.
Once the acquisition is complete, and the data is stored into memory, the original signal can be recovered by re-mixing the signal digitally using DSP techniques. At this point, rather than a physical asynchronous sampling clock signal, a mathematical representation of the asynchronous sampling clock signal can be used as input to the digital mixer, taking care that the phase relationship between the original analog asynchronous sampling clock and the mathematical representation of that signal are identical.
Note that the two pre-samplers are 180 degrees out of phase. This is important when it comes to reconstruction of the signal. After the digital mixing step of signal reconstruction, the numerical signal contains the sum and difference spectral content from the original acquired data. Conveniently, during the final combining of the signals, the portions of the spectrum that are 180 degrees out of phase cancel, and all that is left is the original spectrum, plus a portion of the sum spectrum which is removed with a 75 GHz low pass filter. This leaves only the content from DC to 70GHz that was originally applied to the scope for acquisition.
The final combining step is essentially a summation divided by two. This function returns the input amplitudes to their original value, but also has the effect of averaging the noise of the overall acquisition, thereby reducing the total noise of the measurement channel.
The insatiable demand for faster data communications is fueling the need for ever-faster real-time oscilloscopes to verify and debug higher-speed system designs. With conventional architectures, oscilloscope BWs are limited to the processing speeds of available ADCs. To overcome this limitation, oscilloscope designers have turned to interleaving techniques that allow the use of multiple ADCs in parallel to increase BW and sampling rates. Frequency or mixer-based acquisition channels support higher BWs, but suffer from increased noise and signal integrity issues. A key problem is recovering the spectral halves and reconstructing the waveform. A new approach, asynchronous time interleaving, uses symmetrical acquisition paths so all ADCs see the full spectrum, meaning the signal can be recovered by simply re-mixing using DSP techniques. This approach offers the performance gains available from interleaved architectures while preserving signal fidelity and lowering the noise floor.
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