# Capturing and Evaluating High-Frequency Signals

**Coherent interleaved sampling is a new technique that can acquire data faster with more data points than sequential sampling. **

Engineers who need to characterize semiconductor devices, high-speed clocks, fast serial data streams, and other electronic or optical devices that produce high-frequency signals have used sampling oscilloscopes for many years. Now there is new technology that makes the job of evaluating such circuits faster and more precise.

In particular, when an engineer needs to use an oscilloscope with 20-GHz or higher bandwidth to capture and characterize signals, a new sampling technique called coherent interleaved sampling (CIS) is available. It is contained in a class of oscilloscopes called near real-time oscilloscopes (NROs) to distinguish them from real-time and sampling oscilloscopes.

**Differences Among Real-Time, Sequential Sampling, and CIS Methods**

The architecture of a high-speed real-time oscilloscope has an amplifier followed by an 8-b ADC and a bank of acquisition memory. When the oscilloscope is triggered, the memory captures a data stream that flows from the ADC in real time.

Real-time oscilloscopes have a set of amplifier/attenuator combinations through which the input sensitivity is controlled using the volts/division knob. Currently, the fastest ADC sampling rate available for such instruments is 40 GS/s (40 S/ns), and the highest bandwidth for this type of oscilloscope is 20 GHz.

The front end of a traditional sampling oscilloscope begins with a sampling head that contains a track-and-hold with bandwidth from 20 GHz to 70 GHz. The oscilloscope is triggered at the beginning of a repeating signal pattern, the voltage is held steady by the track-and-hold, and the ADC captures just one sample.

A small increment of time is added between the trigger time and the sampling point each time the pattern repeats (**Figure 1**). Through this method, a sequence of samples is obtained that conforms to the shape of the pattern. Because the oscilloscope knows the exact time delay between the beginning of the pattern and each sample, it is possible to reconstruct the shape of the repeating waveform.

Figure 1. Method of Data Acquisition for a Sequential Sampling Oscilloscope

Since the sampling rate is relatively slow, higher resolution ADCs can be used. Often, 14 b of vertical resolution are available. The sequential sampling rate is 200 kS/s or lower, and the memory length of these oscilloscopes is very short. In all cases, the acquired waveform is limited to 4 kpoints of memory miniscule compared to the long record lengths available in real-time oscilloscopes.

An NRO using the CIS method most often captures a repeating data pattern although it also can perform eye-pattern tests and jitter measurements, such as Rj/Dj breakdown, on nonrepetitive signals including live serial data streams. The sampler is phase locked to the clock recovered from the incoming signal. It samples at a rate marginally different from 10 MS/s.

The difference is set so that the sampling rate is not an exact submultiple of the data rate, which would cause the sampling to repeat at exactly the same point each time the pattern occurred. The oscilloscope can capture data continuously at the nominal 10-MS/s rate and store the data points into long memory.

The standard memory length in an NRO is 4 Mpoints; up to 512 Mpoints are available. As with the sequential sampling oscilloscope, an NRO measures the time between the start of the data pattern and each sample, allowing the waveform to be reconstructed.

An NRO does not acquire the samples in order. It maintains a much higher sampling rate than the sequential sampling oscilloscopes and reorders the points to reconstruct the waveform (**Figure 2**). Due to the difference in data acquisition techniques, the CIS method acquires data at least 50• faster than the fastest sequential sampling oscilloscope (10 MS/s compared to 200 kS/s) and a minimum of 1,000• more data points (4 Mpoints compared to 4 kpoints).

Figure 2. Data Pattern Sampled at a Constant Sample Rate Near 10 MS/s

**Coherent Interleaved Sampling**

As its name implies, CIS uses a sampling clock that is phase locked to the bit clock of the signal under test. The sampling clock is derived by means of a phase-locked loop (PLL) in the time base that uses the trigger signal as a phase reference.

This approach has two advantages:

• The instrument's timing accuracy is improved because it is not necessary to maintain calibration of an internal delay generator.

• The PLL filters out any jitter in the trigger signal, maintaining its specified jitter regardless of the trigger signal quality. This is particularly important in cases where an external clock recovery circuit is used to generate the trigger.

Traditional sequential time bases will exhibit additional jitter when clock recovery is used because the trigger signal functions directly as a timing reference. Any jitter on the trigger translates directly into a timing error.

To understand the operation of CIS, consider coherent sampling of a periodic signal such as a repeating bit pattern. The sampling clock derived from the trigger signal via a PLL is set to a frequency slightly lower than an integer submultiple of the bit clock. The sampling interval is set so that the desired number of samples is acquired over one period of the signal under test.

This is shown in **Figure 3** for an 8-b data pattern. The pattern repeats every LT_{b} seconds where L is the pattern length and T_{b} the duration of one unit interval (UI). The sampling rate is determined by the data rate and the pattern length and can be described by the equation:

This equation shows that the sampling rate can become very slow for long pattern lengths and low bit rates. For example, a 1,024-b pattern at 2.5 Gb/s will give a sampling rate of 2.4 MS/s.

Figure 3. Coherent Sampling Data Acquired by Locking to the Data Pattern Rate

CIS improves basic coherent sampling by maintaining the sampling rate regardless of the pattern length or bit rate. A constant sampling rate of 10 MS/s is achieved by dividing the pattern repetition interval, LT_{b}, into K segments and using the segment time to determine the coherent sampling frequency.

This is shown in **Figure 4 **for the same 8-b pattern. The added segments are indicated by the green lines. The data samples no longer are in the proper time order because of the segmentation, so the samples must be reordered after the acquisition is complete.

The sampling rate for CIS can be described by the equation:

The factor K can be varied to maintain a 10-Ms/s sampling rate for any pattern length or bit rate.

**Advantages of CIS**

The available sampling heads for sequential sampling oscilloscopes vary in bandwidth from 20 GHz to 70 GHz. For the NRO, the available bandwidth range is from 20 GHz to 100 GHz and includes both electrical and optical inputs. As a result, the signals captured with these oscilloscopes represent fast electronic events. An NRO, for example, can apply a fast-Fourier transform (FFT) to the captured signal to look for harmonics or give other insights in the frequency domain.

Suppose you have built a high-speed clock or data transmitter and would like to model what the signal will look like after passing through a bandwidth-limited transmission medium. **Figure 5 **shows a 10-Gb/s data stream captured using a 20-GHz bandwidth and a calculation that models what the waveform will look like after passing through a 4^{th} order Bessel filter with 5-GHz roll-off point.

Figure 5. 10-Gb/s Signal Captured Using a 20-GHz Sampling Head in the Top Trace and Modified by a 4^{th} Order Bessel Function With a 5-GHz Roll-Off Point in the Second Trace

In addition to the utility of long memory to see complex waveforms and perform math, the 50• higher sampling rate and an accelerated throughput architecture for handling the data arrays lead to much faster gathering of data for eye-pattern tests. Such tests provide an estimate of the bit error rate (BER), typically for 10^{12} b.

A more accurate estimation can be made if the oscilloscope captures 40 million bits rather than 1 million bits when making the estimate. Overall, the throughput rate of capturing data samples and transferring them into an eye-pattern test can be 3 million S/s, about 75• faster than the fastest sequential sampling oscilloscopes.

This leads to greater confidence in BER estimates. Tests that might have taken several hours now can be done in minutes. Suppose you are trying to troubleshoot rare violations of an eye-pattern test. The capability to acquire data 75• (at least) faster makes it much more likely the error can be seen.

**About the Authors**

Michael Lauterbach, Ph.D., is director-product management at LeCroy where he has worked for 23 years. His doctorate is from Yale in high energy physics; his undergraduate education at Carleton College included a double major in math and physics. 845-578-6057, e-mail: [email protected]

*Michael Schnecker is the marketing manager at LeCroy. He has spent 17 years in the test instrument marketplace. 845-578-2000, e-mail: [email protected]*

*LeCroy, 700 Chestnut Ridge Rd., Chestnut Ridge, NY 10977*

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