Digital signal compression in mixed-signal ATE

Compression techniques can reduce real-time waveform memory requirements or increase the performance of test instruments.

By Daniel Rosenthal, 3 dB Consulting -- Test & Measurement World, 11/1/2008 2:00:00 AM

Signal compression is an appealing technique to use in mixed-signal ATE (automated test equipment) systems because it can reduce the cost of test while improving tester performance. Unfortunately, mixed-signal ATE is one of the last remaining class of systems where designers still cling to the comfort of uncompressed, fixed-rate linear coding.

It was fairly common for manufacturers to compress the signals on older analog testers and then accept and manage the resulting error budgets and uncertainty. But once AWGs (arbitrary waveform generators), digitizers, and DSPs (digital signal processors) were combined to create mixed-signal testers, many in the industry began treating digital-domain signals with absolute exactness.

In contrast, manufacturers of other types of DSP-based systems have embraced more efficient coding techniques: Telecom systems have long used voice-band coding (ADPCM, or adaptive differential pulse code modulation); imaging systems are coded with JPEG; video employs MPEG; and audio systems, of course, use the ubiquitous .MP3 format. The use of these compressed coding techniques has made the economics of digital media distribution practical.

The benefits of signal compression to mixed-signal ATE are many. Most obviously, signal compression allows manufacturers to build a system with less storage memory, leading to lower system cost. Conversely, this advantage could be turned around to yield greater waveform capacity. Compression can reduce the required number and quality of signal interconnects, which consume a significant portion of ATE system real-estate and material costs. In addition, a 4:1 compression can also increase the effective performance of existing interconnects by allowing a 5-GHz infrastructure to support 20-GHz instrumentation.

Bandwidth and Nyquist

ATE system bandwidth is dictated by the Nyquist theorem regarding analog signals (bandwidth & Fs/2, where Fs is the sampling frequency) and the quantization-noise-limited SNR (signal-to-noise ratio). For example, SNR in dBfs (decibels full scale) = 6.02 ENOB + 1.76, where ENOB is the effective number of bits. Both anti-aliasing and reconstruction filters, however, require higher oversampling rates to be used, further driving up memory size and interconnect bandwidth.

Some systems use encoding techniques such as block floating point or DSP techniques such as decimation, but these cannot approach the ideal sample rates dictated by Nyquist.

Designers of mixed-signal ATE systems generally still prefer uncompressed, fixed-rate linear coding. The engineers who resist using signal compression are often concerned about three main issues: measurement accuracy and uncertainty, a compression method’s ability to handle arbitrary (and unknown) measurements, and the ease of integrating the compression algorithm into a system. But these concerns are easily addressed by capabilities in today’s commercial signal-compression algorithms, so designers should not hesitate to incorporate compression into their mixed-signal testers.

For example, at the most basic level, some compression algorithms perform lossless compression, which permits the original signal to be recovered from the compressed signal. While the use of lossless compression will not affect measurement accuracy and uncertainty, the resulting compression ratio could greatly reduce the system cost and footprint. An example of a mixed-signal test in which lossless compression can achieve this objective is an all-codes DAC (digital-to-analog converter) linearity test, in which thousands of samples are reduced to one or two numbers representing the worst-case integral or differential linearity of the device under test. The integrity of the measurement depends on accurately preserving the tested parameter, not on accurately preserving every single analog sample.

Tests of compression algorithms

While working with Samplify Systems, I helped the company conduct tests of its commercially available signal-compression algorithm. One DAC linearity test (Figure 1) that used the algorithm achieved a 5:1 lossless compression ratio of the simulated data with no loss of accuracy or uncertainty. We included noise at the –90-dBfs level and 0.1% nonlinearity in the evaluation signal to approximate actual device errors and ATE system noise.

Figure 1.  Lossless compression cuts memory requirements in a DAC linearity test without compromising accuracy or increasing uncertainty.

As is the case with other compression technologies, using lossy compression, in which the original signal is “lost” and cannot be fully recovered, can yield significant increases in the compression ratio, while the losses remain imperceptible to the user. In another test of the Samplify algorithm, in which we measured jitter on a simulated high-speed serial data signal, we used a test signal that was a noisy square wave with added jitter (σ = 1 sample). We analyzed the data by estimating the probability distribution function of the zero crossing with respect to time and then deriving the probability density function. We then measured the standard deviation, providing an estimate of the RMS (root mean square) jitter (Figure 2).

Figure 2.  For a serial-data test signal, the application of 8:1 lossy compression resulted in a change in the jitter error measurement of less than 3%.

In this example, 8:1 lossy compression resulted in a change in the jitter error measurement of less than 3%. Note that, once quantified, uncertainty introduced by a data-compression process can be managed at the system level just like any other error term. In these cases, the errors are certainly acceptable.

These two examples involved specific types of mixed-signal measurements where compression achieved compelling results. Some engineers, though, are concerned about whether compression can achieve meaningful results when the signals are unknown or arbitrary. After all, the original motivation for basing mixed-signal ATE instrumentation on AWGs and digitizers was to have a tester that engineers could adapt to new tests by simply changing the DSP algorithms rather than by installing new test hardware. Again, due to the practicalities of reconstruction and anti-aliasing filters, these reconfigurable systems must operate in an oversampled mode, and test-program designers must still develop customized resampling DSP algorithms for the signals under test. To achieve sample rates close to the Nyquist rate, these resampling algorithms become extremely complex.

Figure 3.  While the compression ratio may vary depending on the test signals to be generated or measured, compression applied to this simulated OFDM waveform, for example, can offer bit-rate reductions that achieve or better that of ideal Nyquist sampling.

Because compression is transparent to the signals under test, once compression resides in the digitizer, and decompression in the AWG, you no longer need customized DSP algorithms for each test and signal set. While the compression ratio may vary depending on the test signals to be generated or measured, compression can offer bit-rate reductions that achieve or better the bit rates of ideal Nyquist sampling.

For example, Figure 3 illustrates a simulated OFDM (orthogonal frequency-division multiplexing) waveform for testing a WiMAX baseband SOC (system-on-chip) device. Typically, the ADCs (analog-to-digital converters) operate at 2X oversampling of the signal centered at Fs/4. Lossless compression achieved a compression ratio of 2:1, which is equivalent to the ideal Nyquist sampling rate. Because the ADCs on the SOC may have only nine effective bits of resolution, however, you can achieve a compression ratio of 3:1 by operating the compression algorithm in a fixed quality mode to maintain 54 dB of SNR.

Unlike traditional sampling techniques, compression achieves these bit-rate reductions while maintaining the original timing resolution. Hence, compression extends the capabilities of general-purpose testers based on AWGs and digitizers without requiring designers to develop customized DSP algorithms for each test.

To simplify the integration of high-speed signal compression into mixed-signal ATE systems, commercial algorithms are available in several forms. Examples include:

• software libraries for general-purpose computers,

• modules for computing software packages,

• FPGA (field-programmable gate array) cores, and

• data converters with integrated compression.

Signal-compression algorithms implemented as FPGA IP (intellectual property) or embedded in a data converter are particularly appropriate for mixed-signal ATE, because many ATE systems already use FPGAs and data converters. In fact, nearly all digital signal I/O from ADCs and DACs in ATE equipment connects to FPGAs, making either a converter or the FPGA a convenient place to introduce signal compression (Figure 4).

Figure 4.  Nearly all digital signal I/O from ADCs and DACs in mixed-signal ATE connects to FPGAs, providing a convenient and straightforward place to introduce signal compression.

By taking advantage of compression algorithms to incorporate signal compression into a mixed-signal ATE system design, manufacturers will realize savings in the cost of data storage and interconnect complexity as well as in the cost of test program development. Designers need no longer fear that compression will negatively affect measurement accuracy and uncertainty.

For Further Reading

Dalal, Wajih, and Daniel Rosenthal, “Measuring Jitter of High Speed Data Channels Using Undersampling Techniques,” Proceedings of the International Test Conference 1998. ieeexplore.ieee.org.

Mahoney, Matthew, DSP-Based Testing of Analog and Mixed-Signal Circuits,” Wiley-IEEE Computer Society Press, 1987.

Wegener, Al, “Compression Solutions for Test Applications,” Evaluation Engineering, December 2005. www.evaluationengineering.com.