What do pacemakers, anti-lock braking systems, computer disk drives, and cell phones have in common? These products and many others rely on the complex characteristics of one or more waveforms for their correct operation. When the product actually is operating, these signals may be provided by special-purpose circuitry—the base-station infrastructure in the case of a cell phone. Signals may be generated by a transducer that senses a wheel turning on a car or a disk rotating in a computer. Or electrical signals can be generated directly in physiological testing of nerves and muscles.
For all these examples, the problem is to provide the necessary, realistic signals during development and manufacturing test without having the actual signal sources available. This is a job for an arbitrary waveform generator (Arb).
Although not quite ubiquitous, Arbs continue to grow in popularity and have become the preferred instrument for use in many industries. “Arbs are replacing function and sweep generators,” said Jay Long, sales and marketing manager for the Measurement and Control Division at Analogic. “ARB sales are increasing while other signal-source sales are decreasing.”
The main reason for the proliferation of Arbs is the ease with which they can reproduce complex signals whether originally input as mathematical equations, downloaded from a digital storage oscilloscope, or provided as a standard signal in the generator’s firmware.
“Customers are taking advantage of the Arb’s capabilities and have recognized that the best way to thoroughly test a design is to simulate real-world signals for prototype testing,” said Cheryl Diller, a product manager at Hewlett-Packard’s Electronic Measurements Division. “By far, general-purpose simulation and signal substitution are the most common applications we see.”
As more applications have been addressed, features have continued to improve. Arbs are available with sample rates up to 2.6 GS/s, selectable output filtering, multiple outputs, and high voltage/power outputs. An almost endless variety of waveforms can be created by segmenting the Arb’s memory into smaller sections that can be linked and repeated in a user-programmable sequence.
Applications
Disk-drive, communications, and automotive system test have adopted Arbs as the standard test generator. Bruce Virell, marketing manager for Signal Source Products at Tektronix, said, “The performance criteria for future hard drive designs are becoming more stringent, and it is important for designers to simulate precisely controlled high-speed test signals. Suppliers are in a constant race to deliver more data storage capacity and data transfer speed at reduced costs.
“Designers who work with new standards for communications network physical- layer test applications require high clock speeds for better horizontal pulse characterization,” he continued. “The test engineer must characterize the design with both nominal signals and signal anomalies including timing impairments, noise simulations, amplitude variations, and jitter.”
The most prevalent demand for multichannel Arbs, however, stems from the need to generate the synchronized in-phase (I) and quadrature (Q) signals essential for testing modern communications equipment. “To satisfy this requirement, two simultaneous electrical signals must be provided,” said Henry Reinecke, president of Pragmatic Instruments. “Either a dual-channel Arb, capable of synchronizing both channels and operating from a common sample clock, or a pair of generators meeting this requirement is needed.”1
Complex, multiple waveform requirements will exercise an Arb’s capabilities more fully. For example, automotive test engineers use Arbs to simulate cold-starting battery voltage waveforms and anti-lock braking system waveforms.
According to Tom Sarfi, East Coast technical support manager at VXI Technology, “In the automotive industry, Arbs also are used to simulate ignition timing waveforms. Our customers have selected multiple output Arbs because they can reduce the number of VXI slots dedicated to waveform generators while providing multiple independent waveforms simultaneously.”
A sophisticated application of multiple Arbs deals with simulation of a submarine tracking system. In the normal test at sea, a submarine is fitted with three pulse generators called pingers, one each on the sail, the rudder, and the keel. Chirps from these pingers are received by two arrays of nine hydrophones, each mounted at various depths on submerged 1,600-ft booms. A complex software package correlates the signals from these hydrophones to calculate the course, depth, and speed of the submarine. These sea trials are expensive, and their accuracy and repeatability depend on variations in the environment.
Navy engineers recognized the potential of the Arb as a simulator for these tests and implemented a rack-mounted laboratory system that accomplishes the desired results prior to sea trials with laboratory repeatability and at a much lower cost. Electrical Engineer Kes Tomlin and Project Manager Joe Keane, both of the Naval Surface Warfare Center in Carderoc, MD, and Pragmatic’s Mr. Reinecke contributed to this development.
In this Multiple Acoustic Pulse Simulator (MAPS) system, 18 Arbs simulate Gaussian-weighted pinger signals generated by the submarine and received by the hydrophones. The Arbs are completely programmable, and each can generate a unique sequence of pings based on up to 1,000 stored waveforms to represent the movement of the simulated submarine as it would be seen by a specific hydrophone. Each Arb has a 4,096-step sequence generator that allows output pulses from the 128- kwords-memory to be delayed individually to represent varying signal paths.
“The nice thing about our Arbs is that we can control the timings, delays, waveform type, and amplitude of the simulated pulses within a sequence,” Mr. Tomlin said. “We can easily calculate and load points that simulate different submarine speed and run geometries.”
Since this test depends on the relationship between arrival times, the entire system is kept in step by a single master trigger from a GPS-synchronized cesium or rubidium clock. The resulting 1-µs timing uncertainty translates into 0.06-in. ranging accuracy.
“The real test of a newly developed tracking system lies in how it handles nonideal system inputs,” said Mr. Keane. “The ocean environment is unforgiving, and the sound speed is not uniform which refracts the sound path. There are dropouts, varying signal-to-noise ratios, interference of overlapping pulses, Doppler shifting, and surface path reflections.
“The MAPS system simulates these real-world scenarios,” he continued. “This is a very important step in debugging software before sea trials, at a reasonable cost.”
Additional Applications
Finally, there is a large, miscellaneous class of Arb applications that may never have more than one or two people running the same tests in the same ways. These are the esoteric research applications that stretch an Arb’s specifications to the limit, but generally in only one or two areas such as speed or waveform distortion.
Some applications such as radar and video simulation require especially long and complex waveforms. Recently introduced Arbs have FIFOs that allow continuous waveform output even though data must be transferred in blocks from a larger PC memory.
Physiological experiments typically require a very high dynamic range—at least 16-bit resolution, but the waveform speeds often are low. Figure 1 shows a typical cardiac waveform that an Arb can repeat regularly. Editing facilities allow you to alter such a signal to include anomalies that might result from infarctions. Applying an arbitrary sweep function can simulate the irregular beat rate of arrhythmic tachycardia.
Another low-speed application, in this case involving multiple outputs, is simulation of 3F power. Three current and three voltage sinusoids must be correctly related to each other. Typically, six Arbs are locked to a reference frequency, and phase offsets are introduced so the relative positions of the three phases remain constant even as the frequency is changed slightly.
Conclusion
Whatever your application, make certain that the Arb you buy suits your needs (see the sidebar). All Arbs do not operate in the same way, so one that works well in your present application may be hopeless in another. Direct waveform lookup and direct digital synthesis (DDS) are the two basic types. Some instruments offer both modes, using direct waveform lookup for arbitrary and pulse outputs and DDS for repetitive sines and triangles. Other Arbs use one or the other approach exclusively.
Read the specification and datasheet, and discuss your needs fully with the Arb manufacturer. If you’re still not sure what effect a particular Arb may have in your case, borrow one and try it.
References
1. Jacob, G., “Easily Generated Complex Waveforms Accommodate Many Applications,” EE-Evaluation Engineering, August 1997, p 37.
Note: This article can be accessed on EE Online at www.evaluationengineering.com. Select EE Archives and use the key word search.
2. Gould, B., Arbitrary Waveform Generators: A Primer, Wavetek Instruments Division, 1992.
Sidebar
All Arbs Are Not Created Equal
DDS is used in many Arbs and function generators. The advantages of a DDS-based design are its very fine frequency resolution and fast output speed switching capability. However, there are drawbacks, the most severe being waveform degradation at high frequencies.2
Figure 2 shows a block diagram of a simple DDS system. During each clock period, the phase accumulator register (PAR) adds a phase increment to the previous total. The current PAR total is used to address the reference waveform memory. The size of the PAR generally is much larger than the size of the waveform memory. High resolution is maintained in the PAR, but the actual reference waveform memory output results from rounding up or truncating down to the next address value.
The PAR will overflow after a number of successive phase increments are added. Each time the PAR overflows, the remainder generally will have a different value. This means that the output waveform addresses will precess through the reference waveform memory.
In a DDS-based generator, the average output frequency can be set to very high resolution although any single cycle will be only approximately correct. Phase jitter will be higher than in a simple Arb, especially at high output frequencies.
“A DDS-based Arb will jump from point to point in the Arb waveform, sometimes early, sometimes late, so the average rate is the desired sample clock frequency,” according to Mark Albert, director of marketing at B&K Precision. “At higher clock rates, the unit actually will leap over points in the waveform to keep up. Unfortunately, this can introduce jitter in the resultant waveform. And skipped points can be disastrous, especially in single-point waveform-generation applications.”
In a simple memory-lookup type of Arb, the address register and the reference waveform memory are the same size. This means that there always is a one-to-one correspondence between the reference waveform data and the output waveform.
If a crystal-controlled clock is used with an integer division, there may be an issue of frequency resolution, especially at high output frequencies. But, the stability of the waveforms a simple Arb can output is related only to the Arb’s clock stability and to whatever internal timing jitter there may be. Phase jitter is much less dependent upon output frequency than it is in a DDS-based Arb.
The highest possible resolution results in a DDS-based Arb if the maximum value of the PAR corresponds to one complete waveform cycle. For example, if the PAR can count to a maximum of 10,000 separate values, each value represents an increment of 0.036° or 2.16 arc-minutes of a complete waveform cycle.
In this example, phase increments are multiples of 0.036° and may be as large as 179.964° without violating the Nyquist criteria. The range of frequencies the generator can produce is 4,999:1. Some commercial DDS-based generators have PARs at least 48 bits long or 2.81475 × 1014, giving a range from microhertz to megahertz, all with very fine frequency resolution.
Figure 3 shows sine-wave distortion that results from the large phase increments that are required to produce high-frequency output waveforms using a DDS approach. The peaks of the individual cycles are distorted, and each one is different because slightly different reference waveform addresses have been generated for each cycle. It’s harder to see the differences in the zero-crossings of each cycle, but they, too, vary for the same reason.
There is a critical phase-increment value that makes the effective length of the PAR equal to the length of the reference waveform memory. For example, if the reference memory contains 16k points (16,384), this value is about 0.022° of a complete cycle. For this size phase increment, all the reference waveform memory data points will be output with no duplication and without skipping any.
For a pulse output waveform with increased phase increments, initially the successive pulses vary in width only. In the extreme case, pulses are missed entirely. For these reasons, DDS-based Arbs generally are not suitable for high-speed arbitrary waveform generation.
On the other hand, direct memory-lookup Arbs can incorporate more flexible memory addressing because of the one-to-one correspondence between the address and the output waveform. This can take the form of segmented memory with looping capabilities, effectively allowing the generation of very long and complex waveforms.
Signal Sources
2.0-GS/s Waveform Generator
The DBS 2050 VXI Waveform Generator has a maximum sampling rate of 2.0 GS/s with an analog bandwidth of >850 MHz at 0.5 Vpk-pk and an 8-Mword memory with 8-bit resolution. It can be operated as two 1.0-GS/s generators. The low-pass Bessel output filter is switchable to cutoffs of 2 MHz, 20 MHz, or 200 MHz. Operating parameters can be configured by plug-and-play drivers. Applications include test of disk drives, 100Base-T equipment, and avionics. $29,995. Analogic, (978) 977-3000.
Multifunction Generator
The 4070 Synthesized Arbitrary Waveform/Function/Pulse Generator has a 32-kword memory with 12-bit resolution and samples up to 40 MS/s. Waveforms up to 21.5 MHz at 2 mV to 5 Vpk-pk are output. Since the synthesizer is separate from the waveform generator, the sample clock has timing edges spaced at the reciprocal of the sample rate, which avoids jitter and skipped points. Flash memory is used for operating software, making the device field-upgradable via internet, e-mail, or floppy disk. It accepts external modulation. Output modes include sine wave, FM, PM, sweep, and voltage-controlled oscillator. $1,495. B&K Precision, (800) 462-9832.
1.2-GS/s Generator
The AWG1200 Arbitrary Waveform Generator outputs up to 1.2 GS/s with a 260-ps rise time. The 12-bit memory is 1 Mwords expandable to 4 Mwords. The generator is on a full-sized, single-width, PCI-compliant board. Outputs include eight TTL markers and a clock pulse. Segmented memory allows discontinuous memory sequences to be accessed as a continuous stream. The integrated clock synthesizer which drives the Arb has 1-Hz resolution. Starts at $15,950. Chase Scientific, (831) 464-2584.
40-MS/s Generator
The NI 5411 Arbitrary Waveform Generator creates a 40-MS/s output from its 12-bit, 2-Mword or 8-Mword memory. Output waveform frequency generation in the 32-bit DDS is 16 MHz, and the amplitude is ±5 V or ±10 V. It also has a 16-bit digital pattern output. Interface and mounting can be via PCI, PXI/CompactPCI, or ISA computer hardware. It has the capability for waveform linking and looping and a 50 W or 75 W output impedance. Starts at $3,495. National Instruments, (800) 258-7022.
20-MS/s Generator
The 2714A Arbitrary Waveform Generator has a variable sample rate from 0.1 S/s to 20 MS/s with a 12-bit, 128-kword nonvolatile memory. The sequence generator offers 100 steps and can be looped to more than 1,000,000 times and linked to 10 standard waveforms and 100 user-defined waveforms. Waveform creation software is part of the package. The selectable analog filter cutoff is 7 MHz. The unit operates in the continuous, triggered, gated, burst, toggle, or master-slave mode under program control. $1,995. Pragmatic Instruments, (800) 772-4628.
15- and 30-MS/s Generator
The DS340 and DS345 Function and Arbitrary Waveform Generators create arbitrary waveforms from a 16 kword, 12-bit memory and generate sine, triangle, ramp, or square waves in the function generator mode. Frequency resolution is 1 µHz. The maximum sampling rate is 15 MS/s for the DS340 and 30 MS/s for the DS345. Linear and logarithmic sweeps can be output. The equipment can be set up by front-panel controls, an IEEE 488 bus, or an RS-232-C line. DS340: $1,195; DS345: $1,595. Stanford Research, (408) 744-9040.
16-Channel Generator
The 3616A D/A and Waveform Generator is a 16-channel, 16-bit digital-to-analog converter. Each channel has its own output amplifier with a 50-mA drive at ±10 V or ±20 V. A built-in timer controls arbitrary waveform generation for low-frequency applications such as automotive and medical equipment development. The 484-kword, 16-bit memory can be shared; a 996-kword memory is optional. Up to three modules fit on a single-wide VXIbus card. $3,000. VXI Technology, (949) 955-1894.
Universal Generator
The Model 39 Universal Waveform Generator has a 64-kword, 12-bit memory and generates up to 30 MS/s as an arbitrary waveform generator. It has waveform linking, looping, and triggering capabilities and is used for automotive testing, medical research, and telecommunications evaluation. In addition to arbitrary waveforms, the device generates sine, cosine, haversine, havercosine, triangle, ramp, and sinx/x outputs. Two or more units can be phase-locked to a single clock to get multiphase outputs. $1,695. Wavetek, (800) 223-9885.
2.6-GS/s Generator
The AWG 610 Arbitrary Waveform Generator outputs 50 kS/s to 2.6 GS/s from an 8-Mword, 8-bit memory. Each waveform can be one of several predefined special-purpose streams for standard testing or created locally or transferred via IEEE 488, floppy disk, or 10Base-T Ethernet. Any defined sequence of one to 8,000 steps can be repeated up to 64k times or continuously. The low-pass Bessel output filter cutoff is selectable as 20 MHz, 50 MHz, 100 MHz, or 200 MHz. It has a 5.2″ × 3.9″ display, 2.1-GB hard disk, and 3½” floppy disk. $34,995. Tektronix, (800) 426-2200.
Copyright 1999 Nelson Publishing Inc.
August 1999