Unusual Applications Highlight Versatility Of Arbitrary Waveform Generators
We can see it every day—a scene played back on our television revealing, in slow-motion, the discrete steps of a pivotal action. On many occasions, reviewing an important event reveals that our first impressions may have been wrong.
The same is true in the scientific and technical arena, where occurrences must be recorded and played back to study the events and the results contained in the response. The process begins by recording and digitizing the event or condition. In general, the record is an electrical waveform derived from a digital storage oscilloscope, the output of an analog-to-digital converter, or a signal derived by other computer techniques.
In other circumstances, the recording may be accomplished in the analog domain and then digitized. Regardless, a record or digital file of the data is needed to play back the event.
The arbitrary waveform generator (AWG) is then called upon to recreate the captured waveform. With its numerous facilities, an AWG may operate on the signal to increase or decrease the amplitude, increase or decrease the frequency, repeat the signal as frequently as needed or modify the waveform in many complex ways.
A traditional AWG, employing variable sampling rates, must be used to achieve perfectly repeatable output waveshapes when generating complex aperiodic signals. A traditional AWG addressing scheme outputs every sample in the waveform in succession throughout the entire waveform lookup table.
The frequency of the waveform is determined by the frequency of the sample clock and the number of points in the lookup table. Either the sample clock frequency, the length of the lookup table or both may be adjusted to obtain the desired output frequency. With the traditional AWG, each waveform is repeated precisely.
Conversely, using a direct digital synthesis (DDS) system, the sample clock rate is fixed and the lookup table length is fixed. The addressing scheme used in this system is known as a phase accumulator. An increase in frequency is achieved by skipping addresses in the lookup table, using fewer samples and completing the cycle in fewer steps using fewer addresses. Subsequent scans through the lookup table rarely duplicate the same precise address pattern, typically producing amplitude modulation effects in the output signal.
The convenience of the DDS-based system is the simplicity of a single output filter which corresponds to the fixed sample clock frequency. The disadvantage is the lack of precision in the output.
Furthermore, the traditional AWG can provide a sequence generator feature which allows looping and linking of the waveforms. The DDS-based addressing method, however, restricts the implementation of a sequence generator and limits the utility of this approach.
To help understand the effectiveness of an AWG in simulation testing, we will look at two applications: one on vehicle airbag deployment systems and the other on psychophysical threshold testing. In each application, the signals are not significantly altered to better portray the fundamental benefits of AWGs in simulation tasks. The AWG features of primary importance are the fidelity and precise repetitiveness of the waveforms and the ability to incorporate a sequence generator and its intrinsic benefit of virtual memory expansion.
Time-Space Simulation
Obviously, destructively testing a large number of vehicles to study, design and test airbag deployment systems is impractical. However, a very real need exists to define and simulate the innumerable sequence of events encountered in real-life auto accidents.
These crash scenarios are then applied to the airbag deployment module to evaluate the appropriateness of deployment and to establish deployment timing. An alternate series of parameter adjustments relate to vehicle speed, and passenger occupancy position, body size and weight.
To accomplish these simulations, a system using three high-definition AWGs with sequence generators was assembled. Each AWG represented the acceleration vector associated with one of the principal directions of motion of the vehicle. One generator provided information relating to the line of travel and the other two signified lateral motion.
Pulse width modulation converters were used to condition the signal for digital processing in the airbag deployment module.
To assure good correlation to actual vehicular accidents, real crash waveforms were taken from the output of actual sensors. These signals were recorded and digitized to facilitate accurate reproduction and manipulation.
Three major adjustments of the waveform were needed to fulfill the scenario profiles. The magnitude of the acceleration was defined by the amplitude of the sensor signal, set using the signal level control in the AWG or by suitably scaling the waveform image in the digital waveform memory. The event duration and the frequency profile of the sensor output were determined by both the sample clock and the number of samples used to define the sensor signal.
Another consideration in configuring the waveforms was the influence of secondary crash events which frequently occur in real-life auto accidents. For instance, in a situation of a vehicle following too closely, the first contact is striking the rear of the car in front. Due to the resulting rapid deceleration, this car is then rear-ended. The second impact may well be the more severe and could be the reason for airbag deployment.
The third parameter was the time of onset for each of the three signals. In general, a single trigger will initiate the entire series of events. Timing of each output was readily achieved using the sequence generator in the AWG to provide the delays between sensor signal generation.
This approach used one waveform to create a minimum delay element, which was iterated as many times as required to provide the needed delay, followed immediately by the sensor waveform. With this approach, the value of the delay may be programmed independently of the other parameters of the sensor signal. With each of the AWGs suitably set up for the desired test scenario, all three sensor signals were available to stimulate the airbag deployment module.
At this point, the vehicle computer took over, conditioning the waveforms for subsequent logical analysis. In a typical system, the computer assessed the validity of the inputs and inspected the timing and degree of severity of the event.
At least two inputs must qualify for the airbag deployment system to activate. Any false initiation of this command could result in a more serious condition, such as the premature or unnecessary deployment of the airbag.
AWGs facilitate the creation of any crash scenario and are especially convenient in accomplishing limit testing. Clearly, one of the more sensitive parameters is to determine the error rate of a deployment system.
Likewise, knowledge of the manufacturing variations of the actual deployment electronics is essential for providing a reliable system. It is partially through the capabilities of test facilities like these that automobile safety has risen to the level currently being realized.
Sound Titration
Psychophysical testing using an AWG was undertaken to assess the brain response of cats with brain tumors. First, the cats were trained to discriminate between two normal sounds and then their brain responses were measured. Following surgery, the same series of discrimination tests was given and, again, the responses measured.
The procedure titrated between two sounds: a twig snap and a bird chirp. This pair of sounds was used because each evoked a uniquely different psychophysical response, and the degree of response was easily measured and compared.
To begin, the two sounds were recorded and the digital image of each sound was stored in the waveform memory of an AWG. Next, a series of intermediate sounds was synthesized to facilitate a means of measuring the threshold of discernment of the sounds. A comparative study was made possible using a number of cats.
A very simple process was developed to create the series of sounds needed to fulfill the timbre-dimension requirements of the project. The transition between the two specific sounds, the twig snap and the bird chirp, was to be gradual, controllable and repeatable to provide comparability of the discernment measurement results over a reasonable sample group. The final result was obtained by incrementally changing the proportion of each sound and combining them to create the various composite sounds.
Implementation consisted of capturing and digitizing the two specific sounds. The digital files of both signals, each using the same number of samples, were then stored in the waveform memory of a high-resolution AWG with a sequence generator.
This instrument provided 16 bits of resolution, which enhanced the fidelity of the sounds. Also, the needed intermediate sounds could be implemented using the resident math function, and each of the sounds was stored in waveform memory.
The sequence generator seamlessly output each titrated waveform in succession.
Each intermediate sound was synthesized using a simple arithmetic rule of linearly changing the proportion of each sound and adding the proportional sounds together:
S = RxT+(1-R)B
where S = sound (composite)
R = transition ratio (range 0.0 to 1.0)
T = twig snap signal
B = bird chirp signal
The actual signals contained many samples and could not readily be depicted in simple monitor screen presentations. As a result, a segment of the signals was selected to portray the process.
A series of six screens offers a cursory illustration of the waveform titration sequence. The twig snap is shown as Titrate 1.0. This screen illustrates 100% twig snap and 0% bird chirp. The bird chirp is shown in Titrate 0.0, showing 0% twig snap and 100% bird chirp.
For brevity, only four intermediate proportions are shown. A visual inspection of the waveforms reveals the influence of the various transition ratio proportions.
This procedure was iterated for as many values of R as required to attain the degree of gradualness desired. As a final convenience, the internal sequence generator automatically outputs each of the stored sounds for a specified period of time.
More complex relationships can be accommodated; but regardless of the number of steps used, this procedure of modifying one sound toward the other by gradually altering the amplitude of each sample is completely general in its applicability. That is, it transforms the first sound into the second sound regardless of the complexity of the two waveforms or the subtlety of the dimension uniting them.
This application illustrates the benefits of a sequence generator. Through looping and linking, the sequence generator directly controls the duration of each waveform and provides seamless switching to each successive waveform.
About the Author
Henry Reinecke Jr. is President of Pragmatic Instruments. Before he became co-founder of Pragmatic, he had 21 years of management experience with Wavetek as Senior Vice President of Worldwide Operations and General Manager of the San Diego Instrument Division. Previously, he was employed by Monsanto and Non-Linear Systems. Mr. Reinecke has a bachelor’s degree in electrical engineering from New Jersey Institute of Technology and a master’s degree in electrical engineering from Massachusetts Institute of Technology. Pragmatic Instruments, 7313 Carroll Rd., San Diego, CA 92121-2319, (619) 271-6770.
Copyright 1996 Nelson Publishing Inc.
February 1996