Smooth the Discontinuities in AWG Waveforms
Using the filters in an arbitrary waveform generator, you can minimize discontinuities in waveforms.
Martin Rowe, Senior Technical Editor -- Test & Measurement World, 2/1/1999
| Arbitrary waveform generators (AWGs) let you produce a myriad of waveforms, including continuous waveforms. To create a continuous waveform, you can define a set of points in the instrument’s memory, then use the instrument’s looping function to repeat the waveform indefinitely. That’s great, as long as the relationship between your last point and first point don’t produce a discontinuity. A discontinuity results when the AWG produces an unwanted step in its output. If you continuously ran the upper 1024-point waveform in Figure 1 , you would get a clean AM signal. The amplitude at the waveform’s end matches that at its start. The lower trace shows what might happen if you incorrectly edited the waveform. You’d get two discontinuities, one when the AWG goes from point 511 to point 512, and another when it goes from point 1023 back to point 0.
If you were to look at the two signals in the frequency domain, you’d see the results of the discontinuity. The lower plot in Figure 2 shows a spreading of the spectrum caused by the discontinuity.
Fortunately, AWGs contain filters that can minimize discontinuities. A finite-impulse response (FIR) filter will smooth discontinuities by applying a sin(x)/x function to the output data. In effect, the FIR filter averages the beginning and the end of a waveform, which smooths the data before the AWG’s digital-to-analog converter creates the output voltage. Sometimes you can minimize discontinuities yourself. Suppose you create a composite signal from two signals where neither signal is a harmonic of the other. As an example, take dual-tone multifrequency (DTMF) tones composed of two sine wave tones. The telephone “1’’ key generates a DTMF signal composed of a 697-Hz tone and a 1209-Hz tone. Suppose you set the AWG’s sampling rate to 69.7 kHz, or 100 samples/cycle of the 697-Hz tone. That 100 samples will produce 1.73458 cycles of the 1209-Hz tone. If you set the AWG to repeat after 100 samples, you’ll get a discontinuity in the 1209-Hz tone because it hasn’t completed a cycle when the AWG’s output returns to point 0. You can minimize discontinuities by using more of the AWG’s memory. Rather than repeat every 100 points, find some number of cycles for each frequency that gets the two close to each other. The FIR filter can do the rest. For example, if you use 1500 points, you’ll get 15 cycles of the 697-Hz tone and nearly 26 cycles of the 1209-Hz tone.1 If you’re testing a telecom product that receives DTMF tones, you’ll need more than just the tone for the “1’’ key. Try simulating the two frequencies for each tone on a spreadsheet or with a math software package. Look for an integer numbers of cycles where the two waveforms have approximately the same amplitude. Program those numbers of cycles into the AWG’s memory and let the filters smooth out the discontinuity. T&MW FOOTNOTE FOR FURTHER READING Strassberg, Dan, “Choosing a waveform generator: The devil is in the details,” EDN, September 1, 1998, p. 75. Waveform Creation Made Easy, LeCroy, Chestnut Ridge, NY, www.lecroy.com/Tutorials/WaveformCreation/WaveformCreation.html. |
