Waveform Generators as Low-Distortion Function Generators Abstract VXIbus test system developers traditionally use "analog" function generators to produce clean, undistorted sine waves. Waveform generators use digital techniques to produce sine waves (and other functions) with less distortion in many cases. Waveform generators have built-in sine wave functions with stated distortion specifications. These specifications can be improved upon by using the arbitrary memory capability of the waveform generator. Introduction Digital waveform generators are obsoleting analog function generators by offering all the basic features of traditional function generators plus the advanced features of a waveform generator. Traditional function generators can generate sine, square, and sawtooth waveforms of programmable frequency. But only waveform generators can modify these waveforms to produce test stimuli which are completely user-specified. Figure 1 shows a ringing pulse waveform (created with WaveCAD software) as an example of the level of customization available. Also, waveform generators produce the basic waveforms (like sine) with less distortion than function generators. Function Generators vs. Waveform Generators Analog function generators and digital waveform generators use fundamentally different techniques to generate sine waves. A good way to differentiate the two is to explain how each generates a sine wave. The sine wave function in an analog generator begins with a reference oscillator which is divided up or down to develop the desired frequency. The divider output is a triangle wave. A low pass filter (LPF) is then used to convert this triangle wave to a sine wave by filtering out high-frequency harmonics present in the triangle wave until only the fundamental (a sine wave) is left (see Figure 2). Distortion in an analog function generator is thus limited by the ability of this filter to remove all harmonics. Waveform generators, like function generators, start with a reference oscillator which is divided up or down. This frequency is then used as a sample clock which controls the rate at which stored data is clocked to a high-speed Digital to Analog Converter (DAC). The analog waveform from the DAC is then filtered to remove sampling "noise" that could generate spurious outputs (see Figure 3). The function generator requires a programmable low-pass filter because the output frequency may be changed over a wide range. If only one filter cutoff frequency existed then distortion increases as the programmed frequency drops well below the cutoff. Therefore this cutoff frequency must slide to reduce distortion. In contrast, the waveform generator requires only one super high-quality low-pass filter, with a cutoff above its highest output frequency, to filter all sampling spurs and eliminate distortion. In reality, several filters are included (some for purposes other than sine waves). The end result is typically less distorted than a function generator. Built-in Sine Waveforms Each waveform generator has its own formula for generating its built-in sine waves. The Racal Instruments Model 3151 Waveform Generator uses a 500 point sine wave (stored in ROM) to produce its standard sine function. At output frequencies above 200KHz the number of points is reduced. Above 10 MHZ a two-point sine wave is used with the limitation that at least five cycles must be generated. This is the case because the filter is producing the shape of the sine wave for a two-point waveform. A Way to Improve Distortion Specs Unlike function generators, waveform generator distortion specs can be improved using arbitrary waveforms. Built-in sine waveforms can be improved upon by using arbitrary waveforms to increase the number of points in the sine wave. This technique is most effective at low frequencies. For example, a 10kHz built-in sine wave uses 500 points (or samples) which forces the sample clock to run at 10kHz x 500S = 5MS/s (5 MegaSamples/s). This creates a slight problem. The 5MHz sample clock rate is below the 25MHz cutoff frequency of the 3151's LPF. This means that some sampling spurs will remain in the output signal, increasing distortion. On the brighter side, however, these spurs are small (the largest being -33dBc). An alternative would be to download a 20,000 point arbitrary waveform. The sample clock must run at 10kHz x 20,000S = 100MS/s. In this case, the sample clock spurs are in range to be cut off by the LPF (attenuation >100dBc with 25MHz, 7 pole, elliptic filter). In addition, having the sample clock rate farther away from the sine frequency decreases the amplitude of the spurs themselves (-60dBc). In the end, the largest distortion spur is calculated to be in the area of -160dBc. Using Low Sample Rates Waveform generators operate using many of the same principles that CD ROM players use. This is especially true when the waveform generator is operating at sample rates above the LPF cutoff frequency. But, since waveform generators don't have the half a gigabyte of memory that a compact disc has, it is sometimes useful to lower the sample rate below the filter cutoff to save memory. For example, a TV test developer is attempting to generate a long sequence of NTSC test patterns that would require 5 Megabytes of waveform memory at a 50MS/s sample rate. The developer is using a Model 3151 Waveform Generator which has 512k of memory. The highest frequency sine wave in the signal is 3.58MHz. The developer solves his problem by creating an equivalent 512k test sequence and lowers the waveform generator's sample rate to 10MS/s. The price paid for this waveform memory flexibility is an increase in output sample spur distortion. To illustrate this, Figure 4 shows the frequency spectra (neglecting LPF effects) of the 3.58MHz sampled signal generated at 10MS/s and 50MS/s. Notice that the spectrum envelope is in the shape of a sinc (sine(x)/x) function. Also, the fundamental frequency is reflected about integer multiples of the sample frequency as "sidebands." These sidebands occur because sampling a signal (such as a test pattern) is equivalent to amplitude modulating the test signal with sampling pulses. While sidebands are characteristic of AM, the sinc function is characteristic of the frequency spectrum of a sequence of pulses (ie. the sample clock). Also notice that in Figure 4, as the sample clock is slowed from 50MS/s to 10MS/s. The ratio of the amplitude of the first spur to the 3.58MHz signal becomes more significant. This means more distortion. At 50MS/s the first spur is 22dB below the fundamental (or carrier). At 10MS/s the first spur is only 5dB below. In general, every time the sample clock is dropped by 50%, the first spur increases by about 6dBc. Summary Digital waveform generators such as the Model 3151 are superior to analog based function generators for many reasons, some of which were discussed here. The waveform generator is flexible enough to enable the test program developer to develop more realistic tests. TOC 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13