Noise Generation with a Waveform Generator Abstract VXIbus test system developers have traditionally used rack-mount, analog noise generators as noise stimuli because they are specialized items not available for the VXIbus. Today, there is an alternative to the analog noise generator available in VXIbus format. Digital waveform generators such as Racal Instrument's Model 3151 produce a variety of different noise types (i.e. white and gaussian, both narrowband and bandlimited). These functions are calculated, downloaded to the waveform generator, and injected into a Unit Under Test (UUT). Techniques for generating this are presented below. Introduction All equipment operating in the real world experiences noise. Whether the noise emanates from an electric machine, an ignition system, a radio transmitter, or from the galaxy itself, a random component is always being added to data and signals within all equipment. To combat noise and improve product quality, test engineers use noise generators to inject noise into circuits. Performance of the products may then be evaluated in a manner consistent with real world conditions. White Gaussian Noise The noise that is incident on any system at any time is the sum of many small disturbances. Most noise sources are considered to be Gaussian; i.e. the amplitude probability from moment to moment has a Gaussian (bell-shaped) distribution. The sum of many small Gaussian fluctuations is also Gaussian. For this reason, Gaussian noise sources are frequently used to model noise from the real world. Random signals which uniformly span the entire frequency spectrum (up to 100GHz or so) are called "white" noise by analogy to white light which contains uniform amounts of all colors. This characteristic also commonly occurs in nature. When these two characteristics are combined, the result is called white Gaussian noise. Although many other types of noise may be generated, this type of noise is the focus here because it is the most common. Noise almost always couples to signals in an additive manner which is where the term Additive White Gaussian Noise (AWGN) comes from. Bandlimited Noise vs. Narrowband Noise Bandlimited noise has a frequency spectrum bounded by an upper frequency limit (i.e. white noise put through a low-pass filter). Because most systems have a limited bandwidth of operation, only noise within the limited bandwidth will actually interfere with circuit operation (the rest is filtered out). Therefore, we can assume that bandlimited AWGN is the most realistic noise to inject in a baseband signal. Narrowband noise is white noise which has been passed through a narrow bandpass filter. Narrowband noise is used to simulate noise which is superimposed on a carrier passing through a bandpass IF filter; e.g. in a receiver. A Model for Bandlimited AWGN Bandlimited noise may be calculated using Mathcad or other math programs. For a CDMA application, the test developer is attempting to produce AWGN bandlimited to 1.3MHz. A long trace is used (4096 points in this example) to approximate true randomness. The number of points may be increased to another power of 2 (e.g. 212 = 4096) to enable Mathcad's FFT function. For maximal resolution, the Model 3151 Waveform Generator's clock is set to 100MHz. Assume that 100MHz = 4095 in our "digital" frequency domain. Therefore, to get 1.3MHz our model should use a digital frequency which is 1.3% of 4095 or 53. The following is a Mathcad model creating 1.3MHz bandlimited AWGN: The above Mathcad "program" listed generates the desired bandlimited noise. Below is a plot of the section of this waveform that will appear in an oscillograph of the 3151's output shown in Figure 1. The probability density function of the AWGN signal is calculated below. This is done to demonstrate that the amplitude distribution of the signal is indeed Gaussian. The Gaussian function for a normal distribution with the same mean value as the AWGN function is superimposed as a comparison. A white noise waveform has a uniform power spectrum. Therefore, the Mathcad FFT function is used to verify and display amplitude vs. frequency. A Model for Narrowband AWGN Building on the previous example, let's now say that AWGN is to be added to an IF carrier in a channel limited by a bandpass filter from 781kHz to 1.3MHz. Remaining in the frequency domain, the noise from the last example is used again. The bandpass filter is simulated at the low end by zeroing out the frequency spectrum up to the lower frequency of 32 (which corresponds to 781kHz). Notice that the top end of the narrow band spectrum was left alone since it was already bandlimited. To go full circle and bring the narrow band noise back to the time domain, the Inverse Fast Fourier Transform algorithm is employed. Downloading Noise Waveforms The next task is taking these numbers and converting them to the proper format for downloading to the Model 3151 Waveform Generator. WaveCAD software, which is provided with the 3151, as well as the VXIplug&play drivers, have ASCII file import capability. This will be utilized, but first the Mathcad data must be transferred to a file. This is easily done. The factor of 100 is to increase the amplitude so the signal has good resolution. The numbers are rounded since the vertical points are actual Digital to Analog Converter (DAC) values. We have now created two files: BNDLIM.PRN and NRWBAND.PRN. To load these files into WaveCAD, select File-Waveform-Import from the pull down menus. A dialog box will appear prompting for a file specification. Specify one of the files just created and WaveCAD will display the waveform on the screen. To download to the Model 3151 (connected to this computer either through the VXIbus, MXIbus or GPIB) use the Instrument Configuration box to put the instrument in User Mode and set the sample clock (SCLK) to 100MHz. Energize the output relay by clicking on the "Output On" check box. Then click on the download button. If a scope is connected to the 3151's output, an AWGN signal will be displayed. Injecting Noise into a Circuit Noise should be injected into the circuit in an additive manner because this is the way noise is normally coupled into circuits. There are several ways to inject noise (or any signal): using a summing amplifier, an opamp summing node, or with a current transformer. If the test circuit is available, a summing amplifier (available for VXIbus) is an easy way to add the two signals. The signal may be applied directly to the summing node of a summing amplifier circuit, if one is available. Be sure to insert an impedance in series with the noise to add the proper amount of noise. Last, a current transformer can inject normal mode or common mode noise into a wire, depending on how it is configured. Just a turn or two around a toroid core will do. These are just a few ideas; there are many other easy ways to inject noise. Summary This example uses a Model 3151 waveform generator to produce Additive White Gaussian Noise and can be easily modified for various uses. This adds a new dimension to the VXIbus arena, a noise generator. References: 1. Goodyear, C.C., Signals and Information (The Butterworth Group, London, 1971) pg. 208. TOC 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13