Hello,

I'm using a 33600A Series waveform generator to generate a carrier frequency modulated with a gaussian noise (in frequency).

There is two parameters attached to this gaussian noise, the frequency deviation and the bandwidth. I'm not completely certain to understand the meaning of those terms and can not find a clear mathematical definition of this gaussian noise in the docs. And for my application I need to know exactly how this is defined.

I need to have a 'real' gaussian noise. By 'real' I mean that the RF spectrum is gaussian even if I sample it during a very short time window (typically 100 fs).

I have the feeling that the arbitrary function generator is not acting this way, but pick one frequency in a gaussian distribution (with a width related to the frequency deviation) and switch to another one after short time (related to the bandwidth). As a consequence the RF spectrum is gaussian only if integrated over a sufficiently long time.

Any idea ?

Thanks,

The 33600 family of Function/Arbitrary Waveform Generators use digital means for generating the waveforms and the modulating waveforms (in this case I an guessing you are using a Sine Wave as the carrier frequency, with Gaussian Noise as the modulating waveform). These digital signal streams are combined (in this case frequency modulated) and then sent to filters and waveform DACs for conversion to analog signals.

The synthesizer runs at 1 GSa/second to the waveform DACs, which are followed by an analog filter to limit the signal bandwidth. So nothing can happen in the 100 femtosecond scale (1e-13, versus generator sample rate 1e-9).

As regards the Gaussian noise, it is generated digitally, using a mathematical formula which will generate random numbers with Gaussian amplitude distribution - but the amplitude is limited by the digital nature - numbers can only get as large as the number of bits used to represent them, so you will never see an infinite amplitude noise value which is theoretically possible in some systems. Instead, the maximum positive and negative value will be the max and min of the numerical representation internal to the generator.

The Bandwidth of the Gaussian noise signal is determined by how fast we run the noise generator circuitry. You can see the actual bandwidth (spectral content) by running the 33600 into a spectrum analyzer, using Gaussian noise as the base waveform without modulation. As you change the bandwidth, you will see the spectrum change, with the maximum frequency increasing and decreasing as you change the Bandwidth setting of the generator.

So lets get back to modulation. We now have two streams of numbers in the generator, one representing the carrier (Sine) waveform and one representing the Gaussian Noise (modulating) waveform. In Frequency Modulation, the noise waveform is applied to the frequency control registers of the Carrier waveform, causing instantaneous change of the frequency as each waveform DAC sample is produced. So if the modulating waveform has a value of +765 (for example) the carrier frequency will be slightly higher than the center frequency, and if the next sample is -4567 the carrier frequency will be somewhat lower than the center frequency.

Now, we need to control just how much frequency change occurs with this stream of numbers coming into the modulator. So the incoming modulation waveform data stream gets multiplied by a scaling factor, to limit the maximum frequency excursion of the carrier to some value. This value is the "frequency deviation" setting to which you refer, the maximum frequency excursion from the center frequency. If you set the frequency deviation to 5 kilohertz, for example, then the maximum instantaneous frequency excursion of the carrier will be 5 kHz. One way to see this is to modulate a carrier with a very slow TRIANGLE (symmetrical RAMP) waveform, and view the signal on a spectrum analyzer or frequency counter. You will see the carrier frequency slowly increase to the frequency of (carrier + Deviation) and then slowly decrease to the frequency of (carrier - Deviation).

I hope this is helpful to understanding of what the noise and FM modulation functions are doing in the 33600 (and 33500) family generators. I am not sure what the exact application is, but I also want to point out that if you are viewing the spectral content of FM signals, remember that it is fairly complex, modeled by Bessel Functions, so there will be many side bands for any single combination of Sine Carrier and Sine Modulation signals even at fixed frequencies. So the signal modulated by Gaussian noise will be even more complex than the sine/sine case.