## Pinning for gigasamples

04.10.2015 19:27

I recently stumbled upon this video back from 2013 by Shahriar Shahramian on the Signal Path blog. He demonstrated an Agilent DSA-X series oscilloscope that is capable of 160 Gsamples/s and 62 GHz of analog bandwidth. Or, as Shahriar puts it, an instrument that doubles the value of the building it is located in. It is always somewhat humbling to see how incredibly far the state-of-the-art is removed from the capabilities accessible to a typical hobbyist. Having this kind of an instrument on a bench in fact seems like science-fiction even for the telecommunications lab at our Institute that has no shortage of devices that are valued in multiples of my yearly pay.

I was intrigued by the noise level measurements that are shown in the video. At around 7:00 Shahriar says that the displayed noise level at 62.3 GHz of analog bandwidth is around 1 mV RMS. He comments that this a very low noise level for this bandwidth. Since I am mostly dealing with radio receivers these days, I'm more used to thinking in terms of noise figures than millivolts RMS.

The input of the scope has an impedance of 50Ω. Converting RMS voltage into noise power gives:

N = \frac{1\mathrm{mV}^2}{50 \Omega} = 2.0\cdot 10^{-8} \mathrm{W}
N_{dBm} = -47 \mathrm{dBm}

On the other hand, thermal noise power at this bandwidth is:

N_0 = kTB = 2.5\cdot 10^{-10} \mathrm{W}
N_{0dBm} = -66 \mathrm{dBm}

So, according to these values, noise power shown by the oscilloscope is 19 dB above thermal noise, which means that oscilloscope's front-end amplifiers have a noise figure of around 19 dB.

This kind of calculation tends to be quite inaccurate though, because it depends on knowing accurately the noise bandwidth and gain. In another part of the video Shahriar shows the noise power spectral density. You can see there that power falls sharply beyond 62 GHz, so I guess the bandwidth is more or less correct here. Another thing that may affect it is that the RMS value measured includes the DC component and hence includes any DC offset the oscilloscope might have. Finally, noise should have been measured using a 50Ω terminator, not open terminals. However Shahriar says that his measurements are comparable to the instrument's specifications so it seems this hasn't affected the measured values too much.

Of course, I have no good reference to which to compare this value of 19 dB. For example, cheap 2.4 GHz integrated receivers I see each day have a noise figure of around 10 dB. A good low-noise amplifier will have it in low single digits. A Rohde & Schwarz FSV signal analyzer that I sometimes have on my desk is somewhere around 12 dB if I remember correctly. These are all at least one order of magnitude removed from having 60 GHz of bandwidth.

I guess having a low noise figure is not exactly a priority for an oscilloscope anyway. It's not that important when measuring large signals and I'm sure nobody is connecting it to an antenna and using it as a radio receiver. Even calling Shahriar's demonstration the world's fastest software-defined radio is somewhat silly. While the capabilities of this instrument are impressive, there is no way 160 Gsamples/s could be continuously streamed to a CPU and processed in real-time, which is the basic requirement for an SDR.

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