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Trace noise (phase) as a function of IF bandwidth

Question asked by JoeGwinn on Apr 21, 2008
Latest reply on Apr 24, 2008 by JoeGwinn
We are measuring small changes in electrical length in video amplifiers (1 to 30 MHz) and coaxial cables as a function of temperature, all at ten megahertz (with time-mark modulation components to perhaps 30 MHz).  

The typical total electrical length is about 300 nanoseconds for cables and 5 nanoseconds for each amplifier, and the changes are in the few picoseconds, so the desired resolution is one picosecond or smaller, all with 10 MHz sinewave signals.

Vector Network Analyzers have absolute phase angle uncertainties of order 0.3 degrees rms, which is far too coarse.  However, the trace noise (phase) width is better, with 0.03 degrees rms for an IF bandwidth of 3 KHz being typical.  (This from the E5061A data sheet.)

The basic question is how the trace noise (phase) varies with IF bandwidth.  First-order theory implies that trace noise in phase will vary with the square root of the ratio of bandwidths, so if we used an IF bandwidth of 10 Hertz, the trace noise (phase) would be (0.03)(Sqrt[10/3000])= 0.0017 degrees rms.

However, a VNA may not be first order, and there will be multiple noise sources, not all being gaussian.  Comments?