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Expected phase uncertainty versus IFBW

Question asked by JoeGwinn on May 21, 2009
Latest reply on May 26, 2009 by JoeGwinn
I'm assessing some measurements made on quarter-inch diameter coax cables 75' and 180' long using an E5071C at various frequencies.  The intent is to measure the electrical length of these cables as a function of cable temperature.  The nominal propagation speed of these heliax cables is 84% of light, the actual speed varying slightly with test frequency, which varies between 5 MHz and 15 MHz.   At these test frequencies, cable loss is a few dB.

The E5071C is used with an IF bandwidth (IFBW) of 30 KHz, and S21 [Phase 90.00 deg/ ref 0.00 deg] is what is measured.  The resulting data are phase values at the three frequencies 5, 10, and 15 MHz.

The question is to estimate the degree of uncertainty in these phase measurements.

The E5071C datasheet (5989-5479EN dated 3 February 2009) says in Table 3 that the phase uncertainty in that frequency range and with the received signal level is 0.3 degrees rms, for an IFBW of 10 Hz, assuming that the instrument has been calibrated (it has).

My understanding is that this uncertainty is proportional to the square root of the ratio of the IFBW values, so the 30 KHz uncertainty is (0.3)Sqrt[30000/10]= (0.3)(54.77)= 16.43 degrees rms.