9.13
Phase and Frequency
As a part of its measurement process, the 933A performs a fast Fourier
transform (FFT) of the windowed voltage and current samples.
In
accordance with IEC 61000-4-7, this process is performed twenty times per
second, using overlapping 1024-sample Hanning window data. This yields
new FFT results twenty times per second for each voltage and current
input, for a total of 120 FFT’s per second. Phase angle may be determined
from the relationship between the real and imaginary component of the
fundamental-frequency bin of the FFT. (Since the window is 100 ms wide,
each bin is 10 Hz apart; therefore, this is bin 5 for 50 Hz and bin 6 for 60
Hz.)
So long as there is significant measured energy in the bin, frequency offsets
do not affect the measured phase angle. This is true as long as the signal
being measured is the main source of energy in the bin; i.e.
there is
minimal leakage from adjacent bins, and minimal noise. Provided that
the frequency is anywhere near nominal (within 10 Hz or so), the phase
measurement is perfectly usable.
The phase measurements may be compared to determine phase angle
between voltages and currents or between any two voltages or currents.
Because the sampling process may be synchronized via IRIG (GPS) to
UTC, absolute phase angle measurements may be made and compared
between two units located at some distance from one another.
Frequency is measured by taking the difference in phase angle between
subsequent measurements, based on the identity
f
=
dφ/dt
. Frequency is
averaged over one second prior to being displayed or made available for
output.
The 933A is the first product to make absolute (i.e.
relative to UTC
time) phase-angle measurements available in an economical unit which
will be widely applied. Measurements of phase angle have been available
before, but most products have not offered accurate time synchronization,
and therefore most users are not experienced with the concept of absolute
phase. When synchronized to either GPS or IRIG-B, all phase angles in
the 933A are reported as absolute phase angles, relative to UTC (USNO)
top-of-second. A phase angle of zero degrees is defined as corresponding
to the positive maximum of a cosine wave being coincident with 1PPS-
UTC(USNO). Relative phase angles, for example between phases, or
between a voltage and a current, may be calculated by subtraction.
Relative phases of harmonics may also be found by subtraction; however,
the harmonic number prior to subtraction must multiply the fundamental,
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