11.12 DC Offsets
115
power (vars) of the voltage, and the compensation is performed using the same basic method as
described above for copper loss.
11.12
DC Offsets
DC offsets may be present in the signals applied to the input of the 1133A, although this is
unusual. More commonly, small dc errors in the measurement circuit result in non-zero average of
the samples.
This potential source of error must be corrected to obtain maximum accuracy, since the 1133A
makes wideband measurements of power, voltage, and current. Components at any frequency
within the measurement bandwidth, including dc, will affect the measurement. Therefore, part of
the measurement process is to average the (windowed) data, measuring the dc component. The
effects of dc offsets are then subtracted from the results.
11.13
Phase and Frequency
As a part of its measurement process, the 1133A 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 is synchronized
via GNSS 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 measure-
ments, based on the identity
f
=
dφ/dt
. Frequency is averaged over one second prior to being
displayed or made available for output.
The 1133A 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. All phase angles in
the 1133A 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
