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Chapter 3, TECHNICAL DESCRIPTION
3.3.18 Main Output Processor - Output Offset and Expand
3.3.19 Main Output Processor - Vector Magnitude and Phase
3-12
Following the output filter, an output offset facility enables ±300% full-scale offset
to be applied to any or all of the X(1), Y(1), X2, Y2 output signals. The output
expand facility allows a ×10 expansion, performed by simple internal digital
multiplication, to be applied to the same output signals.
The processor also implements the magnitude and signal phase calculation, which is
useful in many situations. If the input signal V
constant amplitude, and the output filters are set to a sufficiently long time constant,
the X and Y channel demodulator outputs are constant levels. The function
(X
2
2
+ Y
) is dependent only on the amplitude of the required signal V
not dependent on the phase of V
computed by the output processor, and made available as the magnitude output. The
phase angle between V
(t) and the X demodulation function is called the signal
s
phase: this is equal to the angle of the complex quantity (X + jY) (where j is the
square root of -1) and is also computed by the processor.
The magnitude and signal phase outputs are used in cases where phase is to be
measured, or alternatively where the magnitude is to be measured under conditions
of uncertain or varying phase.
One case of varying phase is that in which the reference input is not derived from the
same source as that which generates the signal, and is therefore not at exactly the
same frequency. In this case, if the input signal is a sinusoid of constant amplitude,
the X channel and Y channel demodulator outputs show slow sinusoidal variations at
the difference frequency, and the magnitude output remains steady.
However, the magnitude output has disadvantages where significant noise is present
at the outputs of the demodulator. When the required signal outputs (i.e. the mean
values of the demodulator outputs) are less than the noise, the outputs take both
positive and negative values but the magnitude algorithm gives only positive values.
This effect, sometimes called noise rectification, gives rise to a zero error which in
the case of a Gaussian process has a mean value equal to 0.798 times the combined
root-mean-square (rms) value of the X and Y demodulator noise. Note that unlike
other forms of zero error this is not a constant quantity which can be subtracted from
all readings, because when the square root of the sum of the squares of the required
outputs becomes greater than the total rms noise the error due to this mechanism
disappears.
A second type of signal-dependent error in the mean of the magnitude output occurs
as a result of the inherent non-linearity of the magnitude formula. This error is
always positive and its value, expressed as a fraction of the signal level, is half the
ratio of the mean-square value of the noise to the square of the signal.
Hence when the magnitude output is being used, the output filter time constants
should be set to give the required signal-to-noise ratio at the X channel and Y
channel demodulator outputs, rather than attempting to improve the signal-to-noise
ratio by averaging the magnitude output.
For analogous reasons, the magnitude function also shows signal-dependent errors
when zero offsets are present in the demodulator. For this reason, it is essential to
reduce zero offsets to an insignificant level (usually by the use of the Auto-Offset
(t) is a reference frequency sinusoid of
s
(t) with respect to the reference input) and is
s
(t) (i.e. it is
s
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