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520.345 Electrical and Computer Engineering Laboratory
Experiment No. 10
Synchronous Detection
The Formal Lab report for this experiment will be due at the beginning of your lab session on
December 2
nd
or 3
rd
2010.
Introduction
One of the most frequently encountered problems in electrical engineering is the measurement of a
small amplitude signal that has been corrupted by large amounts of additive noise. As long as the
signal of interest is periodic, a very powerful technique known as synchronous, or "lockin",
detection can be used to detect the signal even when the "signaltonoise" ratio is much less than
one.
The technique is based on a very simple property of additive noise, namely that the time
average value of the noise is almost always zero whereas the time average value of a properly
processed signal can be made nonzero.
The only requirement for the processing of the signal is
that a "reference" signal is available that has the same period as the small amplitude signal to be
detected.
Theory of Synchronous Detection
The principle of lockin detection can be explained in either the time domain or the frequency
domain.
The time domain explanation is as follows. Let the small amplitude signal to be measured
be denoted as s(t) and the additive noise
by n(t). The situation is shown below in Figure 1.
The reference waveform r(t) required has the property that it is given by +A for the half period for
which s(t)>0, and that it is A for the half period for which s(t)<0.
In other words, the reference
waveform must have the same phase (or be exactly 180 degrees out of phase) as the signal
waveform.
Let the period of the signal be denoted as T.
Next, assume we can build an analog
circuit which multiplies both s(t) and n(t) by +A for one half period and by A for the other half
period continuously with time.
The output of this multiplier circuit will then be time averaged by a
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simple RC low pass filter with a 3dB bandwidth much less the frequency bandwidth of the signal,
s(t). Mathematically, the time average value of the output, y(t), of the low pass filter can be
expressed as
⟨ ⟩ ± ⟨²(³)´(³)⟩ µ ⟨²(³)¶(³)⟩
(1)
where the notation
⟨
⟩
means time average or statistical average value.
Because the properties of
the inphase reference are such that
⟨²(³)´(³)⟩ · ¸
and the noise is assumed statistically
independent of the reference waveform causing
⟨²(³)¶(³)⟩ ± ⟨²(³)⟩⟨¶(³)⟩ ± ¸
, the time average
value of the low pass filter output is nonzero only if the periodic signal, s(t) is present.
The explanation in the frequency domain is almost as simple if we assume the input signal is a
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 Spring '10
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