Page 102 - Photodetection and Measurement - Maximizing Performance in Optical Systems

System Noise and Synchronous Detection

System Noise and Synchronous Detection 95

to give a sinusoidally varying light output, with frequency f mod . The light,
perhaps after suffering large loss by absorption, is detected by an optical
receiver, in this case in transimpedance configuration. The detected signal,
which contains both the weak modulation due to the LED’s light as well as DC
due to amplifier offsets and perhaps static ambient lighting, other disturbing
AC signals, and of course noise, is applied to one input of an analog multiplier.
Although not essential, the signal is shown here AC-coupled, to remove at least
the DC offset and the lowest frequency signals. The other multiplier input
comes from the same sine-wave generator used to power the source. After the
multiplier the product is filtered in an RC low-pass filter.
At a frequency well above its 1/2pRC characteristic frequency, the low-pass
filter looks like an integrator. Hence this circuit fragment forms the product of
our signal with a sine wave and integrates it. Mathematically, the action of this
synchronous detector is similar to that of computing the sine Fourier trans-
form. That technique is used to determine the amplitude of a particular fre-
quency (f ) component of an input signal. If the input signal which varies with
time t is S(t), we compute the integral:

Ú S t () sin (2p ft dt (5.1)
)
In similar fashion the structure of Fig. 5.1 determines the amplitude of the sinu-
soidal component of our input signal. If the signal is still approximately sinu-
soidal, and in phase with the reference, it determines the amplitude of the signal
itself.
In the frequency domain (Fig. 5.2), the synchronous detector functions as an
electrical filter, centered on f mod . The passband width of this filter is determined
by the RC product of the low-pass filter and is of the order of ±1/2pRC Hz. It
is as though the one-sided, positive-frequency low-pass characteristic of the RC
network, with a cutoff frequency of 1/2pRC, has been mirrored about the zero-
frequency axis, and frequency-translated by multiplication by f mod to become a
two-sided bandpass distribution centered on f mod.
The advantage of the modulation/synchronous detection process is clear from
Fig. 5.2. We have produced an electronic filter, centered precisely on the signal
we expect to find, with a bandwidth that can easily be adjusted simply through
the choice of two components (R and C). The filter lets through the desired
signal, but also the noise and interfering signals contained in the bandwidth
f mod ±1/2pRC. The act of translating to higher frequency should avoid some of
the worst noise and interference. It is straightforward to reduce the filter band-
width by choosing a large value for the RC time constant. A 1MW resistor and
a 1mF capacitor give a one second time constant, or a bandwidth of ±0.16Hz.
This bandwidth will be obtained whether f mod is at 1kHz, 10kHz, or 1MHz.
Achieving adequate stability of a 0.16-Hz-wide filter at 10kHz by conventional
active, or passive LCR filters would be a daunting task. The synchronous filter
is relatively straightforward to set up for an arbitrarily narrow passband, is as
stable as the reference oscillator, and even automatically tracks a modulation

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