Instrumentation & Measurement Magazine 24-2 - 75

Fig. 5. Simple synchronous demodulation set ups. (a) Capacitive detection of proof-mass displacements in a micro-accelerometer; (b) A photodetector.

the return signal is multiplied by the reference signal and
then filtered by a low-pass filter. By sweeping the frequency
of the reference signal in a specific range, the accelerometer
response can be obtained at different frequencies, which can
also be used to measure the system frequency response. In
the case of the photodetector (Fig. 5b), the reference signal is
applied to a mechanical light chopper to modulate the output light according to its frequency. Optical choppers include
a wheel that has several apertures that are equidistant from
each other. The number of apertures and rotation speed determines the frequency of the signal applied to the sensor. The
light reaching the sensor creates an electric current at the same
frequency, which, after amplification, is applied to the lock-in
for demodulation and filtering. The lock-in amplifier will eliminate signal or noise components at any other frequencies. This
method is advantageous in removing unwanted signals such
as leakage current signals. I addition, it is possible to separate
the desired signal from the rest of the outputs due to stray light
entering the system.

Historical Perspective and Applications
Synchronous demodulators have been around for more than
a century. In the literature, they are sometimes referred to as
lock-in amplifiers or phase sensitive detectors, which basically
express the same concept. The initial ideas of this system were
first introduced in the early 1920s under the title of carrier reinforcement, mostly for telecommunication applications [2]. A
few years later, early circuit arrangements were published [3],
and the 1930s saw the development of some of the improved
versions of the circuit [4]. Most of the articles that explored this
technique further have been published since the 1960s. Many
articles offered various forms of describing the performance of
the system; however, there was no satisfactory, in-depth analysis of the method in literature until the mid-1970s [5].
The simple and yet versatile concept of synchronous demodulation combined with reliability and high-precision has
April 2021

led to making it the go-to method for many precision measurements. Synchronous demodulators are one of the essential
tools in scientific measurements that allow the extraction of
very weak signals to confirm the existence of various phenomena. We can find many examples of the use of this method
in multiple articles, especially in the fields of telecommunications, microscopy-nanoscopy, medicine, electronics, and
optics. Just to point out some of these examples, we can express the use of this technique in satellite receivers, modulated
Wheatstone bridges, inductive displacement sensors, capacitive displacement sensors, radiometers, position-sensitive
photodetectors, spectrophotometers, nuclear magnetic resonance, complex DNA and bio-molecular signature detection,
electron spin resonance, interferometers, control of gas absorption stabilized lasers, optical spectroscopy, and crystal
research, just to name a few [6], [7].

Advanced Topics
Mixing
Accurate measurement or comparison of a signal phase is
fundamental to systems that require phase information. The
majority of such systems use a mixer (i.e., multiplier) as part
of the signal processing chain [8]. As discussed earlier, a mixer
could be used as a phase detector theoretically. In practice,
however, mixers often exhibit some nonideal properties when
used as phase detectors. Depending on the tolerance of the
mixer to these nonidealities, a suitable mixer must be chosen
for a particular application. Most of the synchronous demodulators use double-balanced mixers, although a simple circuit
like a single diode may be used as a phase detector mixer in
some applications.

DC Offset
One of the nonideal parameters that affect the operation of a
mixer in phase-detection applications is the output dc offset of

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