# Instrumentation & Measurement Magazine 24-2 - 74

```Fig. 2. (a) Two sinusoidal functions with the same frequency (in orange and blue) and their product (in green). The highlighted area represents the average or dc
component of the product signal which, in this case, is nonzero. (b) Two sinusoidal functions with the same frequency (in orange and blue) and their product (in
green). In this case, the dc component is zero and the highlighted area will average out. The unit on the y-axis is arbitrary.

detection. Moreover, any dc shift added by the test device to
the measuring signal is also suppressed by synchronous detection. If any fixed component of the measured signal is
multiplied by the reference signal, a harmonic signal fluctuates around zero, which disappears with the time-averaging.
Fig. 3 depicts a synchronous demodulation measurement
setup which consists of a local oscillator as a reference signal.
This signal is applied to the DUT, sometimes followed by an amplifier and a phase shifter. The resulting signals are multiplied,
and the dc component of the output signal is extracted after filtering it with a low pass filter. If the DUT introduces a phase shift
Δ ϕ in comparison to the reference signal, adding an equal phase
shift to the reference signal can compensate it before multiplying. For the proper functioning of this method, the frequency
of the local voltage oscillator must be specified. Moreover, the
phase of the signal must be stable to produce a suitable result.
To measure the amplitude and phase simultaneously, we
can use the configuration shown in Fig. 4. This set up is basically the same as the previous setup, with the difference that
the measurement is done in two channels. In one channel, the
phase difference between the signal and the reference signal
is zero, and in the other channel, the phase difference is 90 degrees. In this way, if the final signal in channel X is proportional
A sin  .
to Acosϕ, then the final signal of channel Y is  A cos     2  


The amplitude can be extracted as X 2    Y 2 and phase is equal
to arctan  YX .

Among the applications of the synchronous demodulators, sensor excitation for obtaining the sensor transfer
function is more prominent than the others, when we elaborate on the measurement set up further. Pervasive sensors are
used to measure temperature, light, sound, and other types
of environmental parameters. Some sensors act as a source
of voltage or current, depending on the parameter. Most sensors have transfer functions that follow a specific relationship
according to the physical parameter. We can characterize this
transfer function by: ac excitation of the sensor with synchronous demodulation; sweeping the frequency; and recording
the amplitude and phase of the output signal. Given that this
technique is prevalent in sensing applications, Fig. 5 depicts
the simple synchronous demodulation set up for measuring
a sensor's output signal for a capacitive accelerometer and a
photodetector.
In both cases, a reference signal is used for ac excitation,
which acts as a carrier to modulate the sensor response. In the
case of the accelerometer (Fig. 5a), the reference signal is fed
to a shaker to apply a proportional acceleration signal to the
sensor. In these devices, the inserted force on the proof mass
creates a displacement in the direction of applied acceleration.
The resulting displacement leads to a change in a capacitor
that has been included in the accelerometer's structure. A dc
voltage will also be used for the measurement. The sensor output signal returns to the lock-in after amplification. Finally,

Fig. 3. A synchronous demodulation measurement setup.

Fig. 4. Schematic of two-channel synchronous demodulator.



74



IEEE Instrumentation & Measurement Magazine

April 2021

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# Instrumentation & Measurement Magazine 24-2

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