Instrumentation & Measurement Magazine 24-2 - 72

Synchronous Demodulation for
Low Noise Measurements
Erfan Ghaderi and Behraad Bahreyni

his paper provides an overview of the applications of synchronous demodulators for low noise
measurements in a tutorial manner. Synchronous demodulators have been around for nearly a century and used
extensively for precise measurements and reduction of noise
bandwidth in a wide range of applications. The purpose of
this paper is to briefly introduce the method that is recognized
and formalize its performance. The theory explains how to
amplify a narrowband signal to reduce the amount of measurement noise and how the process can be simply considered
as a multiplier followed by a low-pass filter. We also introduce
some of the applications and design considerations for using
synchronous demodulation. Some of the advanced topics are
briefly discussed with reference to the most recent contribution in this field for those interested in a deeper understanding
of the content.

Signals and Noise
A significant challenge that high-performance systems face is
the issue of noise. Noise, as a measurable quantity, is a property of the system that affects the basic range of operation
under normal conditions. Nowadays, noise can originate
from electrical, electronic, photonic, and mechanical sources,
among others, as we integrate more heterogeneous systems. In
addition, with a strong tendency to reduce the size of devices
and systems, various components operate in close proximity
to each other, which has caused more noise and interference in
modern designs. Noise becomes significantly more important
when measuring weak signals, and more attention should be
paid to noise when the variations of the processed signals are
similar to the existing noise fluctuations. In a noisy environment, external noise sources must be considered in addition to
the internal sources of noise. Of course, as a first step in reducing noise, we need to become more familiar with the signals we
usually encounter during measurements.
Fig. 1a shows the power spectral density (PSD) of a signal
that one may obtain from a measurement. Due to its random
nature, the noise has frequency components at all frequencies
and covers the entire spectrum. Two significant types of noise
72

contribute to the total noise of the systems: thermal noise floor,
that has an approximate constant magnitude as a function of
frequency; and flicker noise, that nearly all electronic devices
exhibit, which is inversely proportional to frequency (i.e.,
∝ 1/f a, where typically α≈1).
Most of the time, we are interested in detecting a particular
signal at a specific frequency band. Fig. 1b shows the desired
signal that needs to be detected (highlighted in green) while
the rest of the spectrum may be considered as noise (highlighted in red). The area below the graph gives the power
level. In many situations, the relative power of signal to noise
is a better indicator of system performance than knowing the
absolute noise levels. It can be seen that the power in the frequency band of interest is smaller than the sum of the power at
all other frequencies, i.e., noise power. We can improve the signal-to-noise ratio (SNR) by applying a narrowband filter that
covers the signal band, as seen in Fig. 1c and Fig. 1d, where the
SNR is further increased by using a narrower filter.
Using a bandpass filter for definition and reduction of noise
bandwidth is a passive technique. Moreover, this technique
effectively improves SNR as long as one is far from the frequency band where the flicker noise becomes dominant (i.e.,
low frequencies). Synchronous demodulation, as discussed
below, offers the advantage of measuring DUT behavior using a reference signal of sufficiently high frequency to reduce
or eliminate the effect of 1/f noise and improve the SNR or the
possibility of picking up weaker signals.
A synchronous demodulator, also known as lock-in amplifier or phase-sensitive detector, is a type of measurement
system that can extract a weak electrical signal from a noisy
environment by utilizing a reference signal with a specified
frequency to excite the Device-Under-Test (DUT). It acts as
a filter with a very narrow frequency band that can improve
the SNR and ultimately filter out undesired signals, including noise. Synchronous demodulators have been around for
a long time, and many important experiments in the world
of science have been performed by this method [1]. The concept of the synchronous demodulator is discussed in the next
section.

IEEE Instrumentation & Measurement Magazine
1094-6969/21/$25.00©2021IEEE

April 2021

Instrumentation & Measurement Magazine 24-2

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 24-2