05-02-2013, 11:21 AM
What is a Lock-in Amplifier?
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Introduction
A lock-in amplifier, in common with most AC indicating
instruments, provides a DC output proportional to the AC
signal under investigation. In modern units the DC output
may be presented as a reading on a digital panel meter or as a
digital value communicated over a computer interface, rather
than a voltage at an output connector, but the principle
remains the same.
The special rectifier, called a phase-sensitive detector (PSD),
which performs this AC to DC conversion forms the heart of
the instrument. It is special in that it rectifies only the signal
of interest while suppressing the effect of noise or interfering
components which may accompany that signal.
The traditional rectifier, which is found in a typical AC
voltmeter, makes no distinction between signal and noise and
produces errors due to rectified noise components. The noise
at the input to a lock-in amplifier, however, is not rectified but
appears at the output as an AC fluctuation. This means that
the desired signal response, now a DC level, can be separated
from the noise accompanying it in the output by means of a
simple low-pass filter. Hence in a lock-in amplifier the final
output is not affected by the presence of noise in the applied
signal.
Phase-Sensitive Detection
As mentioned above, the heart of the lock-in amplifier is the
phase-sensitive detector (PSD), which is also known as a
demodulator or mixer. The detector operates by multiplying
two signals together, and the following analysis indicates
how this gives the required outputs.
Figure 1 shows the situation where the lock-in amplifier is
detecting a noise-free sinusoid, identified in the diagram as
“Signal In”. The instrument is also fed with a reference signal,
from which it generates an internal sinusoidal reference which
is also shown in the diagram.
Reference Channel
It has been shown that proper operation of the PSD requires the
generation of a precision reference signal within the instrument.
When a high-level, stable and noise-free reference input is
provided, this is a relatively simple task. However there are
many instances where the available reference is far from perfect
or symmetrical, and in these cases a well designed reference
channel circuit is very important. Such circuits can be expensive
and often account for a significant proportion of the total cost
of the instrument.
The internally generated reference is passed through a phaseshifter,
which is used to compensate for phase differences that
may have been introduced between the signal and reference
inputs by the experiment, before being applied to the PSD.
Phase-sensitive Detector
There are currently three common methods of implementing the
PSD, these being the use of an Analog Multiplier, a Digital
Switch or a Digital Multiplier.
Analog Multiplier
In an instrument with an analog multiplier, the PSD comprises
an electronic circuit which multiplies the applied signal with a
sinewave at the same frequency as the applied reference signal.
Although the technique is very simple in principle, in practice it
is difficult to manufacture an analog multiplier which is capable
of operating linearly in the presence of large noise, or other
interfering, signals. Non-linear operation results in poor noise
rejection and thereby limits the signal recovery capability of the
instrument.
Digital Switching Multiplier
The switching multiplier uses the simplest form of demodulator
consisting of an analog polarity-reversing switch driven at the
applied reference frequency. The great advantage of this
approach is that it is very much easier to make such a
demodulator operate linearly over a very wide range of input
signals.
However, the switching multiplier not only detects signals at
the applied reference frequency, but also at its odd harmonics,
where the response at each harmonic relative to the
fundamental is defined by the Fourier analysis of a squarewave.
Such a response may well be of use if the signal being detected
is also a squarewave, but can give problems if.
Low-pass Filter and Output Amplifier
As mentioned earlier, the purpose of the output filter is to
remove the AC components from the desired DC output.
Practical instruments employ a wide range of output filter types,
implemented either as analog circuits or in digital signal
processors. Most usually, however, these are equivalent to one
or more stages of simple single-pole “RC” type filters, which
exhibit the classic 6 dB/octave roll-off with increasing
frequency.
There is usually also some form of output amplifier, which may
be either a DC-coupled analog circuit or a digital multiplier. The
use of this amplifier, in conjunction with the input amplifier,
allows the unit to handle a range of signal inputs. When there is
little accompanying noise, the input amplifier can be operated at
high gain without overloading the PSD, in which case little, if
any, gain is needed at the output. In the case of signals buried
in very large noise voltages, the reverse is the case.
Output
The output from a lock-in amplifier was traditionally a DC
voltage which was usually displayed on an analog panel meter.
Nowadays, especially when the instruments are used under
computer control, the output is more commonly a digital number
although the analog DC voltage signal is usually provided as
well. Units using an analog form of phase-sensitive detector use
an ADC to generate their digital output, whereas digital
multiplying lock-in amplifiers use a digital to analog converter
(DAC) to generate the analog output.
Single Phase and Dual Phase
The discussion above is based around a single-phase
instrument. A development of this is the dual-phase lock-in
amplifier, which is not, as some people think, a dual channel
unit. Rather it incorporates a second phase-sensitive detector,
which is fed with the same signal input as the first but which is
driven by a reference signal that is phase-shifted by 90 degrees.
This second detector is followed by a second output filter and
amplifier, and is usually referred to as the “Y” output channel.
The original output being referred to as the “X” channel.