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LCLS-TN-05-27

A Prototype Wire Position Monitoring System

Wei Wang and Zachary Wolf
Metrology Department, SLAC




1. INTRODUCTION ¹

The Wire Position Monitoring System
(WPM) will track changes in the
transverse position of LCLS Beam
Position Monitors (BPMs) to 1µm [1]
over several weeks. This position
information will be used between
applications of beam based alignment to
correct for changes in component
alignment.

The WPM system has several
requirements. The sensor range must be
large enough so that precision sensor
positioning is not required. The
resolution needs to be small enough so
that the signal can be used to monitor
motion to 1µm. The system must be
stable enough so that system drift does
not mimic motion of the component
being monitored.

The WPM sensor assembly consists of
two parts, the magnetic sensor and an
integrated lock-in amplifier. The
magnetic sensor picks up a signal from
the alternating current in a stretched wire.
The voltage v induced in the sensor is
proportional to the wire displacement
from the center of the sensor [2]. The
integrated lock-in amplifier provides a
DC output whose magnitude is
proportional to the AC signal from the
magnetic sensor. The DC output is either
read on a digital voltmeter or digitized
locally and communicated over a
computer interface.



Figure 1. WPM signal flow


2. PHASE-SENSITIVE DETECTION

Inside the lock-in amplifier, a special
rectifier, called a phase-sensitive detector
(PSD), performs the AC to DC
conversion and forms the heart of the
electronic system. The PSD rectifies only
the signal of interest while suppressing
the effect of noise or interfering
components which may accompany the
signal.

In order to function correctly, the detector
must recognize the signal of interest. This
is achieved by supplying it with a
reference voltage of the same frequency
and with a fixed phase relationship to that
of the signal. This is most commonly
¹Work supported by the DOE contract DE-AC02-76SF00515. This work was performed in support of the
LCLS project at SLAC.



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done by ensuring that the reference and
signal are derived from the same source.
In our project, the reference signal comes
from half of the magnetic sensor, which
is two transformer cores wired in series
opposition [2]. The use of such a
reference signal ensures that the system
will track any changes in the frequency
of the signal of interest, and the reference
circuit is locked to it. This inherent
tracking ability allows extremely small
bandwidths to be obtained for signal-to-
noise ratio improvement since there is no
frequency drift, as is the case with
analog tuned filter/rectifier systems.

The phase-sensitive detector (PSD) 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 2 shows the situation where the
ideal lock-in amplifier is detecting a
noise-free sinusoid, identified in the
diagram as Signal In. The system is
also fed with a reference signal, from
which it generates an internal sinusoidal
reference which is also shown in the
diagram.


Figure 2. Ideal lock-in output

The demodulator operates by multiplying
these two signals together to yield the
signal identified in the diagram as
Output. Since there is no relative
phase-shift between the signal and
reference, the demodulator output takes
the form of a sinusoid at twice the
reference frequency, but with a mean, or
average, level which is positive.

Figure 3 shows the same situation, except
that the signal phase is now delayed by
90° with respect to the reference. It can
be seen that although the output still
contains a signal at twice the reference
frequency, the mean level is now zero.


Figure 3. Phase delay output

From this it can be seen that the mean
level is:
proportional to the product of the
signal and reference frequency
amplitudes
related to the phase angle between
the signal and reference

It will be appreciated that if the reference
signal amplitude is maintained at a fixed
value, and the reference phase is adjusted
to ensure a relative phase-shift of zero
degrees, then by measuring the mean
level, the input signal amplitude can be
determined. As stated before, the
reference signal is from the half
transformer. Small movement of the wire
will not cause any noticeable change of
magnitude in the reference signal, and the
relative phase-shift is zero degrees.


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The mean level is the DC component of
the demodulator output, so it is a
relatively simple task to isolate it by
using a low-pass filter.

The above discussion is based on the case
of noise-free input signals, but in real
applications, the signal will be
accompanied by noise. This noise, which
by definition has no fixed frequency or
phase relationship to the reference, is also
multiplied by the reference signal in the
demodulator, but does not result in any
change to the mean DC level. Noise
components at frequencies very close to
that of the reference do result in
demodulator outputs at very low
frequencies, but by setting the low-pass
filter to a sufficiently low cut-off
frequency, these can be rejected. Hence
the combination of a demodulator and
low-pass output filter allows signals to be
measured even when accompanied by
significant noise.

3. THE LOCK-IN AMPLIFIER

The block diagram of a typical lock-in
amplifier is shown in figure 4.


Figure 4. Typical lock-in amplifier

A. SIGNAL CHANNEL

In the signal channel the input signal,
including noise, is amplified by an
adjustable-gain, AC-coupled amplifier, in
order to match it more closely to the
optimum input signal range of the PSD.
Systems are usually fitted with high
impedance inputs for voltage
measurements. Many also incorporate
low impedance inputs for better noise
matching to current sources, although in
some cases the best results are obtained
through the use of a separate external
preamplifier.

The performance of the PSD is usually
improved if the bandwidth of the noise
voltages reaching it is reduced from that
of the full frequency range of the system.
To achieve this, the signal is passed
through some form of filter, which may
be simply a band rejection filter centered
at the power line frequency and/or its
second harmonic to reject line frequency
pick-up.

B. REFERENCE CHANNEL

It has been shown that proper operation
of the PSD requires the generation of a
precision reference signal within the
system. When a high-level, stable and
noise-free reference input is provided,
making lock-in measurements 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.

The internally generated reference is
passed through a phase shifter, 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.

C. MIXER

The mixer is a multiplier. It takes the
input signal and the reference and
multiplies them together. When we
multiply two waveforms together we get
the sum and difference frequencies as the


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result. As the input signal to be measured
and the reference signal are of the same
frequency, the difference frequency is
zero and you get a DC output which is
proportional to the amplitu