1 Application of FPGA based Lock-in ampliﬁer for ultrasound propagation measurements using the

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Application of FPGA based Lock-in ampliﬁer for

ultrasound propagation measurements using the

pulse-echo technique

Stanisalw Galeski, Rafał Wawrzy´

nczak, Claudius Riek and Johannes Gooth

Abstract—We describe application of a state-of-the art digital

FPGA-based Lock-In ampliﬁer to measurements of ultrasound

propagation and attenuation at ﬁxed frequency in low tem-

peratures and in static magnetic ﬁelds. Our implementation

signiﬁcantly simpliﬁes electronics required for high resolution

measurements and allowing to record the full echo train in single

measurement and extract changes in both phase and amplitude

of an arbitrary number of echa as a function of an external

control parameter. The system is simple in operation requiring

very little prior knowledge of electrical engineering and can

bring the technique to a broad range of solid state physics

laboratories. We have tested our setup measuring the magneto-

acoustic quantum oscillations in the Weyl semimetal NbP. The

results are directly compared with results previously obtained

using standard instrumentation.

Index Terms—Ultrasound attenuation, speed of sound; pulse-

echo measurements.

I. INTRODUCTION

Measurement of the speed of sound is one of the most pow-

erful techniques available to solid state physicists. Since the

speed of sound is directly related to the materials elastic mod-

ulus it is a thermodynamic probe and thus is highly sensitive to

phase transitions and quantum oscillations (QO). In addition,

measurement of phonon attenuation provides a handle for the

study of dissipation mechanisms complementary to usually

employed thermal and charge transport experiments [1], [2].

Indeed, to this day ultrasound techniques have been employed

in the study of a wide range of materials from low dimen-

sional [3], [4] and frustrated magnetic insulators [5] to heavy

fermions [6], [7]. In addition, ultrasound measurements are

one of the few techniques that can be used in the study

of Dirac and Weyl semimetals where other thermodynamic

probes often lack sensitivity due to the extremely small charge

carrier densities present in these systems [8], [9], [10], [11].

In a typical pulse-echo experiment two piezoelectric trans-

ducers are ﬁxed to opposite parallel faces of the sample.

Subsequently a radiofrequency (RF) pulse is applied to one

of the transducers producing a pulse of acoustic waves at

MHz frequencies, that travels through the sample towards

the second transducer. On arrival to the second end of the

sample part of the mechanical energy is transformed back

S. Galeski, R. Wawrzy´

nczak and J. Gooth are with Max Planck Institute for

Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany.

S. Galeski and J. Gooth are with Physikalisches Institut, Rheinische

Friedrich-Wilhelms-Universität Bonn, Nussallee 12, 53115 Bonn, Germany.

C. Riek is with Zurich Instruments Germany GmbH, Mühldorfstrasse 15,

81671 München, Germany.

into an electrical signal by the second piezoelectric transducer

with the remainder being reﬂected back into the sample. In a

sample with small attenuation the initial pulse can be reﬂected

there and back several times giving rise to a ‘train of echoes’

recorded by the receiving transducer. In a typical measurement

the probe pulse is repeated with a kHz frequency allowing to

record both the amplitude and time of arrival of the echoes

as a function of external parameters such as magnetic ﬁeld,

temperature or mechanical strain [2]. Although knowledge of

the length of the sample allows to determine the absolute

speed of sound and attenuation per cm, ultrasound experiments

gain a new dimension with the application of phase sensitive

techniques. Here, the relative change of amplitude and phase

shift of the echoes are recorded allowing to attain relative

accuracy of at least one part in 105in ∆v

v[2].

Although very powerful, the standard implementation of

analogue phase sensitive ultrasound measurements is usually

technically complex and requires good knowledge of electri-

cal engineering. In a usual implementation a signal in the

5−500 MHz range is provided by a frequency generator

and then divided into two parts one going to the sample and

one serving as a reference signal. The signal is subsequently

modulated into pulses, ampliﬁed using a power ampliﬁer and

send into the input transducer. On arrival to the receiver side,

the signal is ampliﬁed and multiplied by the reference and

a replica shifted by 90 degrees, and passed through a low

pass ﬁlter. This is the functionality of a lock-in ampliﬁer.

Subsequently in and out of phase components of the signal

are averaged in a narrow time window, usually containing a

single echo, using boxcar averagers. Then the output from the

boxcar averager is passed to voltage meters and recorded with

a computer. The amplitude and phase of the arriving echo are

recorded over multiple repetitions of the sequence to improve

the signal-to-noise ratio [12].

This measurement procedure has been signiﬁcantly simpli-

ﬁed by the use of the digital technique. Here the full arriving

echo train is directly recorded by a digital oscilloscope and

then post-processed using a computer [13]. Although such

approach simpliﬁes the used electronics it puts additional

requirements on the data transfer between the oscilloscope and

the computer and requires design of specialistic software for

data processing.

Here we propose a further simpliﬁcation of the measurement

utilizing the Zurich Instruments UHFLI lock-in ampliﬁer with

an integrated Arbitrary Waveform Generator (AWG) option

and based on FPGA (Field-Programmable Gate Array) tech-

arXiv:2210.13221v3 [physics.ins-det] 12 Jan 2023

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1ApplicationofFPGAbasedLock-inamplierforultrasoundpropagationmeasurementsusingthepulse-echotechniqueStanisalwGaleski,RafaWawrzy´nczak,ClaudiusRiekandJohannesGoothAbstractWedescribeapplicationofastate-of-theartdigitalFPGA-basedLock-Inampliertomeasurementsofultrasoundpropagationandattenuationatxe...

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