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A single-chip integrated transceiver for high
field NMR magnetometry
Cite as: Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436
Submitted: 15 October 2018 •Accepted: 13 December 2018 •
Published Online: 2 January 2019
Marco Grisi,1Gaurasundar Marc Conley,1Pascal Sommer,2Jacques Tinembart,2and Giovanni Boero1,a)
AFFILIATIONS
1´
Ecole Polytechnique F´
ed´
erale de Lausanne, CH-1015 Lausanne, Switzerland
2Metrolab Technology SA, CH-1228 Plan-les-Ouates, Switzerland
a)Electronic mail: giovanni.boero@epfl.ch.
ABSTRACT
We present the design and performance of a broad-band single-chip integrated transceiver specifically conceived for nuclear
magnetic resonance magnetometry. The single-chip transceiver is realized using a standard silicon complementary metal-oxide-
semiconductor integrated circuit technology. A radio-frequency (RF) transmit amplifier, a transmit/receive switch, a low noise
RF receive amplifier, a quadrature (IQ)-mixer, and two intermediate frequency amplifiers are integrated on a single silicon chip of
1.8 mm2. The advantages and problematic aspects with respect to conventional discrete electronic approaches are discussed. We
show the results of magnetic field measurements performed at 1.4 and 7.05 T, using solid and liquid samples having volumes from
40 µl down to 100 pl. Particular attention is devoted to the comparison of the experimentally measured magnetic field standard
deviation with respect to the Cramer-Rao lower bound value. With a sample of distilled water (T1T23 s, T∗
220 ms) having
a volume of 40 µl, a standard deviation of 2.5 nT at 7.05 T (i.e., 0.5 ppb) in 1 s of averaging time is achieved, with a projected
Cramer-Rao lower bond of 8 pT (i.e., 1.1 ppt).
Published under license by AIP Publishing. https://doi.org/10.1063/1.5066436
I. INTRODUCTION
Nuclear magnetic resonance (NMR) is the method of
choice for high accuracy and high resolution measurements
of high magnetic fields (i.e., larger than 0.1 T).1–20 High field
NMR magnetometers are commonly used to measure the
magnetic field value, spatial homogeneity, and temporal evo-
lution in magnets for magnetic resonance imaging (MRI),1–7
for physics experiments,8–11 and for calibration of sensors
based on other physical principles.21,22 NMR based methods
are used also for magnetometry down to the earth’s magnetic
field. At low fields, large samples,23,24 optical or microwave
hyperpolarization,12,25,26 flowing water prepolarization,27–30
or non-inductive techniques31–35 are necessary to achieve a
sufficiently large signal-to-noise ratio (SNR).
The Larmor resonance frequency of a nucleus in a mag-
netic field B0is f0= (γ/2π)B0, where γis the gyromag-
netic ratio of the nucleus. For 1H nuclei, (γ/2π) = 42.577
478 92(29) MHz/T.36 Hence, in NMR magnetometry, the
value of the magnetic field is obtained from a frequency
measurement. High field probes are commonly realized with
solenoidal coils wrapped around a sample of natural rubber or
water (1H nuclei),2,3,7,8,14,23 heavy water (2H),18,20,37 hexafluo-
robenzene (19F),3,5 or optically hyperpolarized gaseous helium
(3He).12,15,16 For low temperature measurements, 27Al nuclei
in micrometer sized aluminum particles are also used.38 The
coil is interfaced to the electronics via matching and tuning
capacitors in order to implement an impedance matched res-
onator at the Larmor frequency, which allows to minimize
the influence of the noise of the detection electronics on the
measured SNR and, hence, on the achievable magnetic field
resolution.
Commercial NMR magnetometers generally consist of a
main electronic unit and a set of probes capable of variable
frequency operation, whose combined range covers frequen-
cies up to about 1 GHz, corresponding to magnetic fields of
about 20 T. In the design of NMR probes, the search for dis-
crete electronic components with no or as little as possible
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-1
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ferromagnetic parts in their package is a practical problem
to which manufacturers have to dedicate considerable atten-
tion. Additionally, the overall size of the assembly of the dis-
crete components is a limiting factor for compact probes to be
used in small spaces or when arrays of probes are required. In
this work, we show the use of a complementary-metal-oxide-
semiconductor (CMOS) single-chip integrated transceiver in
probes aimed at NMR magnetometry of high magnetic fields.
The electronics needed at the front end of the probe is entirely
integrated on a single 1.8 mm2chip, drastically reducing the
number of components to be placed in close proximity to the
sensitive volume of the probe. Besides allowing for a design
with lower and/or more predictable field distortions, inte-
grated circuit solutions reduce in the long term fabrication
and design costs, especially in the implementation of arrays
of probes.
Recent developments demonstrated the use of CMOS
transceivers for compact NMR probes for spectroscopy and
relaxometry, where external resonators were combined with
integrated electronics.39–41 Among these, we have previ-
ously shown the design of a broadband single-chip CMOS
transceiver for multi-frequency compact probes, demonstrat-
ing its use for multi-nuclear spectroscopy.39
In this work, we describe a single-chip transceiver with
broadband quadrature (IQ) demodulation capabilities and
show its use in variable frequency probes aimed for high field
NMR magnetometry. The first CMOS integrated probes for
NMR magnetometry13,14 achieved a resolution of about 50 ppb
(i.e., 350 nT or 15 Hz) at 7.05 T in a measuring time of 1 s. Here,
we experimentally demonstrate effective resolutions down to
about 0.5 ppb at 7 T (i.e., 2.5 nT or 0.1 Hz) in 1 s of averag-
ing time. We show that the experimentally measured magnetic
field resolution is presumably limited by the fluctuations of the
magnetic field under investigation. In order to demonstrate
that this extrinsic noise is dominant over the intrinsic noise of
the instrument, we implemented also a compact two-channel
probe allowing for simultaneous but independent magnetic
field measurements at a distance of about 1.5 mm. This dif-
ferential measurement allows to suppress the common field
fluctuations and to estimate the intrinsic magnetic field reso-
lution of the instrument. For an averaging time of 1 s at 7.05 T,
the achieved instrumental resolution limit is down to about
0.008 Hz (i.e., 0.18 nT or 0.025 ppb), with a Cramer-Rao lower
bound (CRLB) limit down to about 0.0003 Hz (i.e., 0.008 nT or
0.001 ppb).
II. SINGLE CHIP INTEGRATED TRANSCEIVER
Figure 1 shows the block diagram of the realized single-
chip transceiver, together with the components of the exter-
nal (i.e., non-integrated) resonator. A photograph of the chip
connected by wire bonding to the printed circuit board (PCB)
of the probe is shown in Fig. 2(e). The chip area is about
1.8 mm2, and its total power consumption is about 40 mW.
The chip is realized using a standard CMOS integrated circuit
technology (HCMOS9GP 130 nm, ST Microelectronics).
As shown in Fig. 1, the single-chip integrated transceiver
consists of an RF power amplifier, an RF low-noise pream-
plifier, a (π/2) broadband phase shifter, two frequency mix-
ers, two audio-frequency (AF) amplifiers, and transmit-receive
switches. The working principles and detailed schemat-
ics of switches, transmitter, and receiver were previously
reported.39 In the following, we summarize their key fea-
tures. The integrated switches allow commutation between
transmitter (TX) and receiver (RX) modes in some ns and
FIG. 1. Block diagram of the single-chip integrated IQ transceiver (contained within the green line) and of the discrete LC resonator with electronically controlled variable
capacitors. Land Rcrepresent the inductance and resistance of the solenoidal coil employed. The tuning and matching capacitors are implemented using reverse-biased D1
(matching) and D2 (tuning) varicap diodes, biased with the control voltages Vm(0 to −30 V) and Vt(0 to 30 V).
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-2
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FIG. 2. Single channel NMR magnetometer. (a) Block diagram of complete NMR magnetometer, (b) picture of the main electronic unit (PT2026, Metrolab Technology SA),
(c) picture of the probe (a modified version of the probe 1226, Metrolab Technology SA), and (d) picture of the modified probe which contains the single-chip integrated CMOS
transceiver instead of the standard transceiver made of discrete electronics component. The total gain is about 75 dB (54 dB in the integrated single-chip transceiver and
21 dB on the probe PCB). (e) Picture of the single-chip integrated transceiver. The single-chip transceiver is first glued with a conductive paste on the Cu ground plane of the
PCB, subsequently it is wire-bonded, and finally the circuit and the bonding wires are covered with a black hard epoxy.
provide more than 50 dB isolation between the two channels.
No switches are used in series with the output stage of the
transmitter, which operates with no power losses. The output
impedance of the transmitter is about 50 Ω. When the external
coil is tuned and matched to 320 Ω, the transmitted current is
about 10 mA and the transmitted power is about 10 mW. The
receiver consists of a low-noise RF amplifier (LNA), a double
balanced mixer, an AF amplifier, and a differential to single-
ended conversion stage. The LNA has a gain of 35 dB, whereas
the mixer and the AF part have a global gain of 19 dB. Hence,
the overall RX gain is 54 dB. The wideband fully differential
LNA bandwidth is 1–300 MHz, and its frequency-dependent
input impedance is ZLNA = 1/jωCg, with Cg= 1 pF. A resis-
tor Rm= 320 Ωfixes the real part of the input impedance
and protects the LNA from the energy discharge associated
with TX to RX switching. The measured recovery time of the
receiver is about 1 µs, and its equivalent input noise with the
external resonator matched to 320 Ωis about 2.3 nV/Hz1/2
(i.e., the RX electronics has an effective noise figure of about
5 dB). With respect to the chip we reported in Ref. 39, we
introduced a (π/2) shifter and duplicated the receiver chan-
nel in order to allow IQ operation. The (π/2) shifter is realized
dividing by two the frequency of two counter-phase chan-
nels. First, a πphase shift is generated on-chip using two
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-3
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chains of inverters whose number of inverters differs by one
unit. A dummy inverter is used to compensate the relative
delay. Then, division by two using true single-phase clock-
ing (TSPC) dividers is implemented.42 This topology of digital
dividers is broadband, but the quality of the divided signal
deteriorates rapidly for frequencies below 10 MHz.43 In our
design, we tested the phase shift between the I and Q output
channels inducing a continuous signal at the receiver input,
and we measured an error of about 4◦at 3 MHz and 0.3◦at
1 GHz.
III. MAGNETOMETERS
We realized three NMR magnetometers, two based on the
use of the single-chip IQ integrated transceiver described in
Sec. II and one based on a single-chip integrated transceiver
with a co-integrated planar microcoil (i.e., a fully integrated
probe) described in Ref. 39.
The first one consists of a modified version of a commer-
cial single-channel probe, where the transceiver discrete elec-
tronics is replaced with our single-chip integrated transceiver
and connected to a commercial main electronic unit con-
taining analog and digital signal generation and processing
(Fig. 2). The single-chip transceiver is interfaced to external
variable-frequency resonators, as shown in Fig. 1. The work-
ing frequency of the resonator is adjusted by DC voltages,
obtained from the analog outputs of a digital-to-analog con-
verter (DAC), acting on reverse biased variable capacitance
diodes (BB181 and BB182, NXP Semiconductors).
The second one consists of a two channel probe with
two single-chip integrated transceivers, connected to com-
mercial electronics for RF generation, analog-to-digital and
digital-to-analog conversion, and digital signal processing
(DSP) [Fig. 3(a)]. Impedance matching and frequency tun-
ing are obtained with mechanically adjustable capacitors
[Fig. 3(c)].
The third one consist of a fully integrated probe [Figs. 4(a)
and 4(b)], connected to commercial electronics for RF gener-
ation, analog-to-digital and digital-to-analog conversion, and
digital signal processing [Fig. 4(c)].
A. Single channel probes
Figure 2(a) shows a block-diagram of the magnetome-
ter based on single channel probes. It mainly consists of a
commercial main electronic unit (PT2026, Metrolab Technol-
ogy SA) [Fig. 2(b)] and of a modified version of a commercial
probe (Model 1226, Metrolab Technology SA) [Fig. 2(c)]. The
overall size of the probe is 16 ×12 ×230 mm3. As shown in
Fig. 2(a), the main unit is composed by an analog-to-digital
converter (ADC) (16 bits, 2 MHz), used to translate the NMR
signal in the digital domain, a two-channel RF generator, a
pulse generator, a micro-processor (µP), and a digital sig-
nal processing (DSP) unit. The pulse generator determines
pulse width and repetition rate acting on the transmit-receive
(TX/RX) switches of the single-chip integrated transceiver.
The RF generator is designed to switch between two different
frequencies, one used for excitation in TX mode and the other
used to demodulate the NMR signal in RX mode. Once the
field is approximatively determined, the TX frequency is set
to the Larmor frequency f0, whereas the RX frequency is set
at about 50 kHz above (or below) the TX frequency. This dou-
ble frequency approach allows one to use, simultaneously, a
large intermediate frequency (IF) of 50 kHz together with a
long pulse length of 50 µs. A large IF is required to avoid
the deterioration of the signal-to-noise ratio due to the 1/f
noise (the corner frequency is about 20 kHz). A long pulse
length is required, with large coils, to achieve acceptable
flip angles with the limited output power of the integrated
transmitter. Thanks to the on-resonance excitation, the off-
resonance effects due to a long pulse length and a large IF are
avoided.
The current version of the main unit has a single ADC, i.e.,
only the I signal or the Q signal can be digitized. As shown
in Fig. 2(a), in order to fully exploit the capabilities of the
single-chip integrated IQ transceiver realized in this work, the
I and Q signals are digitized by a 8-channel ADC (PCIe-6259,
National Instruments) installed in an external PC, which we
used also for digital signal processing in LabView™(National
Instruments). The signal processing algorithms used to obtain
the resonance frequency and, hence, the value of the magnetic
field are discussed in Appendix A.
As shown in Table I, we realized several single-channel
probes, all based on a modified version of the commercial
probe. The main modification is the use of our single-chip
integrated transceiver instead of discrete electronic compo-
nents [Figs. 2(d) and 2(e)]. The single channel probes are inter-
faced with the external electronics, as shown in Fig. 2(a). In
the probe, an additional amplification of 21 dB is implemented.
Hence, the total gain of the receiver chain is 75 dB.
Probes A to C can measure magnetic fields from 3.3 T
to 10.6 T (140 MHz to 450 MHz) and contain samples of
natural rubber, silicone rubber, or distilled water. Probe D
can measure magnetic fields from 1.1 T to 3.5 T (47 MHz to
150 MHz) and contain a sample of natural rubber. Natural
rubber is a solid elastomer, based on cis-polyisoprene, com-
mercially available also in the form of long cylindrical rods
of a few millimeter diameter (NR E6247, Maagtechnic). It has
1H spin density of 6.4 ×1028 spins/m3, a transverse relax-
ations T21 ms, and longitudinal relaxation times T180 ms
at 1.4 T and T1400 ms at 7 T. The NMR spectrum con-
sists of three lines with chemical shifts 5.1 ppm, 2.1 ppm, and
1.7 ppm with respect to tetramethylsilane (TMS) and relative
amplitudes 1:4:3. Due to the relative broad linewidth, only two
peaks with relative intensity 1:7 are clearly visible also at high
magnetic fields. Silicone rubber is a solid elastomer, based on
polydimethylsiloxane (PDMS), which we obtained by mixing
the two viscous liquids of a commercially available prepara-
tion kit (Sylgard 184, Dow-Corning) and subsequently filling a
cylindrical glass container. The obtained silicone sample has
a1H spin density of 4.6 ×1028 spins/m3,T22 ms, and
T1600 ms at 7 T. The NMR spectrum consists of a single
line with a chemical shift of about 0 ppm with respect to TMS.
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-4
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FIG. 3. Two channels NMR magnetometer. (a) Block diagram of the complete NMR magnetometer. RF source: Anritsu MG3633A. AF amplifier: EG&G 5113 (Gain: 100,
lowpass filter: 100 kHz). DAQ board: National Instruments PCIe-6259. (b) Schematics in section view of the two-channels probe head at the end of the fabrication process.
(c) Photograph of the resulting probe. In between (b) and (c), the PDMS mold is removed, and the acrylic embedded coils are fixed and soldered to the printed circuit board
(PCB). An identical circuit on the other side of the PCB implements the second channel. The magnetometry experiments are performed by inserting the two-channels probe
into a 7.05 T superconducting magnet (Bruker 300 MHz, 54 mm warm bore, B07.05 T, f0300 MHz).
In both these solid elastomeric materials, the magnetic dipo-
lar interactions are partially averaged by motional narrowing,
giving rise to relatively long T2relaxation times with respect
to the majority of solid materials. The distilled water sam-
ple has a 1H spin density of 6.6 ×1028 spins/m3, relaxation
times T1T23 s, and a single resonance line at 4.7 ppm
from TMS.
The effective transversal relaxation time T∗
2(i.e., the effec-
tive decay time of the NMR signal after the pulse excitation)
is given by the combination of the intrinsic transversal relax-
ation time T2and the static magnetic field inhomogeneity.
In our measurements, we obtained T∗
2T2for the natu-
ral rubber and silicone rubber samples and T∗
220 ms for
the distilled water sample. Water is commonly used for NMR
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-5
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FIG. 4. Single channel NMR magne-
tometer based on a fully integrated
probe. (a) Picture of the fully integrated
probe. The planar microcoil is shown in
details. (b) Block diagram of the fully inte-
grated probe. (c) Block diagram of the
complete NMR magnetometer. RF gen-
erator: Anritsu MG3633A. AF amplifier:
EG&G 5113 (Gain: 1000, lowpass filter:
100 kHz). DAQ board: National Instru-
ments PCIe-6259.
magnetometry in its pure form but also with the addition
of water soluble paramagnetic salts3,7,8,20 in order to reduce
the values of T2and T1, usually in such a way to obtain
T1T2T∗
2.This allows to optimize the achievable magnetic
field resolution for a given value of T∗
2(i.e., for a given field
inhomogeneity).
B. Two channel probe
We have realized also a two channel probe (probe E in
Table I). As we will discuss in details in Sec. IV, the use of
a two channels probe allows to elucidate the origin of the
discrepancy between the experimentally measured magnetic
field resolution and the theoretically expected value. Since
the main unit shown in Fig. 2 does not allow for simultane-
ous measurement of two channels, the NMR measurements
with this two-channel probe have been performed with a
different setup, as shown in Fig. 3(a). A single RF genera-
tor (Anritsu MG3633A) is used for excitation and frequency
down-conversion.
Each channel is based on a small solenoidal coil (diame-
ter of 800 µm and length of 1200 µm) consisting of ten loops
of an enameled copper wire having a diameter of 100 µm,
wrapped around a PMMA capillary (ID = 550 µm, OD = 700 µm,
Paradigmoptics). The capillary is filled with distilled water. The
effective sample volume inside the solenoidal coil is about
300 nl. The fabrication process consists of four main steps:
(1) a first mold aimed at structuring a second silicone (Sylgard
184, Dow-Corning) mold is 3D printed (Clear Resist, Formlabs
printer), exposed to UV for 30 min, and hard baked at 80 ◦C
for 2 h; (2) the silicone mold is produced by casting and cur-
ing at 80 ◦C for one day; (3) the 10 loops micro-solenoids are
wrapped around PMMA capillaries, filled with water and sealed
with a tube sealing compound (Cha-seal) at the extremities; (4)
the capillaries are inserted into silicone slots included in the
mold, and an acrylic resin (Paladur, Heraeus Kulzer, Germany)
is cast to embed the solenoids in a susceptibility matched
environment [Fig. 3(b)]. After removal of the silicone mold, the
resulting probe head is fixed and soldered to a printed cir-
cuit board (PCB) on which variable capacitors (capacitor trim-
mer, Johanson Manufacturing) are used to tune and match the
two resonators at the desired frequency [Fig. 3(c)]. The probe
head is constituted by two specular circuits, one realized on
the top layer and the other on the bottom layer of the PCB.
Thanks to the good magnetic susceptibility matching between
copper, acrylic, and water,44 and the small distance between
the two coil axis (about 1.5 mm), the simultaneous shimming
of two samples allows to achieve an effective relaxation time
T∗
220 ms.
C. Fully integrated miniaturized single
channel probe
A fully integrated probe was also realized (Fig. 4). In this
probe, a transceiver and a microcoil are integrated on a sin-
gle silicon chip with an area of 1.1 mm2. The chip is real-
ized using a standard CMOS integrated circuit technology
(HCMOS9GP 130 nm, ST Microelectronics). The microcoil is
connected directly to the transceiver without matching and
tuning capacitors [Fig. 4(b)]. This miniaturized probe (and its
use for multi-nuclei NMR spectroscopy of subnanoliter solid
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-6
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TABLE I. Characteristics and performance of the realized magnetometers based on the single-chip integrated transceiver.
Measured standard deviations of the NMR resonance frequency. The Cramer-Rao lower bound (CRLB) values are computed
from Eq. (A3) (the number of averages is either 20 or 5, corresponding all cases to an averaging time of 1 s). The experiments
are carried out using a matched filter [i.e., the time domain signal is multiplied by exp(t/T∗
2)]. Notations: NR: natural rubber,
MQ: silicone rubber, Navg: number of averages, and s0and N: NMR signal amplitude at the beginning of the free induction
decay and voltage noise spectral density (both at the input of the ADC).
Probe A B C D E F
Frequency (MHz) 300 300 300 60 300 300
Magnetic field (T) 7.05 7.05 7.05 1.4 7.05 7.05
Sample NR MQ H2O NR H20 H2O
Sample volume (µl) 17 25 40 50 0.3 0.0001
Nuclei 1H1H1H1H1H1H
T2(ms) 1 2 3 000 1 3000 3000
T∗
2(ms) 1 2 20 1 20 120
T1(ms) 400 600 3000 80 3000 3000
Chem. shift (ppm) 5.1 0 4.7 5.1 4.7 4.7
2.1 2.1
1.7 1.7
Coil turns 2 2 2 8 10 22
Coil diameter (mm) 3 6 6 4 0.8 See text
Coil length (mm) 2.4 2 3 4 1.2 . . .
Wire material Cu Cu Cu Cu Cu Cu, Al
Wire diam. (mm) 0.2 0.3 0.3 0.3 0.1 See text
Pulse length (µs) 35 35 35 35 6 2.5
Repetition time (ms) 50 50 50 50 200 200
Navg 20 20 20 20 5 5
Averaging time (s) 1 1 1 1 1 1
Measurements 300 300 300 300 300 300
Measuring time (s) 300 300 300 300 300 300
Receiver gain (dB) 75 75 75 75 94 114
s0(V) 1 1 1 1 1 0.13
N(µV/Hz1/2) 8.5 8.5 8.5 8.5 70 720
s0/N(105Hz1/2) 1.2 1.2 1.2 1.2 0.14 0.0018
Standard deviation
(Hz) 0.2 0.2 0.1 0.6 0.16 0.13
(nT) 4.5 4.5 2.5 14 3.8 3
(ppb) 0.7 0.7 0.5 10 0.5 0.4
CRLB
(Hz) 0.027 0.01 0.00033 0.027 0.005 0.036
(nT) 0.63 0.22 0.008 0.63 0.12 0.84
(ppb) 0.09 0.01 0.001 1 0.09 0.016 0.12
and liquid samples) was previously described in Refs. 39,45,
and 46. In a nutshell, the microchip [Fig. 4(a)] contains a
radio-frequency (RF) power amplifier, a low-noise RF pream-
plifier, a frequency mixer, an audio-frequency (AF) amplifier,
and fully integrated transmit-receive switches. The integrated
coil [Fig. 4(a)], which has an internal diameter of 50 µm and
an external diameter of 150 µm, is realized using the top four
metal layers of the CMOS technology. The total number of
turns is 22. The 13 turns in the highest metal are 0.9 µm
thick and 3.6 µm wide. The remaining three metals have three
turns each, 0.35 µm thick, and 6.4 µm wide. In Ref. 46, we
reported NMR spectroscopy experiments of liquid samples
confined into 3D printed microchannels placed on top of the
microcoil sensitive region. A spectral resolution of 3 Hz was
achieved. Here we use the same approach to perform NMR
magnetometry with a sample of distilled water of 100 pl.
IV. EXPERIMENTAL RESULTS
To evaluate the performance of the realized magnetome-
ters, in particular, their magnetic field resolutions at high
magnetic fields, we performed measurements in a 1.4 T per-
manent magnet (Varian EM360, B01.4 T, f060 MHz) and
in a 7.05 T superconducting magnet (Bruker 300 MHz, 54 mm
warm bore, B07.05 T, f0300 MHz).
A. Resolution with the single channel probes
In Fig. 5, we report the results of experiments performed
with the probe C (see Table I). The experiments are performed
with an excitation pulse length of 35 µs and a repetition time
of 50 ms. The measured signals are acquired and averaged in
groups of 20 (i.e., a total time of 1 s for a single measurement).
The pulse length of 35 µs maximizes the steady state signal
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-7
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FIG. 5. Measurements with the single channel probe (see Fig. 2 and probe C in
Table I). The measurements are performed in a 7.05 T superconducting magnet
(Bruker 300 MHz, 54 mm warm bore, B07.05 T, f0300 MHz) with a 40 µl
sample of distilled water. Experimental settings: pulse length: 35 µs, repetition
time: 0.05 s, number of averagings: 20, averaging time: 1 s (see more details in
Table I). (a) NMR frequency measurements (red) and frequency measurements
performed using an RF generator (Anritsu MG3633A) as signal source (blue). The
results of the measurements are expressed as deviation (in ppb) from the initial
value set to zero. (b) Progressive standard deviation of the data shown in (a). The
black dashed line in (a) and (b) indicates the 300 s time interval used to compute
the resolution values reported in Table I.
amplitude at the pulse repetition time of 50 ms (i.e., the mag-
netometer is operated in the Ernst angle47 conditions). With
these parameters, the corresponding signal amplitude at the
input of the analog-to-digital converter is about 1 V with a
noise spectral density of 8.5 µV/Hz1/2 for all the probe heads
and samples. The sampling frequency is fixed at 650 kHz. The
resonance frequency (and, hence, the magnetic field value) is
obtained by digital signal processing of the acquired signal
(see details in Appendix A). All standard deviations reported
in Table I refer to a set of 300 successive measurements, each
with an averaging time of 1 s, obtained in a total measuring
time of 5 min. The standard deviation is expressed in Hz, in T,
and in parts per billion (ppb) with respect to the abso-
lute value of the magnetic field (and the Larmor frequency).
Table I shows a comparison between the standard deviation
experimentally obtained and those expected from CRLB limit
(Appendix A). For all measurements performed in the 7.05 T
superconducting magnet, the measured standard deviation of
the frequency in the conditions reported above is about 0.2 Hz
(0.7 ppb). Hence, as shown in Table I, the measured standard
deviations are one to three orders of magnitude larger than
CRLB limit.
In order to elucidate the origin of discrepancy between
the measured magnetic field resolution and the value expected
from the Cramer-Rao lower bound, we investigated the two
possible sources of frequency noise within the electronics of
the magnetometer. In order to investigate the frequency noise
originating from the analog-to-digital conversion (ADC) and
subsequent digital signal processing, we acquired a 50 mV
sinusoidal signal at 50 kHz generated by an arbitrary wave-
form generator (HP 33120A) and measured its frequency in
conditions identical to the one used to acquire and process
the NMR signals (i.e., repetition time: 50 ms, number of aver-
ages: 20, averaging time: 1 s, number of measurements: 300,
measurement time: 300 s, matched filter: 1 ms). The mea-
sured total standard deviation of the frequency due to the
waveform generator, the ADC, and the signal processing is
lower than 0.002 Hz (i.e., more than two orders of magni-
tude lower than the measured standard deviation reported in
Table I).
In order to measure the frequency noise due to the analog
part of the magnetometer, we used an external RF generator
(Anritsu MG3633A) to induce, with an inductor placed in prox-
imity of the detection coil, an artificial NMR signal into the
probe head. The RF generator output was adjusted in order to
produce a signal having the same amplitude as the NMR sig-
nal. Also in this case, we performed the experiment in the same
conditions as for the NMR measurements (i.e., repetition time:
50 ms, number of averages: 20, averaging time: 1 s, number of
measurements: 300, measurement time: 300 s, matched fil-
ter: 1 ms). The measured standard deviation of the frequency
is 0.025 ppb (0.004 Hz). Figure 5(a) shows a direct compari-
son between the measurement of the NMR frequency into the
7.05 T magnetic field and the measurement of the frequency of
the artificial NMR signal produced by the external RF genera-
tor. The standard deviation obtained with the artificial NMR
signal is almost two orders of magnitude lower than the one
measured with the real NMR signal. These results indicate that
the equivalent magnetic field noise introduced by the mag-
netometer electronics has negligible impact on the measured
magnetic field resolution. In other words, the standard devi-
ations of the measured resonance frequencies and magnetic
fields values reported in Table I are presumably dominated
by magnetic field fluctuations, with a negligible contribution
from the electronic noise of the magnetometer, as observed
also in previous studies.3,5,48
As shown in Fig. 5(b), the standard deviation of the fre-
quency depends on the total measurement time considered.
All measurement results reported in Table I are performed
with a total measurement time of 300 s. Figure 5(b) shows
the progressive standard deviation of the two data series.
For the real NMR signals, the standard deviation increases
from 0.7 ppb for a measurement time of 300 s to 3.5 ppb
for a measurement time of 12 h. For the artificial NMR
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signal, it increases from 0.025 ppb in 300 s to 0.2 ppb
in 12 h.
B. Resolution with the two channels probe
As shown in Table I, the standard deviation of the mea-
sured resonance frequencies are one to three order of mag-
nitude larger than the CRLB limit (Appendix A). In order to
elucidate the origin of this discrepancy, we implemented a
two channels probe, with the aim to measure simultaneously
the resonance frequency in two spatial locations very close to
each other (about 1.5 mm in the magnet bore of 54 mm). With
this approach, we aim to demonstrate, in a more direct fashion
than the one described above, that the main contribution to
the standard deviation in the measured resonance frequencies
is effectively due to magnetic field fluctuations. The use of two
samples measured simultaneously allows us to decouple the
contributions of magnetic field fluctuations and RF frequency
instabilities, common in the two channels, from the intrinsic
thermal noise sources within each single chip receiver, which
are uncorrelated. Similar differential measurements have been
reported also in Ref. 3.
The two-channel probe employs two samples of 300 nl
of distilled water (Fig. 3 and probe E in Table I). Thanks to the
small size of the coils, excitation pulses of 6 µs are sufficient to
maximize the NMR signal for a pulse repetition time of 200 ms,
thus allowing for relatively high IF frequencies (larger than the
1/fnoise corner frequency of about 20 kHz) and negligible off-
resonance effects using a single RF generator. The measured
noise spectral density is 70 µV/Hz1/2. Hence, the CRLB limit
[Eq. (A3) in Appendix A] is 0.005 Hz (0.016 ppb).
The measured standard deviation of the frequency of the
RF generator is 0.006 Hz (measured with the same parame-
ters as for the NMR measurements, i.e., repetition time: 0.2 s,
number of averagings: 5, averaging time: 1 s, matched filter:
20 ms, measurements: 300, measurement time: 300 s). This
means that the standard deviation on the resonance frequency
measurement due to the combined contributions of the CRLB
(0.005 Hz) and of the RF generator fluctuations (0.006 Hz) is
0.008 Hz (0.026 ppb), which represents the instrumental reso-
lution limit for each of the two channels of the probe described
in this section.
Figure 6(a) shows the time domain NMR signal (I and Q)
of a single channel before exponential match filtering. The
signal amplitude of about 1 V decays with a relaxation time
T∗
220 ms. Figure 6(b) shows the real and imaginary parts of
the FFT, whose module is used to measure the magnetic field.
In Fig. 6(c), we show a series of 300 measurements with 1 s
averaging time per measurement plotted as deviation from
the mean values. The standard deviation of the resonance
frequency value for a single channel (red and blue data) is
of about 0.16 Hz (0.5 ppb). This value is about twenty times
larger than the instrumental resolution limit. The standard
deviation of the difference between the measured resonance
frequencies of the two probes [Fig. 6(c), black data] is about
0.024 Hz (0.08 ppb). Since the RF generator frequency fluctu-
ations are common to both channels and the CRLB is increased
FIG. 6. Measurements with the two channels probe (see Fig. 3 and probe E in
Table I). The measurements are performed in a 7.05 T superconducting magnet
(Bruker 300 MHz, 54 mm warm bore, B07.05 T, f0300 MHz) with a 300 nl
sample of distilled water. Experimental settings: pulse length: 6 µs, repetition time:
0.2 s, number of averagings: 5, averaging time: 1 s (see more details in Table I).
(a) Time domain complex NMR experimental signal (I: blue; Q: red). (b) FFT of
the complex experimental NMR signal (real: blue, imaginary: red). (c) Frequency
deviation from frequency average for the channel 1 (blue) and channel 2 (red),
and difference ∆among the two channels (black) resulting from a 5 min series of
magnetic field measurements.
by √2, the instrumental limit is about 0.007 Hz, which is
about a factor of three smaller than the measured value.
The origin of this significantly reduced but still not entirely
negligible difference with respect to the CRLB limit is unclear,
and it might deserve to be investigated in more detail in the
future. We speculate that this residual discrepancy might be
caused by magnetic field fluctuations which cannot be con-
sidered spatially uniform even at the scale of a few mm (i.e.,
at the distance between the two probes), as discussed also
in Ref. 3. In Ref. 3, the measurements were performed with
two probes separated by about 12 mm in a human MRI mag-
net, i.e., with a distance between the probes and a bore size
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scaled up by about one order of magnitude with respect to our
conditions.
As mentioned above, the two-channel probe employs two
samples of 300 nl of distilled water. Despite the small sample
volume, the instrument resolution of 0.008 Hz in 1 s averag-
ing time is more than one order of magnitude better than the
measured fluctuations. This suggest that, although efforts in
the improvement of the signal-to-noise ratio (e.g., by means
of larger samples, electronics with lower noise, and more effi-
cient coils) improves the CRLB limit, these efforts might not
be justified in the presence of intrinsic field fluctuations of
the magnetic field under study. This means that one could use
smaller samples with no effective reduction in the magnetic
field resolution, with advantages in terms of spatial resolu-
tion and field gradient tolerance. As a practical example, we
have shown here that the use of a 300 nl water sample (and
also of a 100 pl water sample, see probe F in Table I and the
detailed description below) is sufficient to achieve a magnetic
field resolution well beyond the magnetic field fluctuations of
our 7.05 T superconducting magnet (Bruker 300 MHz, 54 mm
warm bore, B07.05 T, f0300 MHz).
FIG. 7. Measurements with the single channel fully integrated probe (see Fig. 4 and
probe F in Table I). The measurements are performed in a 7.05 Tsuperconducting
magnet (Bruker 300 MHz, 54 mm warm bore, B07.05 T, f0300 MHz) with
a 100 pl sample of distilled water. Experimental settings: pulse length: 2.5 µs,
repetition time: 0.2 s, number of averagings: 5, averaging time: 1 s (see more
details in Table I). (a) NMR spectrum. (b) Monitoring of the magnetic field over
50 h.
C. Resolution with the fully integrated miniaturized
single channel probe
Figure 7(a) shows the NMR spectrum of a 100 pl of H2O
obtained with the fully integrated single-channel probe (probe
FinTable I) at best shimming conditions. With a spectral res-
olution of 3 Hz (0.01 ppb), the resulting SNR corresponds to a
CRLB limited resolution of 0.036 Hz (0.4 ppb) in 1 s averaging
time at 7.05 T. As for the other probes described above and
reported in Table I, the measured resolution is significantly
worse than the CRLB value. For this fully integrated probe, the
discrepancy between the measured standard deviation and
the CRLB limit is about a factor of five, i.e., significantly smaller
than for the other probes. As shown in Table I, all probes
measured in the 7.05 T superconducting magnet have stan-
dard deviations which differ by less than a factor of two (from
0.13 Hz to 0.2 Hz), further corroborating the hypothesis that
the main source of noise comes from the magnetic field itself.
Hence, despite the drastically smaller sample volume (three
to five orders of magnitude) and the absence of tuning and
matching networks, the broadband fully integrated probe is
capable to measure the field produced by the 7.05 T supercon-
ducting magnet under investigation with the same effective
magnetic field resolution. Figure 7(b) shows the monitoring of
the magnetic field for a period of 50 h using the fully integrated
probe (probe F). The standard deviation of the frequency is
appreciably smaller during the two nights (centered at about
15 h and 39 h after the beginning of the measurements). The
overall change of the frequency is about 20 ppb over the 50 h
of measurements (a variation similar to the 12 ppm over 12 h
shown in Fig. 5).
V. CONCLUSIONS
In this work, we have shown that broadband CMOS
single-chip transceivers are valid and versatile tools to assist
the manufacturing of NMR probes aimed for high field high
resolution high accuracy magnetometry. The use of CMOS
transceivers to implement NMR probes for high field mag-
netometry is trade-off free in terms of performance, and it
offers technology-related practical advantages. One practi-
cal advantage is the reduced size of the overall electronics
needed and the consequent replacement of numerous com-
ponents in proximity of the probe head. Due to the small size
of the single-chip integrated transceiver and to its low power
consumption, the introduced field and temperature-related
distortions are reduced and thus expected to be advanta-
geous also for eventual high accuracy measurements (see
Appendix B). A second advantage concerns the costs in the
long term, reduced by both materials costs and man power
needed to implement each probe: a procedure consider-
ably simplified since a single chip can be used to cover the
whole high field range from 25 mT to 25 T (the single-chip
transceiver has 3 dB bandwidth of 1 MHz–300 MHz), but it
is usable up to 1 GHz with a degradation in the noise figure
of less that 3 dB. Finally, the use of single-chip transceivers
is certainly expected to ease the implementation of arrays
of probes (we show an example of a compact two channels
probe), currently used to map MRI magnets, and under study
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for the monitoring of MRI field gradients.4As extensively dis-
cussed in this work (and in previous ones3,5), the magne-
tometers reported here (including the one based on a fully
integrated broadband probe having a sample volume of only
100 pl) achieve instrumental CRLB limited magnetic field res-
olutions which are one to three orders of magnitude better
than the magnetic field fluctuations of the magnetic fields
investigated.
ACKNOWLEDGMENTS
This work has been supported by the Commission for
Technology and Innovation (CTI/KTI, Switzerland, Grant Nos.
14057.1 and 18505.1).
APPENDIX A: RESOLUTION
The time-domain complex signal s(t) including the NMR
signal and the noise can be written as
sI(t)=s0cos(2πf0t+φ)exp−t/T∗
2+nI(t),
sQ(t)=s0sin(2πf0t+φ)exp−t/T∗
2+nQ(t), (A1)
where s0is the NMR signal amplitude at t= 0 (in V), T∗
2is the
effective transversal relaxation time (in s), and ni(t) is the noise
(in V). For an exponentially damped sinusoidal signal embed-
ded in a Gaussian noise, the minimum standard deviation in
the frequency estimation (in Hz) is given by the Cramer-Rao
lower bound (CRLB),15,25,49 which can be written as
fmin = 1
T∗
2!3/21
(s0/N)q8(1−e−2x)
2πq(1−e−2x)−4x2e−2x
, (A2)
where x=T/T∗
2,Tis the acquisition time (in s), and Nis
the noise voltage spectral density (in V/Hz1/2). The signal-to-
noise ratio SNR = (s0/N) is expressed in Hz1/2. If each estima-
tion of the resonance frequency is obtained from the average
of Navg acquisitions, the standard deviation in the frequency
estimation is
fmin,avg =
fmin
qNavg
. (A3)
For TT∗
2, we have
fmin,avg (∆f)3/2
(s0/N)
1
qNavg
, (A4)
where ∆f=2/πT∗
2is the full width at half maximum of the
Lorentzian peak when a time-domain matched filter is applied
[i.e., the signal s(t) is multiplied by exp (−t/T∗
2)]. The magnetic
field resolution (in T) can be defined as Bmin = (2π/γ)fmin.
Several algorithms can be used to extract the Larmor fre-
quency f0from the NMR signal with noise s(t) in Eq. (A1). In
the following, we briefly describe the three algorithms that
we used, implemented in LabView or MatLab™. For all meth-
ods, the acquired time domain signal is digitally multiplied
by the match filter function exp(−t/T∗
2). In the first method,
the frequency is obtained by complex fast Fourier trans-
form (FFT) followed by frequency peak position determination
(using the peak-finder function in LabView) applied on the
magnitude of the FFT. In the second method, the frequency
is extracted computing the phase (i.e., arctan(sI(t)/sQ(t)),
unwrapping the obtained phase (using the unwrap-phase
function in LabView), and fitting the unwrapped phase for a
time of a few T∗
2(using the linear-fit function in LabView). This
approach is identical to those described in Refs. 15 and 25.
The third method uses the complex FFT algorithm followed
by a Lorenztian fit, both implemented in MatLab. We tested
the three algorithms on artificial NMR signals with Gaussian
noise as well as on the experimentally acquired NMR sig-
nals. When applied on artificial NMR signals with Gaussian
noise, the three algorithms gives standard deviations of the
resonance frequency which differs by less than a factor of
two from the Cramer-Rao lower bound given by Eq. (A2). As
an example, Fig. 8 shows a comparison between the resolu-
tion values obtained from Eq. (A2) and the resolution values
obtained from the Lorentzian fit. When the three algorithms
FIG. 8. Comparison between the resolution values obtained with numerical simu-
lations and the Cramer-Rao theoretical values obtained from Eq. (A2). For each
value of the independent variable [either the signal-to-noise ratio (SNR) or the
effective transversal relaxation time T∗
2, see below], we generate 1000 artificial
NMR signals as in Eq. (A1), all with the same frequency but with uncorrelated ini-
tial phase and uncorrelated Gaussian noise. The simulation results are processed
with a time-domain matched filter (i.e., multiplication by exp(−t/T∗
2)), followed by
a complex FFT algorithm, and finally by a frequency-domain Lorentzian function
fitting (all using MatLab). The Lorentzian function fitting extract 1000 frequency
values. The resolution (in Hz) is defined as the standard deviation of the 1000
extracted frequency values. (a) Dependence of the resolution on the SNR = s0/N,
with the following parameter: T∗
2= 0.02 s, T=2s,andNavg = 1. (b) Dependence
of the resolution on T∗
2, with the following parameters: SNR = 106Hz1/2,T= 2 s,
and Navg = 1.
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are applied on the experimentally measured signals, they give
very similar standard deviations on the resonance frequency
estimation, but their values are significantly larger than the
one obtained on the artificial signals. As discussed in Sec. IV,
this is presumably due to fluctuations of the magnetic field
under investigation.
APPENDIX B: ABSOLUTE ACCURACY
The absolute accuracy of an NMR magnetometer is ulti-
mately limited by the uncertainty in the gyromagnetic ratio
value of the nucleus used. The gyromagnetic ratio of the
1H nucleus is given by (γ/2π) = 42.577 47892(29) MHz/T,
which corresponds to a relative standard uncertainty of about
7 ppb.36 In principle, the accuracy in the value of the frequency
of the RF source is also a potential limiting factor. However,
it is nowadays possible to obtain frequency references hav-
ing an absolute accuracy well beyond the uncertainty of the
gyromagnetic ratio value.
Since the use of bare 1H nuclei is very unpractical, the
1H nuclei in a spherical sample of water at 25 ◦C is com-
monly used for high accuracy NMR magnetometry.36,50 The
magnetic shielding correction for the 1H nucleus in water is
σ0= 25.691(11) ×10−6, giving a shielded gyromagnetic ratio
of (γ0/2π) = 42.576 38507(53) MHz/T, which corresponds to
a relative standard uncertainty of about 13 ppb.36 Recently,
a slightly smaller shielding correction σ0= 25.680(2.5) ×10−6
has been reported50 but not yet considered in the list of
the fundamental physical constants (CODATA).36 The tem-
perature dependence of the shielding correction is −10.36(30)
×10−9◦C−1from 5 ◦Cto45◦C.51
Beside water, several other samples have been used for
NMR magnetometry.3,5,12,15,16,18,20,37,38 (see Sec. I). As for
water, in these gaseous, liquid, or solid samples, the mag-
netic field at the nucleus is not identical to the external one
to be measured. Hence, the absolute accuracy is also lim-
ited by the uncertainty in the shielding parameter value of
the nucleus under investigation in the particular chemical
environment. With modern NMR spectrometers, the shield-
ing parameter can be determined with an absolute accuracy
better than 1 ppm.50 More macroscopically, the absolute accu-
racy is also limited by the uncertainties in the static magnetic
field distortions caused by the probe elements. Such distor-
tions depend on the susceptibility, shape, and orientation with
respect to the magnetic field of the sample itself and of the
nearby objects.9,16,52 In our probes, the main limitation to
the absolute accuracy is the lack of precise knowledge of the
susceptibilities values for the materials surrounding the sam-
ple volume and of the sample itself. The largest values for
the susceptibilities of ordinary diamagnetic and paramagnetic
materials44,53 are about 10−5, which would determine a maxi-
mum field distortions of about 10 ppm. Consequently, a rather
pessimistic estimation of the absolute accuracy of the NMR
magnetometers reported in this work would be 10 ppm. An
absolute accuracy better than 10 ppm is of crucial importance
in fundamental physics studies,8but it is not strictly necessary
in most of the other applications of NMR magnetometers.
REFERENCES
1N. De Zanche, C. Barmet, J. A. Nordmeyer-Massner, and K. P. Pruessmann,
Magn. Reson. Med. 60, 176 (2008).
2P. Sipil¨
a, D. Lange, S. Lechner, W. L¨
ow, P. Gross, M. Baller, G. Wachutka,
and F. Wiesinger, Sens. Actuators, A 145, 139 (2008).
3S. Gross, C. Barmet, B. E. Dietrich, D. O. Brunner, T. Schmid, and K. P.
Pruessmann, Nat. Commun. 7, 13702 (2016).
4B. E. Dietrich, D. O. Brunner, B. J. Wilm, C. Barmet, and K. P. Pruessmann,
IEEE Trans. Med. Imaging 35, 1452 (2016).
5S. Bollmann, L. Kasper, S. J. Vannesjo, A. O. Diaconescu, B. E. Dietrich,
S. Gross, K. E. Stephan, and K. P. Pruessmann, NeuroImage 154, 92 (2017).
6Y.-H. Chu, Y.-C. Hsu, and F.-H. Lin, Sci. Rep. 7, 11630 (2017).
7H. Han, R. P. MacGregor, and B. J. Balcom, J. Magn. Reson. 201, 212
(2009).
8R. Prigl, U. Haeberlen, K. Jungmann, G. Zu Putlitz, and P. Von Walter, Nucl.
Instrum. Methods Phys. Res., Sect. A 374, 118 (1996).
9X. Fei, V. Hughes, and R. Prigl, Nucl. Instrum. Methods Phys. Res., Sect. A
394, 349 (1997).
10R. Yamada, S. Hansen, T. Kiper, J. Lofgren, T. Regan, R. Smith, and G. Boero,
in 2002 IEEE Nuclear Science Symposium Conference Record (IEEE, 2002),
Vol. 1, pp. 590–594.
11I. Bolshakova, R. Holyaka, V. Erashok, and M. Kumada, IEEE Trans Appl.
Supercond. 14, 1818 (2004).
12J. Flowers, B. Petley, and M. Richards, Metrologia 30, 75 (1993).
13G. Boero, C. de Raad Iseli, P. Besse, and R. Popovic, Sens. Actuators, A 67,
18 (1998).
14G. Boero, J. Frounchi, B. Furrer, P.-A. Besse, and R. Popovic, Rev. Sci.
Instrum. 72, 2764 (2001).
15A. Nikiel, P. Bl ¨
umler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. M.
Schreiber, and M. Terekhov, Eur. Phys. J. D 68, 330 (2014).
16A. Maul, P. Bl ¨
umler, W. Heil, A. Nikiel, E. Otten, A. Petrich, and T. Schmidt,
Rev. Sci. Instrum. 87, 015103 (2016).
17T. Maly, J. Bryant, D. Ruben, and R. G. Griffin, J. Magn. Reson. 183, 303
(2006).
18P. Sipil ¨
a, S. Greding, G. Wachutka, and F. Wiesinger, Magn. Reson. Med.
65, 1498 (2011).
19J. Y. Jang, J. H. Han, C. Kim, Y. J. Hwang, S. Hahn, M. C. Ahn, and S. Lee,
IEEE Trans Appl. Supercond. 28, 9001005 (2018).
20K. Borer and G. Fr ´
emont, Nucl. Instrum. Methods 154, 61 (1978).
21C. Schott, R. Popovic, S. Alberti, and M. Tran, Rev. Sci. Instrum. 70, 2703
(1999).
22K. Weyand, IEEE Trans. Instrum. Meas. 48, 668 (1999).
23S. Beguˇ
s and D. Fefer, Meas. Sci. Technol. 18, 901 (2007).
24H. Liu, H. Dong, Z. Liu, and J. Ge, Instrum. Exp. Tech. 61, 55 (2018).
25C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney,
M. Burghoff, W. Kilian, S. Knappe-Gr¨
uneberg et al.,Eur. Phys. J. D 57, 303
(2010).
26N. Kernevez and H. Glenat, IEEE Trans. Magn. 27, 5402 (1991).
27C. G. Kim, K. S. Ryu, B. C. Woo, and C. S. Kim, IEEE Trans. Magn. 29, 3198
(1993).
28B. Woo, C. Kim, P. G. Park, C. Kim, and V. Shifrin, IEEE Trans. Magn. 33,
4345 (1997).
29J. Pendlebury, K. Smith, P. Unsworth, G. Greene, and W. Mampe, Rev. Sci.
Instrum. 50, 535 (1979).
30M. Ulvr and J. Kupec, IEEE Trans. Instrum. Meas. 67, 204 (2018).
31J. H. Shim, S.-J. Lee, S.-m. Hwang, K. K. Yu, and K. Kim, Metrologia 52, 496
(2015).
32H. Aman and T. Plakhotnik, J. Opt. Soc. Am. B 33, B19 (2016).
33V. Acosta, E. Bauch, M. Ledbetter, C. Santori, K.-M. Fu, P. Barclay,
R. Beausoleil, H. Linget, J. Roch, F. Treussart et al.,Phys. Rev. B 80, 115202
(2009).
34Z. D. Gruji ´
c, P. A. Koss, G. Bison, and A. Weis, Eur. Phys. J. D 69, 135
(2015).
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-12
Published under license by AIP Publishing
Review of
Scientific Instruments ARTICLE scitation.org/journal/rsi
35F. Allmendinger, P. Bl ¨
umler, M. Doll, O. Grasdijk, W. Heil, K. Jungmann,
S. Karpuk, H.-J. Krause, A. Offenh¨
ausser, M. Repetto, U. Schmidt, Y. Sobolev,
K. Tullney, L. Willmann, and S. Zimmer, Eur. Phys. J. D 71, 98 (2017).
36P. J. Mohr, D. B. Newell, and B. N. Taylor, J. Phys. Chem. Ref. Data 45,
043102 (2016).
37S. Un, J. Bryant, and R. Griffin, J. Magn. Reson. 101, 92 (1993).
38V. Borovikov, M. Fedurin, G. Karpov, D. Korshunov, E. Kuper, M. Kuzin,
V. Mamkin, A. Medvedko, N. Mezentsev, V. Repkov et al.,Nucl. Instrum.
Methods Phys. Res., Sect. A 467, 198 (2001).
39M. Grisi, G. Gualco, and G. Boero, Rev. Sci. Instrum. 86, 044703 (2015).
40N. Sun, Y. Liu, H. Lee, R. Weissleder, and D. Ham, IEEE J. Solid-State
Circuits 44, 1629 (2009).
41D. Ha, J. Paulsen, N. Sun, Y.-Q. Song, and D. Ham, Proc. Natl. Acad. Sci.
U. S. A. 111, 11955 (2014).
42J. Yuan and C. Svensson, IEEE J. Solid-State Circuits 24, 62 (1989).
43B. Razavi and R. Behzad, RF Microelectronics (Prentice Hall New Jersey,
1998), Vol. 2.
44M. C. Wapler, J. Leupold, I. Dragonu, D. von Elverfeld, M. Zaitsev, and
U. Wallrabe, J. Magn. Reson. 242, 233 (2014).
45M. Grisi, F. Vincent, B. Volpe, R. Guidetti, N. Harris, A. Beck, and G. Boero,
Sci. Rep. 7, 44670 (2017).
46E. Montinaro, M. Grisi, M. Letizia, L. Peth ¨
o, M. Gijs, R. Guidetti, J. Michler,
J. Brugger, and G. Boero, PLoS One 13, e0192780 (2018).
47R. R. Ernst and W. A. Anderson, Rev. Sci. Instrum. 37, 93 (1966).
48J. W. Britton, J. Bohnet, B. Sawyer, H. Uys, M. Biercuk, and J. Bollinger,
Phys. Rev. A 93, 062511 (2016).
49H. Yan, K. Li, R. Khatiwada, E. Smith, W. Snow, C. Fu, P.-H. Chu, H. Gao,
and W. Zheng, Commun. Comput. Phys. 15, 1343 (2014).
50Y. I. Neronov and N. Seregin, Metrologia 51, 54 (2014).
51B. Petley and R. Donaldson, Metrologia 20, 81 (1984).
52E. Growney, G. Friedman, and R. Gerald, J. Appl. Phys. 85, 5205
(1999).
53W. Haynes, CRC Handbook of Chemistry and Physics (CRC Press,
2013), p. 4.
Rev. Sci. Instrum. 90, 015001 (2019); doi: 10.1063/1.5066436 90, 015001-13
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