LOW-DRIFT BROADBAND DIRECTLY COUPLED DC SQUID READ-OUT ELECTRONICS
N. Oukhanski, R. Stolz, V. Zakosarenko, and
H.-G. Meyer.
Institute
for Physical High Technology, Department of Cryoelectronics,
Winzerlaer Str. 10, D-07745 Jena, Germany
Abstract A low drift directly coupled read-out electronics with broad band for
dc superconducting quantum interference devices (dc SQUIDs) is presented. The
electronics has a white noise level referred to the input of about
0.33 nV/Hz1/2 and a corner frequency for the 1/f noise as low as 0.1 Hz. The
electronics was tested with several types of low-Tc dc-SQUIDs. The maximum
bandwidth of 6 MHz and the slew rate of about 3 MF0/s was measured for systems
with SQUIDs. As an example, a SQUID magnetometer with this type of electronics
had a white flux-noise level of 1.7 mF0/Hz1/2 and
magnetic field noise level of 1.4 fT/Hz1/2. For the SQUID
gradiometer these values are 5.3 mF0/Hz1/2 and the
magnetic gradient noise level 38 fT/(Hz1/2 m) correspondingly.
Maximum system dynamic range of 155 dB (± 50 F0) and 150 dB (±100 F0) was achieved at the white
noise frequency region for the SQUID magnetometer and gradiometer,
respectively.
1.
Introduction
The
use of directly coupled technique for the dc SQUID electronics provides
significant advantages for high-sensitive measurements in unshielded
environment due to the relatively high system slew rate, bandwidth and dynamic
range [1 - 4]. Besides, such electronics usually is more compact and less
expensive in production due to a relative simplicity compared to standard
read-out electronics with flux modulation. The working principles of directly
coupled read-out electronics are described more in detail in [4].
By
system development the special attention was focused on a thermal drift and a corner
frequency of 1/f noise (fa) of the electronics as
most relevant parameters for realization of long-time experiments.
In this paper, we present low-drift directly coupled read-out electronics
capable to work over a very wide temperature range from 77 K up to 350 K. This was possible by using high-symmetrical differential
circuitry solution. An input white noise level
of about 0.33 nV/Hz1/2 and the
corner frequency for the 1/f noise
is as low as 0.1 Hz were achieved with a special
designed preamplifier. The measured input thermal
drift is lower than 30 nV/K in a temperature range from 15 °C up to 80 °C. The SQUID
electronics was tested with two low-transition temperature SQUID
sensors. In the flux-locked-loop (FLL) mode this read-out
electronics allows to work with maximum small-signal bandwidth of about
6 MHz.
Often it is necessary to ensure a stable work of the SQUID system
at rather large distances between the SQUID sensor and the read-out
electronics. For instance, the presence of magnetic or conductive materials
nearby the SQUID gradiometer results in a decrease of its balance factor [5]. The new electronics provides sufficient slew rate and
sensitivity to use the sensors unshielded even at cable lengths between the
sensor and electronics of about 1 – 2 m.
2.
The concept of the Read-Out Electronics
|
Fig. 1. The functional diagram of the read-out electronics with SQUID. |
The
important feature of our new SQUID electronics is the very wide working
temperature range from 77 K up
to 350 K. The measured thermal
drift of the new electronics scheme is as low as about 30 nV/K in the temperature range from 15 °C up to 80 °C. The
measurements were performed at the shorted amplifier input. The amplifier was
placed in a metal box with overall dimensions of 110 mm ´ 60 mm ´ 30 mm. Temperature was
maintained by the external heater and was measured with a semiconductor
thermometer inside the box. Mainly this temperature performance was possible
because of the use of high-symmetrical differential circuitry solutions for all
blocks and parts of the FLL-unit (preamplifier as well as integrator and
buffers). First it was simulated using the software tool of MicroSim-PSpice [6]
and then designed for operation in the temperature range from 77 K up to 350 K.
The functional diagram of the read-out electronics
is shown in Fig. 1. The FLL-unit is directly coupled to a SQUID via three
twisted pairs of Cu wire of 1.2 m length. The FLL-unit provides several
basic functions to the user. It amplifies the SQUID voltage deviations, integrates
it (CINT and RINT) and in FLL mode couples
the output current to the feedback coil through the feedback resistors RFB1,2, compensating the
external flux change in the SQUID. Thus the voltage at the output of the FLL
unit is proportional to the magnetic flux in the SQUID. A FLL / Reset
switch disconnects in the reset mode the feedback resistors and reduces the system
amplification to about 10,000.
|
Fig. 2. The view of FLL unit board. |
Maximum
gain-bandwidth product fGBP
for the FLL-unit is about of 400 MHz. To provide stable work of the system
in FLL-mode a simple RINTCINT integrator decreases the
gain-bandwidth product. It is directly connected to the output of the FLL
second stage, which works as a symmetric current source. The values of RINT and CINT determine bandwidth and slew rate of the system.
For our case the system has the maximum stability at fGBP of about 80 MHz. In this case the amplifier
behaves in the reset mode like a low pass filter with 3-dB bandwidth of about
4 kHz with a slope of about 3.3 dB per octave.
Another
important feature is the opportunity to connect the FLL-unit to a grounded as
well as to a ground-free SQUID sensor. For this reason all signal sources
necessary for the SQUID operation are made as differential current sources. The
current noise of each differential current source does not exceed
1.5 pA/Hz1/2. Even the possibility to work with a three-point
SQUID biasing [1] is provided by the scheme (not shown in the Fig. 1) to
reduce the drift caused by change of the wire resistance between SQUID and
FLL-unit with temperature. This leads to a wider range of applications of our
new SQUID electronics.
The
electronics PC-board has dimensions of 69 mm x 24 mm (see picture in
Fig. 2). The FLL unit power consumption is 80 mW from ± 1.5 V power supply.
3.
The Amplifier Noise Performance
The principles described in [2, 7] were used for the
construction of the preamplifiers input stage. This allows us to achieve the
maximum level of system sensitivity in the wide spread of temperatures ranging
from 77 K to 350 K. The matched bipolar transistors from Analog
Devices (MAT02, MAT03, etc.) are used in the preamplifier stage. In this
article we will focus only on the data for the read-out electronics measured at
the room temperature.
For
the analysis of the noise contribution of the input stage we can use the model
(see Fig. 3) of an idealized amplifier connected to the signal source with
an ideal dynamic resistance R and a
voltage noise spectral density SVR
= 4 kBTeff R. Where Teff is the source effective temperature, and kB = 1.38´10 -23 J/K is Boltzman
constant. The amplifier has an ideal input resistance RIN, a gain G(f), and sources of voltage and current
noise at the input with the spectral density SV and SI
, respectively. Using abbreviation N
= RIN
/ (RIN+R), the total noise spectral
density of the external source and amplifier, reduced to the input can be
written as:
|
Fig. 3. Model of an idealized amplifier direct-coupled to the input source with resistance R. |
SVIN = (SVR1/2N)2+(SV1/2N)2+(SI1/2RN)2 . (1)
In
the equation (1) we assume that sources SV1/2
and SI1/2 are
uncorrelated. Then the voltage-noise
spectral density on the output of amplifier is:
SVOUT= G2N2 (SVR
+ SV + SI R2)
. (2)
With
shorted input (R = 0) the equation (2)
is reduced to:
SVOUT = G2 SV , (3)
which is
convenient for experimental determination of SV.
For
determination of current noise SI1/2
the measurements should be performed with R
¹ 0. Then from equation (2) we can obtain
current noise spectral density as:
SI = (SVOUT
/ G2N2 - SVR - SV) / R2 . (4)
The
results of our measurements of SV
at R = 0 are presented in a Fig. 4. The measured
current noise according to our idealized amplifier model (Fig. 3) and
Eq. (4) is presented in Fig. 5. It is determined in the reset mode in
a frequency range from 0.1 Hz to about 20 kHz, where value of RIN is constant: RIN = 1.14 kOhm.
Summarizing the
results, the voltage and current white noise levels are about 0.33 nV/Hz1/2
and 6.5 pA/Hz1/2 with a 1/f
corner frequency of about 0.1 Hz and 10 Hz, respectively.
|
|
|
|
Comparing
the data shown in Fig. 4 and Fig. 5, the contribution of the current
noise (about of 30 pA/Hz1/2) at the frequency of 0.1 Hz is
comparable with Sv1/2(0.1 Hz)
= 0.47 nV/Hz1/2 of the amplifier only if the resistance of a
signal source connected to the input is more than 16 Ohm. The fundamental
Nyquist voltage noise of this resistance of 0.26 nV/Hz1/2 at 77
K is already comparable with this value. If the resistance of the signal source
is lower, we can neglect the amplifiers current noise starting with the
frequency of 0.1 Hz.
4.
Measurements with the SQUIDs
We
have tested our new read-out electronics with two types of low temperature
SQUID sensors. The first one was a magnetometer with a field-to-flux transfer
coefficient of 0.85 nT/F0, and the second one was a
gradiometer with gradient-to-flux transfer coefficient of 7.1 nT/(F0 m). The sensors are
described in details in [9].
In
the system set-up the length of the cable (twisted pairs of varnish-insulated
Cu wire) between the read-out electronics and SQUID sensor is 1.2 m and
1.8 m for magnetometer and gradiometer, respectively. The measurements are
carried out in three layers soft magnetic shielding. Spectra were measured with
a FFT spectrum analyzer HP-35670B for
frequencies below 50 kHz, and with a network analyzer HP-4396B for higher
frequencies.
The noise
spectrum for the SQUID magnetometer is shown in the Fig. 6. It has a white flux-noise level of
1.7 mF0/Hz1/2 which
corresponds to magnetic field of 1.4 fT/Hz1/2. Maximum voltage
swing of this SQUID was 78 µV
peak-to-peak. The increase of the
noise for frequencies lower than several kHz is caused by a not sufficient
magnetic screen factor of the three layers shielding in of our laboratory. As
it is visible from the spectrum, the system small-signal frequency bandwidth (f3dB) is about of 6 MHz
with a flatness of the response within the range of 2 dB. The slew rate of
the system with this sensor is equal to 3.3 MF0/s. The estimated maximum
system dynamic range (definition see in [10]) is about 155 dB.
|
Fig.7. Flux noise spectrum SF1/2 of SQUID gradiometer with sensitivity 7.1 nT/(F0 m) in three layers shielding. Maximum feedback range in FLL mode is ±100 F0. |
|
Fig. 6. Spectrum of flux in SQUID magnetometer with sensitivity 0.85 nT / F0 and corresponding magnetic field in three layers magnetic shielding. Maximum system feedback range in FLL mode is ±50 F0. |
In Fig. 7
the noise spectrum of the system with the SQUID gradiometer having voltage
swing of 45 µV is
presented. The white noise level of 5.3 mF0/Hz1/2 of the
SQUID corresponds to a field gradient of 38 fT/(Hz1/2 m).
The real value of the 1/f corner
frequency is not visible because of building vibrations in the frequency range
below 1 Hz. The slew rate for the system with this SQUID has a value of
about 1 MF0/s. This is apparently
caused by longer connection cables (1.8 m) and lower voltage swing in comparison with the system with the
magnetometer. The bandwidth of 5.9 MHz, and the dynamic range
of 150 dB are comparable with the values measured for magnetometer.
For the both cases the value of the slew rate remains constant to within 10%
over the whole frequency range, except for the limitation at low frequency
caused by the finite feedback range.
5.
summary
A
very sensitive and fast dc SQUID read-out electronics was presented. The low
thermal drift (30 nV/K) of the
electronics and the corner frequency of 1/f
noise (0.1 Hz) are useful for realization of long-time experiments.
High slew rate and sensitivity (0.33 nV/Hz1/2), wide bandwidth
(6 MHz) and system dynamic range achieved even with a long cable between the
sensor and electronics (about of 1 - 2 meters) well suited for high-precision
measurements at unshielded conditions.
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