between the two most used broadband NMR probes: the delay line probe .... general-purpose time-domain circuit simulator SPICE to the same purpose. To our ...
2011 Fifth International Conference on Sensing Technology
A simulation based comparative study of two broadband probes for NMR of magnetically ordered materials Jose F. M. L. Mariano Department of Physics University of Algarve 8100-545 Faro, Portugal Email: jmariano@ualg.pt
Mircea Rogalski Department of Physics Instituto Superior Tecnico ICEMS Lisbon, Portugal
Abstract- Nuclear Magnetic Resonance (NMR) is a valuable
II.
technique for the investigation of magnetically ordered materials. This
paper
presents
a
simulation
based
comparative
study
A.
between the two most used broadband NMR probes: the delay line probe, introduced by Lowe, Engelsberg and Whitson, and the
high-pass,
proposed
by
Panissod.
A practical approach
concerning the probe characteristics was done using SPICE.
Keywords- NMR probe, Broadband, Transmission line, High pass, Simulation, SPICE
I.
INTRODUCTION
Pulse nuclear magnetic resonance (NMR) spectroscopy is a powerful analytical technique which provides extensive chemical information about the composition and structure of unknown compounds. The physical principles of nuclear magnetism and NMR can be found, for example, in the classical text of Abragam [I]. The technique consists of the application of radio frequency (RF) pulses at the resonance frequency, to a tuned LC circuits containing the sample (probe), and the observation of the system response by monitoring the emf induced by the sample in the probe. Most nuclear resonance probes use resonant circuits, which can be tuned in a frequency bandwidth of a few hundred kilohertz. Both the transmitter and the receiver section of the spectrometer have to be tuned to this frequency for the sake of RF field strength and signal-to-noise ratio [2]. However, a variety of applications require the use of broadband probes capable of wideband operation, namely, the automated acquisition of broad NMR lines in samples that are magnetically ordered [3]. Two kinds of designs of broadband probes are currently used in NMR of magnetic materials; the delay-line probe [4] and the high-pass probe [5]. The work described in this paper has driven by the need to decide which of the two designs should be chosen for the probe of a NMR for magnetically ordered materials built in our group. For that purpose we have perform electrical simulations using SPICE to compare the electrical characteristics of the two probes. lnstituto de Telecomunica,8es and Funda,iio para a Olinda e Tecnoiogia was supported part of this work.
978-1-4577-0167-2/11/$26.00©2011 IEEE
Octavian Postolache Instituto de Telecomunical;oes Av. Rovisco Pais, 1049-001 Lisboa, Portugal Email: opostolache@lx.it.pt
161
BROADBAND PROBES FOR
NMR
Delay Line Probe
The use of a transmission line probes in NMR was originally referred by Webb in 1962, applied to double resonance microwave spectrometer [6]. Later, in the mid 70's of last century, Lowe, Engelsberg and Whitson [4, 7] gave it a rigorous analytical treatment and discussed its application to NMR, introducing the concept of delay line probe. The subject was recently revisited by Kubo and Ichikawa [8], who have performed extensive numerical and experimental studies on these probes. This type of probe, although difficult to built, has become the standard in NMR of magnetically order materials, being used, for example, by Redi et al. in a home built scanning spectrometer over a range of 10 - 1000 MHz [3] and by Rosch et al. on a commercial NMR spectrometer adapted to the same purpose and operating from 10 MHz to 500 MHz [9]. Those probes can be constructed by connecting a discrete capacitor to every n turns of a wire coil, thus obtaining the so called lumped parameter delay line probe [7], or by partially surrounding the coil with a metal foil, in a configuration called distributed capacitance delay line probe [3]. Whatever the construction method is, the probe can be modeled by the circuit shown in Fig. I, consisting of a finite number of low-pass T sections,
each
capacitance C s
section =
with
inductance
Ls
C.
Figure 1.
Model circuit of a delay line probe.
=
L'/2
and
The probe is described by is image impedance 2 Z =Zo 1--2
Ri (O e
• +
(1)
'
-
Kulc sim
Kulc exp SPICE
I •
0.8
were Zo=�L'/C is the characteristic impedance of the probe, usually 50 0, and (Oe =2/.JL' C is a cut-off frequency, above witch no signal will propagate in the structure. B.
0.6
. . . 0. .
, . . .
0.4
High pass Probe
•
.
The high-pass probe, shown in Fig. 3, is a much easier to built alternative to the delay line probe. It was introduced by Panissod [5] and has been used, as far as we know, in at least one more NMR spectrometer for magnetically ordered materials [10]. It's based on a constant-k high pass filter terminated with is characteristic impedance Zo, usually 50 0. This type of filter is basically a LC T network which can be conveniently analyzed by the image parameter method. Its image impedance is [II].
R, V -;;?
where (O
e
the
characteristic
Zo= �2L/C
impedance
and
=1/.J2LC is a Iow a low cut-off frequency.
We have built one probe of this type. Fig. 2 shows a photograph of the implemented probe, evidencing its easiness of construction. III.
METHODOLOGY
VALTDATION
The delay line probe was extensively studied by Kubo and Ichikawa [8], who have performed intensive numerical calculations of the electrical characteristics of the probe using the method of moment for electromagnetic field and compared the results to measurements made on delay line probes of their c
c
� i�--��i i�--�-,
. . •
•
•
500
Ftequency (MHz)
1000
1500
Figure 4. Comparison between absolute reflection coefficient simulated (.) and measured (+) by Kubo and Ichikawa [KuIcI against our SPICE simulation (-),for a delay line probe with L = 100 nH,C = 6 pF and k = 0.08.
In order to validate our methodology, we began by simulating in SPICE one of the cylindrical delay line probes simulated in [8] with the structure of Fig. 2. We considered a 5 section structure and estimated the total inductance L = 5 L' = 100 nH based on construction details supplied by the authors. We use C = 6 pF and consider a weak coupling between sections (k = 0.08). The voltage at probe input and the current on the coil was calculated and from this the input impedance and the reflection coefficient was computed. Fig. 4 shows our results and the numerical and experimental results in [8]. As seen in Fig. 4, the SPICE simulation shows a better agreement with the experimental results, thus indicating that SPICE can be used to simulate the probes. IV.
SIMULATIONS RESULTS
For NMR of magnetically order materials, the main characteristics of the probe are input impedance, settling time and filed intensity inside the coil. To compare those characteristics between the two broadband probes we performed simulations using SPICE.
�( L T
Figure 2.
•
•
own construction. Our approach is to use the well-known general-purpose time-domain circuit simulator SPICE to the same purpose. To our knowledge, this is the first time SPICE has been used to simulate broadband probes.
(2)
Z=Zo I-
•
· •
High-pass design of the broadband probe.
Since the limiting factor in the construction of a NMR probe is the coil size, which in turn limits the inductance, we considered two coils, one with L 100 nH, similar to the one suited by Kubo and Ichikawa [8], and another L = 200 nH, similar to the one used by Panissod [5]. We considerer each one of this coils as being part of either a delay line structure (delay) or a high-pass structure (HP), thus obtaining four different probes to simulate. The relevant parameters of the four probes are shown in Table I. =
Figure 3.
Photograph of the implemented high-pass probe.
162
A.
Input impedance
Fig. 5 shows the simulated absolute input impedance l Z I as a function of frequency, for the four probes considered. Both structures exhibit a real and constant input impedance across their bandwidths, although the transition band is somewhat
L
Probe Type Delay Delay HP HP
C
(nH) 100 200 100 200
(pF)
Zo (Q) 58 50 50 52
6 16 80 150
flO
B.
(MHz) 919 398 40 20
100 90
§:
is[
Settling Time
Fig. 6 shows the simulated voltage output of the four probes in response to a step voltage input with 0.1 ns rise time. We considered the settling time to be the time need for the voltage at the probe's input to achieve ± 2 % of its final value. The delay line probe shows, for the same inductance, a settling time that is, typically, three times smaller than the high-pass probe (ta � 7 ns, tc � 30 ns, tb � 18 ns, td � 58 ns). It is then clear that the delay-line probe leads to a smaller dead time of the receiver, following the application of the high power pulses. However, this is not a determining factor in the choice of probe, because the typical time for the formation of an echo on a magnetic sample is in the order of I ]l s.
PARAMETERS OF THE SIMULATED PROBES
TABLE 1.
larger for the delay structure (3.5 octaves) than the high-pass structure (2.5 octaves). This is not an issue since we can, within certain limits, increase the cut-off frequency so that the bandwidth is as broad as needed.
22 --
80
20
70
18
60
16
50
�
I: \ ,: \ I \ I
30 -- delay 100nH
20
12
�
10
::J
U
8
�
6
""." HP 100nH 10
. _. _.
delay 200nH
4
- - - HP 200nH 0 6 10
10
·
Frequency Figure 5.
'0 10
� 0 L-�--�����--��-������==-'0 6 7 8 9 10 10 10 10 10 Frequency (Hz)
Simulated input impedance for the four probes.
Figure 7.
, .....
� I
I I
:;-
:::: -0.1
2:.
I
I
'J " I ,
,-- ,
Ie ...
,
'
I I I I ; I , I , , ; I I , I , , II
C.
Id
, ,
. , ,
-0.3
-
,
NIt ·
-0.2
,
, ---
-._-'
- ---
1
Intensity of the magnetic field inside the coil
Since, even at 1 GHz, the wavelength of the RF field (30 cm) is much higher than the length of the coil (approx. I cm),
+/2%
the near-field condition is verified and the magnetic field B inside the coil can be evaluated by integration of the Biot Savart law
dB
;I
-- delay 100nH """. delay 200nH
-I " -0.4 "
;1
._._.
10
20
30
Time
40 (ns)
50
60
=
f-io 4Jl'
idi x r ,3
(3)
over the length of the coil, were , is the distance from the
HP 100nH
- - - HP 200nH
-0.5
o
Current flowing through the coil vs. frequency,for the delay-line and high-pass structures.
Ib
I.
0.2
o
2
(Hz)
0.3
0.1
14
.s c
40
delay 200nH
. " ... HP 200nH
70
Figure 6. Step response of the four simulated probes. ta, th, t" and td are the settling times for probes delay 100 nH,delay 200 nH,HP 100 nH and HP 200 nH respectively.
163
center of the current carrying element dl to the observation point and i is the current on that element. Equation (3) shows
that, for the same coil geometry B depends only on i. So, in order to evaluate the intensity of the magnetic field inside the coil, one needs only to compute the current flowing through the coil.
For the simulation we have considered a 200 nH coil in both the delay-line and the high-pass structures and we adjusted the capacity so that both probes had their transmission bandwidths in the frequency range between 10 MHz and 1 GHz. Results of the current intensity as a function of frequency appear in Fig. 7. It is evident from the graph that the delay probe displays a more constant field strength over frequency, when compared with the delay-line probe. However, this is not a need in magnetic materials, as pointed out by Panissod [5], although very important in NMR of non magnetic materials. V.
CONCLUSIONS
In this paper we presented the results of a practical approach based on SPICE simulations on the study of two broadband probes for NMR of magnetically ordered materials. The usage of Spice in this kind of simulation provides results that compares well with numerical and experimental measurements previously reported [8]. Our results have showed that although the delay line probe performs better in terms of settling time and magnetic field strength over frequency, the easiness of building of the high pass probe, as shown in Fig. 2, largely overcome those features, making it the probe of choice to use in our locally built NMR spectrometer for magnetic materials. The experimental behavior of that probe used as NMR sensor will be reported elsewhere.
164
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[2]
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[3]
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[4]
T. J. Lowe and M. Engelsberg, "A fadst recoverypulsed nuclear magnetic resonance sample probe using a delat line," Rev. Sci. Tnstrum., vol. 45, no. 5,1974,pp. 631-639.
[5]
P. Panissod, J. P. Sarteaux, and P. Mutzig. Broadband automated NMR spectrometer for ferromagnetic materials. Unpublished, 1994
[6]
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[7]
1. J. Lowel. and D. W. Whitson, "Homogeneous RF field delay line probe for pulsed nuclear magnetic resonance," Rev. Sci. Instrum, vol. 48,1977,pp. 268-274.
[8]
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[9]
P. Rosch, M. T. Kelemen, T. Wokrina, and E. Dormann, "A low-cost upgrade of a commercial magnetic resonance spectrometer to a broad band system for NMR and ESR," Meas. Sci. Techn., vol. 11, 2000, pp. 1610-1616.
[10] S. Nadolski,M. Wjcik,E. Jedryka,and N. Nesteruk, "Automated pulsed NMR spectrometer for modern magnetic materials," Journal of Magnetism and Magnetic Materials,vol. 140,pp. 2187-2188,Feb. 1995 [11] D. M. Pozar,Microwave Engineering, 2nd ed. New York: John Wiley & Sons,1998
