PIERS Proceedings, Suzhou, China, September 12–16, 2011
1004
Filter for Processing of NMR Signal
Martin Friedl, Jiřı́ Sedláček, Lubomı́r Fröhlich, and Radek Kubásek
Brno, FEEC BUT, UTEE, Kolejnı́ 2906/4, Brno 612 00, Czech Republic
Abstract— One of the fields of science, where is going forward continual development, is the
area of nuclear magnetic resonance (NMR). Bulk of the NMR issues concerns on signal processing
in analog and digital form in NMR signal. In this paper is focused our attention on design of
active analog filter with frequency dependent negative resistor (FDNR). There is designed active
ARC filter based on ladder structure of the LRC filter, then the filter DCR is made through the
use of Brutton transformation and finally the DCR filter is converted to the filter with FDNR
elements. The designed and realized filter is used as a low pass filter, which aims to filter out
the noise of NMR signal. The filter is placed behind the mixer, which converts the useful NMR
signal to baseband. The designed and realized filter performs role of the anti-aliasing filter before
the A/D converter.
1. INTRODUCTION
The paper deals with the design of low-pass filter with lossy FNDR element. The purpose of
the using the filter is as anti-aliasing filter in NMR spectrometer signal path, see Fig. 1. Signal
of resonant nucleus detected by probe can be expected at µV level. Low noise preamplifier will
increase the level of NMR signal before mixer. The mixer bring useful signal to base-band. Interfrequency signal required to be filtered by low-pass filter with appropriate order. There is possible
to use Bessel or Butterworth approximation. Filter has to have low noise parameters. In general,
noise parameters are the most significant in all signal path design.
2. FILTER DESIGN
There is by the design of frequency RLC filters the biggest problem with the quality, size and price
of coils. Consequently, for low and medium frequencies, RLC filters are preferably replaced by
active filters RC (ARC). Their basic principle consists in replacement the coil through the use of
an active element with resistors and capacitors [1]. One of the suitable method is solution consists
in the creation the ARC circuit with transfer function of the 2th order, which is equal to transfer
functions of RLC filter through the use of FDNR blocks [2]. The filters with FDNR elements replace
coils indirectly using Bruton’s transformation [3], which transforms the initial RLC structure into
equivalent behaving the CRD structure (Fig. 2). This new structure does not contain an element of
inductive character, but uses the properties of the synthetic element FDNR, which are preferably
used for low pass filter.
The active circuits realized of the FDNR elements can be separated into different types according
to their basic circuit characteristics [4]. The lossy FDNR grounded circuit (Fig. 3(b)) can be realized
by the use one active element (OA) and in this circuit the lossy are represented by a parallel
MAGNET
PROBE
OSCILATOR
FDNR + GAIN
A/D
COUPLER
GAIN
40 dB
TRANSCEIVER
MIXER
LOW
PASS
FILTER
GAIN
20 – 60 dB
Figure 1: The anti-aliasing filter for mirror band after mixer and noise suppression.
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
L1
L3
L2
C1
R1
C2
Rp2
Rp1
R
R2
1005
R3
Bruton
transformation
C
Cp1 FDNR
2
FDNR
1
Cp2
Figure 2: Principle of the active LP filter design.
CB
R1
IN
1kΩ
L1
L2
9,8 mH
31,8 mH
C1
R
L3
CA
9,8 mH
C2
25,7 nF
Dp
_
R2
1kΩ
25,7 nF
Cp
+
(a)
(b)
Figure 3: (a) The LRC low pass 5th order, (b) the grounded FDNR with the parallel lossy.
1 kΩ
C3
4,7 nF
IN
C1
R1
C2
33 nF
820 Ω
4,7 nF
R2
R3 820 Ω
C4
R4
27 kΩ
OPA355
4,7 nF
C5
4,7 nF
R2
163Ω
R5
27 kΩ
C6
10 nF
OPA355
Figure 4: The optimized ARC filter with the lossy FDNR blocks.
capacitor. These lossy correspond to resistors Rp1 and Rp2 parallel connected to capacitors in the
initial circuit of the RLC filter (Fig. 2). Thus it is very easy these lossy to simulate and to observe
filter response to different sizes of the resistors Rp1 and Rp2.
The final design of the low-pass RLC filter of the 5th for cut-off frequency 10 kHz is on Fig. 3(a).
Through the use Bruton’s transformation and grounded lossy FDNR element (Fig. 3(b)) we obtain
circuit of the ARC filter with lossy FDNR elements.
The results of the simulation (Fig. 6) show that parallel lossy of FDNR elements have highly
influence to the resulting characteristic (the black curve). Therefore the optimization [5–7] was
done and the resulting transfer characteristic of ARC filter with the real OA (OPA355) [8] corresponds to the red curve. It is clear that by the using of the optimization was achieved almost the
same characteristic as it is at the RLC filter (the blue curve). There is possible of the using the
optimization to reach almost identical transfer as with the lossless FDNR elements with the lossy
FDNR elements. The optimization consists in spreading lossy from the lateral branch of the filter
to the whole circuit.
The resulting realization of the filter is on the Fig. 5. The measuring was done with the help
of vector analyzer Bode 100, by company OMICRON Lab [9]. During parameters verifying of
designed circuit was also searched the characteristic sentence of real active elements. Very crucial
is mainly sufficient width of the OA band, which is one of the key presumptions of the distortion-less
function of the filter in demanded band-pass and it is necessary to solve it with the regard to cut-off
frequency of the filter with the sufficient reserve, minimally one or two orders higher [10]. Very
good results were achieved by OA by company Texas Instrument [8] OPA355, which are determined
also for active filters and they have sufficient width of the band (GBW 200 MHz). The designed
low-pass filter was completed with the three amplifiers for processing of NMR signal.
At first, the transfer characteristic of the filter was measured (Fig. 6 — the green curve) and
after the transfer characteristic of the filter with amplifiers (Fig. 7) consequently there is obvious
gain 22 dB.
PIERS Proceedings, Suzhou, China, September 12–16, 2011
1006
Figure 5: The realized filter with the amplifiers.
Figure 6: The magnitude response of the filters: LRC, ARC, ARC optimization and the realized filter.
Figure 7: The measured magnitude response of the filter with amplifiers.
3. CONCLUSIONS
This contribution deals with synthesis and optimization of ARC low pass filter based on modified
simple and economic lossy building blocks (FDNR). The designed frequency filter will be used for
pre-processing of analogue signals before digitalization in the NMR signal processing area whereas
the resulting characteristics of the designed and measured filter show, that it is possible using it
with utilize of the optimization.
The quick progress of modern technologies enables realization of modern structures of analogue
frequency filters. In this context, there is necessary to evolve the synthesis and optimization meth-
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
1007
ods of these structures with regard to the possibilities of the modern active components (voltage OA
with GBW approximately 1 GHz, current conveyors, transimpedance OA). In the future research,
it will focused on optimization of the basic building block of 2nd order and their characteristics
with the modern active elements above they will be analyzed from the point of view of their usage
in circuits of higher orders and area of higher frequencies.
ACKNOWLEDGMENT
This work has been supported by the project of the BUT Grant Agency FEKT-S-11-5.
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