Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 25–28, 2013
159
A Comparison of the Dynamic Range of FDNR Building Blocks
Z. Szabó, J. Sedláček, and M. Friedl
Department of Theoretical and Experimental Electrical Engineering
Brno University of Technology, Kolejni 2906/4, Brno 612 00, Czech Republic
Abstract— A multitude of various active selective blocks are utilized for the design of active
filters based on RLC prototypes. The design of low-pass filters is often realized by means of
the Bruton transformation, in which the RLC prototype structure is transformed into an RCD
structure. The basic building blocks applied within the latter structure are denoted as dual
capacitors (FDNR). These active blocks, realized in various circuit configurations with different
numbers of active circuit elements (operational amplifiers, OA), have recently been described by
several authors [1, 2].
At present, it is possible to fabricate ARC filters for the frequency range within units of MHz, using simple and economical selective FDNR building blocks that work successfully with one active
element (OA). The fabrication is enabled by modern active elements (such as voltage operational
amplifiers working in the GBW of approximately 1 GHz or CFA amplifiers applicable up to higher
frequencies) and by the synthesis method based on purposefully lossy RLC prototypes [3, 4].
This research report presents a comparison of the dynamic ranges of the most widely utilized
lossy FDNR building blocks (types I and V), and the authors intend to employ the proposed
comparative outline to help improve the practical exploitation of these capacitors in the process
of optimizing active frequency filters.
1. DESIGN AND REALIZATION OF FILTERS HAVING LOSSY PARAMETERS
The process of designing active filters based on RLC prototypes involves the application of several
different types of active selective blocks. The design of low-pass filters very often employs the Bruton
transformation, in which the structure of an RLC prototype is transformed to the RCD structure.
Here, the elementary structural blocks applied are active elements known as dual capacitors (and
frequently referred to in literature as FDNRs — frequency dependent negative resistors). In highpass ARC filters, synthetic inductors (SI) are often utilized as active blocks simulating the properties
of a coil. These active blocks, realized in different circuit configurations and having different
numbers of active circuit elements (operational amplifiers or OAs), have been described in sources
such as [1, 2, 4].
In order to provide experimental verification of partial conclusions made within previous investigation into the properties of the designed active lossy block filters, several above-specified networks
were realized as test samples on printed circuits. The related transmission properties (mainly
the modular frequency characteristics and the circuit dynamics) obtained by means of computer
modeling were compared with the experimentally measured values.
2. UNIVERSAL MEASURING STATION
A universal measuring station was set up together with the concept of a suitable measurement
methodology in order to facilitate the measurement of transmission properties of various two-port
networks within a wider frequency range. A block diagram of the measuring station is presented
in Figure 1. Figure 2 then shows the first-designed model connection of the realized 5th order
low-pass sample filter with lossy dual capacitors; the buffer amplifiers are indicated as well.
Buffer
Buffer
Generator
1
Spectral
analizer
1
50 Ω
50 Ω
G
DUT
50 Ω
50 Ω
Figure 1: Block diagram of the measurement apparatus testing the designed filtering circuits.
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Figure 2: Block amplifiers and the filtering circuit.
(a)
(b)
Figure 3: Comparison of voltage transmission functions in various FDNR building blocks. (a) FDNR I (series
loss), (b) FDNR V (parallel loss).
3. COMPARISON OF THE DYNAMIC RANGE OF LOSSY DUAL CAPACITOR
CIRCUITS
In addition to comparing the transmission characteristics of individual types of lossy dual capacitors
in relation to real parameters of active elements, we employed computer modelling techniques to
examine possible dynamic range of the above-described connections. A comparison of the circuit
types most frequently applied in practice (types I and V) is presented in Figure 3, which shows the
graphs of the resulting transmission functions in individual circuit types on the outputs of the dual
capacitors and the actual active elements (OA).
The diagrams (Figure 3) clearly indicate that in type I circuits connected in series, the dynamic
range over which the active block can operate is larger by about 20 dB compared to type V dual
capacitors connected in parallel. The status is caused by the fact that, at the resonance point, the
output of the active element (OA) included in a type V circuit exhibits a voltage gain larger by
approximately 20 dB compared to the functional block output. This significantly increases the risk
of the active element saturation and reduces the potential dynamic range for this circuit (type V)
with parallel connection of the lossy element. Therefore, it is possible to conclude that, compared
to the series connection (type I circuit), the hitherto frequently applied connection of low-pass
filters with a parallel lossy element (type V circuit) exhibits a potential dynamic range smaller by
approximately 20 dB. This precondition substantially reduces application possibilities of the type
V circuit, especially in cases where the highest attainable dynamic range of the processes signals is
required.
3.1. Measurement Results for the Low-pass filter with a Type V FDNR (Parallel Loss)
Figure 4 shows a connection diagram for the designed filter. The filter dynamics measurement
(Figure 5) confirmed the result following from the modelling of the circuits, namely that this type
of circuit exhibits a comparatively low dynamic range (approximately 300 mV with the supply
voltage of 5 V, and approximately 200 mV with the supply voltage of 3.5 V).
3.2. Measurement Results for the Low-pass Filter with a Type I FDNR (Series Loss)
The connection diagram related to the designed filter is shown in Figure 6; the measured characteristics are indicated in the graphs provided in Figure 7.
Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 25–28, 2013
161
700
600
U out [mV]
500
400
300
DP_par_AD8045 (Unap=5V)
200
DP_par_OPA656 (Unap=5V)
DP_par_AD8045 (Unap=3,5V)
DP_par_OPA656 (Unap=3,5V)
100
0
0
250
500
750
1000
Uin [mV ]
Figure 4: Connection of the 5th order low-pass with
the threshold frequency of 1 MHz — type V FDNR
— parallel loss.
s
Figure 5: Dependence of the LP output voltage on
the input voltage at the frequency of 500 kHz.
1600
1400
1200
Uout [m V]
1000
800
600
DP_ser_AD8045 (Unap=5V)
DP_ser_OPA656 (Unap=5V)
400
DP_ser_AD8045 (Unap=3,5V)
DP_ser_OPA656 (Unap=3,5V)
200
0
0
500
1000
1500
Uin [m V]
Figure 6: Connection of the 5th order low-pass with
the threshold frequency of 1 MHz — type 1 FDNR
— series loss.
2000
2500
s
Figure 7: Dependence of the LP output voltage on
the input voltage at the frequency of 500 kHz.
The measurement of attainable dynamics (Figure 7) enabled us to verify the correctness of
the conclusions made in the previous subchapters. The measurement results exhibit a markedly
higher level of attainable dynamics in this type of circuit (transmission linearity may rise up to
2000 mV even with the reduced supply voltage of 3.5 V), which fully corresponds to the theoretical
conclusions presented within chapter 3 of this article The measured values indicate that, at lower
supply voltage levels, the AD 8045 operational amplifier provides better results.
4. CONCLUSION
The authors performed a comprehensive analysis of the dynamic properties of lossy active functional
blocks (lossy dual capacitors FDNR and synthetic inductors SI).
The realized research showed that the connection of active blocks with a series equivalent model
offers a large number of advantages compared to the most frequently applied connection including
a parallel equivalent diagram. Substantial benefits of the examined type of connection consist in
the fact that, at higher frequencies, it does not exhibit the parasitic transmission zero that causes
problems in a parallel connection. Another advantage is the significantly larger (even by 20 dB)
attainable circuit dynamics.
The conclusions made on the basis of computer modelling of the above-described circuits were
fully verified via measurements performed on the related filter samples. We realized practical
connections of various types of second or higher-order low-pass and high-pass filters to verify possible
application of these blocks with modern operational amplifiers up to the frequency range of units
of MHz.
ACKNOWLEDGMENT
The research described in the paper was financially supported by the grant of the Czech Ministry
of Industry and Trade No. FR-TI1/368, project of the BUT Grant Agency FEKT-S-11-5/1012 and
project CZ.1.07.2.3.00.20.0175, Elektro-výzkumnı́k.
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