Filter Design Solutions For Rf Systems Leonardo Pantoli And Vincenzo Stornelli

Filter Design Solutions For Rf Systems Leonardo Pantoli And Vincenzo Stornelli
Filter Design Solutions For Rf Systems Leonardo Pantoli And Vincenzo Stornelli
Filter Design Solutions For Rf Systems Leonardo Pantoli And Vincenzo Stornelli

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5. Filter Design Solutions for RF systems • Leonardo Pantoli and Vincenzo Stornelli
Filter Design
Solutions for RF
systems
Printed Edition of the Special Issue Published in Electronics
ww.mdpi.com/journal/electronics
Leonardo Pantoli and Vincenzo Stornelli
Edited by

6. FilterDesignSolutionsforRFsystems

8. FilterDesignSolutionsforRFsystems
Editors
Leonardo Pantoli
Vincenzo Stornelli
MDPI•Basel•Beijing•Wuhan•Barcelona•Belgrade•Manchester•Tokyo•Cluj•Tianjin

9. Vincenzo Stornelli
Universit`a degli Studi dell’Aquila
Italy
Editors
Leonardo Pantoli
Universit`a degli Studi dell’Aquila
Italy
Editorial Office
MDPI
St. Alban-Anlage 66
4052 Basel, Switzerland
This is a reprint of articles from the Special Issue published online in the open access journalElectronics
(ISSN 2079-9292) (available at: https://www.mdpi.com/journal/electronics/specialissues/filter
design).
For citation purposes, cite each article independently as indicated on the article page online and as
indicated below:
LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title.Journal NameYear, Article Number,
Page Range.
ISBN 978-3-03943-547-0 (Hbk) ISBN 978-3-03943-548-7 (PDF)
c2020 by the authors. Articles in this book are Open Access and distributed under the Creative
Commons Attribution (CC BY) license, which allows users to download, copy and build upon
published articles, as long as the author and publisher are properly credited, which ensures maximum
dissemination and a wider impact of our publications.
The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons
license CC BY-NC-ND.

10. Contents
About the Editors.............................................. vii
Preface to ”Filter Design Solutions for RF systems”......................... ix
Leonardo Pantoli, Vincenzo Stornelli, Giorgio Leuzzi, Hongjun Li and Zhifu Hu
Low-Current Design of GaAs Active Inductor for Active Filters Applications
Reprinted from:Electronics2020, 9, 1232, doi:10.3390/electronics9081232.............. 1
Vladimir Ulansky and Ahmed Raza
Sinusoidal Oscillators Operating at Frequencies Exceeding Unity-Gain Bandwidth of
Operational Amplifiers
Reprinted from:Electronics2020, 9, 845, doi:10.3390/electronics9050845............... 15
Stefano D’Amico, Stefano Marinaci, Peter Pridnig and Marco Bresciani
Open-Loop Switched-Capacitor Integrator for Low Voltage Applications
Reprinted from:Electronics2020, 9, 762, doi:10.3390/electronics9050762.............. 35
Francesco Centurelli, Pietro Monsurr `o, Giuseppe Scotti, Pasquale Tommasino and
Alessandro Trifiletti
10-GHz Fully Differential Sallen–Key Lowpass Biquad Filters in 55nm SiGe
BiCMOS Technology
Reprinted from:Electronics2020, 9, 563, doi:10.3390/electronics9040563.............. 59
Min-Hang Weng, Fu-Zhong Zheng, Hong-Zheng Lai and Shih-Kun Liu
Compact Ultra-Wideband Bandpass Filters Achieved by Using a Stub-Loaded Stepped
Impedance Resonator
Reprinted from:Electronics2020, 9, 209, doi:10.3390/electronics9020209.............. 73
Liqin Liu, Ping Zhang, Min-Hang Weng, Chin-Yi Tsai and Ru-Yuan Yang
A Miniaturized Wideband Bandpass Filter Using Quarter-Wavelength
Stepped-Impedance Resonators
Reprinted from:Electronics2019, 8, 1540, doi:10.3390/electronics8121540.............. 85
Qingrong Liu, Mingbo Qiu, Lida Shen, Chen Jiao, Yun Ye, Deqiao Xie, Changjiang Wang,
Meng Xiao and Jianfeng Zhao
Additive Manufacturing of Monolithic Microwave Dielectric Ceramic Filters via Digital
Light Processing
Reprinted from:Electronics2019, 8, 1067, doi:10.3390/electronics8101067.............. 95
Leila Safari, Gianluca Barile, Giuseppe Ferri and Vincenzo Stornelli
A New Low-Voltage Low-Power Dual-Mode VCII-Based SIMO Universal Filter
Reprinted from:Electronics2019, 8, 765, doi:10.3390/electronics8070765.............. 109
Jin Zhang, Ruosong Yang and Chen Zhang
High-Performance Low-Pass Filter Using Stepped Impedance Resonator and Defected
Ground Structure
Reprinted from:Electronics2019, 8, 403, doi:10.3390/electronics8040403............... 123
Krzysztof Bernacki, Dominik Wybra ´nczyk, Marcin Zygmanowski, Andrzej Latko,
Jarosław Michalak and Zbigniew Rymarski
Disturbance and Signal Filter for Power Line Communication
Reprinted from:Electronics2019, 8, 378, doi:10.3390/electronics8040378............... 135
v

11. Johann Cassar, Andrew Sammut, Nicholas Sammut, Marco Calvi, Sasa Dimitrijevic and
Radivoje S. Popovic
Design and Development of a Reduced Form-Factor High Accuracy Three-Axis Teslameter
Reprinted from:Electronics2019,8, 368, doi:10.3390/electronics8030368............... 153
vi

12. About the Editors
Leonardo Pantoliis a Tenure-Track Researcher and Professor with the University of L’Aquila
(IT) and Vice-President and founder member of the spin-off SENSing s.r.l. He received a Degree (cum
laude and mention) in Electronic Engineering and a Ph.D. in Electrical and Information Engineering
from the University of L’Aquila, L’Aquila, Italy, in 2006 and 2010, respectively. In 2007 and 2008, he
spent several months with the “Dpto. Ingenieria de Comunicationes—ETS de Ingenieros Industriales
y de Telecomunicaci´on” of the University of Cantabria, Spain, and the “C2S2 Department” of the
XLIM Research Institute, Brive La Gaillarde, France. From 2013 to 2017 he was Research Assistant
with the University of L’Aquila. From 2017 to 2019 he was Researcher (Law n. 240, 30 December
2010, Art. 24, letter a) with the same University, and in 2017 he obtained a National Scientific
Qualification (Law n. 240, 30 December 2010, Art. 16, paragraph 1) to serve as Associate Professor in
Italian Universities in the sector 09/E3—Electronics. Since 2019 he has been Tenure-Track Researcher
(Law n. 240, 30 December 2010, Art. 24, letter b) with the same University of L’Aquila. His research
activities include the development of methods and algorithms for the design of RF, microwave and
millimeter wave nonlinear circuits, the stability analysis of circuits in both linear and large-signal
regimes, active filter design, and MMIC design for aerospace, wireless communication and imaging
applications. He has good experience with GaAs, Si and SiGe technologies.
Vincenzo Stornelliwas born in Avezzano, Italy. He received the “Laurea” degree (cum laude) in
electronic engineering in 2004. In October 2004, he joined the Department of Electronic Engineering,
University of L’Aquila, L’Aquila, Italy, where he is involved as an Associate Professor. His research
interests include several topics in computational electromagnetics, including microwave antenna
analysis for outdoor ultrawideband applications. He serves as a reviewer for several international
journals and as an Editor of the Journal of Circuits, Computers and Systems.
vii

14. Preface to ”Filter Design Solutions for RF systems”
Nowadays, technology developments and system integration capabilities are leading to the
definition of innovative architectures and modules that require the re-design of many electronic
components. Among them, one of the more critical at the system level is filters. In practice, these are
difficult to integrate, and in many cases they perform poorly due to the technological limitations of
passive elements. Tunability and calibration are often difficult to achieve as well. Different solutions
are currently available on the market, and these have already been presented in the literature,
depending on the operational frequencies and applications. For instance, modern communication
systems have strict performance requirements from electronic devices and components, and these
requirements lead to the choice of the technology solutions and component topology to adopt.
Filters can be designed at the electrical, mechanical or electromechanical level; they can be
conceived as discrete or distributed components, and among the electrical ones, they can be realized
with passive or active circuits. Furthermore, tunability is often a desired characteristic, especially in
modern re-configurable systems, but it is usually difficult to achieve. It can be obtained in mechanical
filters with screws driven by micro-motors, and in electrical ones by means of voltage-controlled
variable components. In any case, it is not trivial to obtain a good tunability and to preserve the same
shape factor in the full tuning bandwidth. A further criticism relates to the calibration of these filters,
mainly at the industrial level, since the complete characterization of these components is usually
obtained with a trial-and-error approach, but this is dependent on the expertise of the technicians.
In this regard, automatic test systems optimized for the calibration of the device under test might be
very fruitful.
This Special Issue, named “Filter Design Solutions for RF systems”
(https://www.mdpi.com/journal/electronics/special
issues/filterdesign) will focus on the
state-of-the-art results in the definition and design of filters for low- and high-frequency applications
and systems. Aspects related to both the theoretical and experimental research in filter design, CAD
modeling and novel technologies and applications, as well as filter fabrication, characterization and
testing, are covered.
Leonardo Pantoli , Vincenzo Stornelli
Editors
ix

16. electronics
Article
Low-Current Design of GaAs Active Inductor for
Active Filters Applications
Leonardo Pantoli
1
, Vincenzo Stornelli
1,
*, Giorgio Leuzzi
1
, Hongjun Li
2
and Zhifu Hu
2
1
Department of Industrial and Information Engineering and Economics, University of L’Aquila,
67100 L’Aquila AQ, Italy; [email protected] (L.P.); [email protected] (G.L.)
2
Hebei Semiconductor Research Institute, Shijiazhuang 050000, China; [email protected] (H.L.)
*Correspondence: [email protected]
Received: 30 May 2020; Accepted: 23 July 2020; Published: 31 July 2020
Abstract:Active inductors are suitable for MMIC integration, especially for filters applications, and
the definition of strategies for an efficient design of these circuits is becoming mandatory. In this work
we present design considerations for the reduction of DC current in the case of an active filter design
based on the use of active inductors and for high-power handling. As an example of applications,
the approach is demonstrated on a two-cell, integrated active filter realized with p-HEMT technology.
The filter design is based on high-Q active inductors, whose equivalent inductance and resistance can
be tuned by means of varactors. The prototype was realized and tested. It operates between 1800 and
2100 MHz witha3dBbandwidth of 30 MHz and a rejection ratio of 30 dB at 30 MHz from the center
frequency. This solution allows to obtain a P1 dB compression point of about−8 dBm and a dynamic
range of 75 dB considering a bias current of 15 mA per stage.
Keywords:active filters; active inductor; MMIC; tunable filters
1. Introduction
On-chip passive filters are affected by the limited Q-factor of inductors and capacitors, due to
ohmic and substrate losses, even on low-loss substrates as Gallium Arsenide. Tunable passive filters
are also affected by the limited Q of varactors, normally used for tunability. Moreover, the bandpass of
the filter is affected by the combination of constant passive inductance and variable capacitance in the
tuning range. Active filters can be realized with several approaches [1–3]; many of them are usually
based on active inductors (AIs), that can achieve very low or even negative equivalent resistance, and
therefore a high filter Q. The AI can be tuned both in terms of equivalent inductance and of equivalent
resistance, yielding constant bandpass with limited losses or positive gain.
In general, active filters usually have limited power handling capabilities also due to the
nonlinearities of the active elements, and they are prone to instability due to the negative resistance
required for the compensation of the losses of the passive elements in the circuit.
In order to increase the dynamic range, usually a high bias current is required for the active devices.
This can lead to higher power consumption that is often unacceptable for integrated circuits and also
not allowed at system level. A possible means to reduce the bias current is provided by Class-AB
bias, which has already been demonstrated [
4]. However, this approach is not always possible or,
at least, it experiences some drawbacks depending on the characteristics of the technology process
(e.g., the availability of complementary transistors, highly linear active devices).
In this paper, we present a design approach of integrated active inductor and its applications
in filters realized in GaAs technology that allows the minimization of bias current, still maintaining
Class-A operations that usually ensure high-power handling capability. Concerning the filter AI base
design, the proposed approach is based on AIs coupled with shunt capacitors in order to realize an
equivalent high-order filter with good performances in terms of shape factor and dynamic range [5–8].
Electronics2020,9, 1232; doi:10.3390/electronics9081232 www.mdpi.com /journal/electronics 1

17. Electronics2020,9, 1232
The topology of the AI is such that only a fraction of the bias current is effectively drawn by the active
device and it is useful to provide the required negative resistance. In addition, each cell makes use of a
single transistor, reducing power consumption and minimizing possible instability concerns.
An example of application is proposed in MMIC technology, potentially tunable in the frequency
range between 1.8 to 2.1 GHz, with a tuning bandwidth of about 15%. The−3 dB bandwidth is almost
constant and equal to 30 MHz, while the out-of-band rejection is significant thanks to the high shape
factor equal to 2.5 for a 30 dB/3 dB bandwidth ratio. The chip has been designed with a standard
process provided by HSRI Foundry that implements 0.13μm GaAs pHEMT devices. Both simulations
and on-chip measurement results are presented with a good agreement between them.
Currently; however, no varactor diodes are available in this technology. Therefore, a fixed-capacitor
version was implemented, with different values of the capacitors. In fact, our aim is to provide a
feasibility proof demonstrating the tunability capability of the filter by replacing the unavailable
varactors with fixed capacitors. A version with the varactors will be implemented and fabricated
as soon as the technology is available. However, good performances with varactors have already
been demonstrated in a hybrid implementation [
5], that indicate the possibility of a successful
implementation with varactors also in monolithic technology.
Noise figure has not been considered in this design since noise performance requirements were
not so strict in the proposed application (as later discussed); therefore, it is quite high. However, noise
reduction techniques have been developed and patented [7] that yield a relatively low noise figure.
They will be dealt with in a future publication.
In the following, the topology and principle of operation of the active inductor is briefly
summarized in Section2. Section2illustrates also the proposed low-current design approach on
an active filter, while in Section3the MMIC design and measurement results are shown. Finally,
the conclusions are drawn (Section4).
2. The Active Inductor Architecture
Active filters can be realized by one or more cells, each including an AI-based shunt resonator
(Figure1). Both the shunt capacitor and the AI are tuned in order to maintain both insertion loss and
bandpass almost constant across the tuning range. Thus, it is straightforward to notice that the AI is
the centerpiece of the filter, as it is also able to control the losses of the cell and; therefore, the overall
quality factor of the filter.

Figure 1.Topology of a single cell for bandpass active filters.
The traditional structure of the AI is shown in Figure2a. The input voltage is sampled by a non-inverting
transconductance amplifier, that drives a current into the capacitor. The voltage generated in the capacitor
is sampled by the inverting transconductance amplifier, that draws an inductive current from the input
of the active inductance. The relations between voltages and currents in the active inductor can be better
2

18. Electronics2020,9, 1232
understood in the complex phasor plane (Figure3). Phases are referred to that of the input voltageV in.
The capacitor voltageV Chas a 90 degrees delay (capacitive delay) with respect to the input voltage and the
inverting transconductance introduces a further 180
◦
phase shift, so generating an inductive currentI indwith
respect to the input voltageV in. An overall excess phase of the output current with respect to the purely
inductive 90
◦
phase shift gives an equivalent negative resistance in addition to the equivalent inductance,
while an insufficient phase shift gives a positive equivalent resistance. The amplitude of the inductive
current with respect to the input voltage determines the value of the equivalent inductance. This amplitude
can be changed, for instance, by tuning the value of the transconductance(s).

(a)

rPu
]v
sWZ
’Z](?
s
]v /]v

(b)
s]v
/]v
rPu?rPu?
]v

s
rPu?
]v

s
Pu?Pu?
rPu?
]v

s
Pu?
s]v
/]v
rPu?
]v

s
Pu?
Figure 2.Active inductor architecture: (a) Traditional topology, (b) improved topology.
3

19. Electronics2020,9, 1232
Figure 3.Phasors of voltages and currents in the AI of Figure2in the complex phasor plane. Vin is
the input voltage, V
Cthe current across the capacitor (Figure2a) or at the output of the phase shifting
network (Figure2b), and I
indthe current drawn from the inverting transconductance amplifier.3.
Low-current design of GaAs active filters based on the proposed AI.
An improved topology of the AI is shown in Figure2b[ 5]. The input voltage is sampled at the input
of a phase-shifting passive network, then transferred to the input of the inverting transconductance
amplifier, that in turn draws the current from the input port. The relations between voltages and
currents are approximately the same as in Figure3; however, some phase shift is also introduced by the
inverting transconductance amplifier, given the high operation frequencies. In this improved topology,
the amplifier is a fixed-bias, class-A linear amplifier, stable and with fixed gain. The tuning of the
phase and amplitude is; therefore, performed by the phase-shifting passive network that includes
varactors. This approach allows one to obtain stable and easily tuned AI, and consequently filters with
a relatively high gain compression point.
For relatively high-power handling, the current in an AI, conceived with a class-A polarization,
may become relatively high. With class-A operation, this requires a high bias current in the active
device, where the whole output current flows. A possible means of reducing the DC current is the use
of a class-B or class-AB amplifier in the AI [4]. This is certainly a feasible approach that significantly
reduces the DC power requirements of the filter, even if it may cause some concerns on intermodulation.
However, this approach is not always possible, depending on the characteristics of the active device.
For instance, a very sharp pinch-offof the transistor makes the class-B or AB impractical; therefore,
adifferent approach is here proposed and successfully applied to the design of an active filter.
In order to have a high-Q filter, the current at the input of the active inductor must be purely
inductive, or nearly so, that is, with a 90 degree phase relation with respect to the voltage across it.
The current through a passive inductor has less than 90 degrees with respect to the applied voltage,
due to losses. This current can be seen as the vectorial sum of a purely inductive current, and of a
purely resistive current in phase with the applied voltage, much smaller in amplitude, due to the losses
in the inductor. The compensation of the losses can be obtained by summing another current, opposite
in phase with respect to the resistive current and; therefore, equivalent to the current of a negative
resistance. This negative resistance current will be therefore much smaller than the total current in
the inductor.
A possible topology that implements this approach is shown in Figure4. The current from the
input of the AI flows through a passive inductor (I Lin Figure4), because the capacitive current that
enters the gate of the active device is relatively small and can be neglected. Then, the main part of this
current (I passivein Figure4) flows through a relatively large capacitorC g, that has a smaller impedance
4

20. Electronics2020,9, 1232
compared to the passive inductor. Therefore, this current is mainly inductive with respect to the input
voltage, but also has a resistive component, due to the losses in the capacitor and in the inductor. From
the plot in Figure5its resistive nature is apparent from its phase relation to the input voltage.

Figure 4.Improved topology of the AI for class-A low bias current.
Figure 5.Phasors of voltages and currents in the AI of Figure3in the complex plane.V
inis the input
voltage,I
Lthe current through the inductorL.I
passiveis the current through the capacitorC gandI
active
the current drawn from the transistor through the phase-shifting network. Their vectorial sum gives
the current through the inductanceI
L.
A smaller part of the current through the passive inductor flows through the phase-shifting
network (I
activein Figure4). This current can have a negative resistance component with respect to
the input voltage, because it ultimately comes from the active device. The size of the active device,
and the delay introduced by the phase-shifting network must be designed in such a way, that the
negative-resistance component of theI activecurrent compensates the resistive component of theI passive
current through the capacitor. In this way its amplitude is kept to a low value compared to the total
current flowing into the AI. Therefore, the current through the active device is minimized, compared
to the standard design, where all the current flowing into the AI comes from the active device. As a
consequence, bias current and overall power consumption in minimized.
The value of the equivalent inductance is easily tuned by varying the value of the capacitanceC g,
that can be implemented with a varactor; given the relatively high value of the capacitor, the series
L-C
gis inductive, because the operating frequency is higher than the resonant frequency of theLC
series. By changing the value of the capacitor, also the equivalent inductance of theLCseries is varied.
Another varactor can be used also to implement the resonating capacitanceC resof the single cell
(Figure1). The simultaneous tuning of the resonating capacitance and of the equivalent inductance
5

21. Electronics2020,9, 1232
yields a constant bandpass across the tuning frequency range, while the low losses or possibly small
negative equivalent resistance of the AI allow to enhance the Q-factor of the filter.
The proposed design approach has some similarities with the negative impedance converter (NIC)
approach [9,10]. However, the negative resistance is not designed as a one-port, additive network,
but is obtained by suitable phasing of the active inductor loop. Moreover, the very simple AI topology
here addressed, based on a single transistor per cell, greatly reduces the current requirements, and
makes stability enforcement quite straightforward, ensuring at the same time also high-power handling
together with low-power consumption.
When properly implemented, the proposed approach does not cause any reduction in the tuning
range or increase in losses with respect to the traditional approach. The main result is the reduction of
the current required from the active device, with consequent increase of power handling with the same
active device.
It is also important to notice that the proposed design approach is not based on equations but
on the optimization of network parameters (currents, voltages, equivalent impedances) at both small
and large signals. It suggests a suitable architecture for the realization of active filters based on
active inductors. An analytical approach is hard to realize since the filter makes use of AIs that are
implemented as closed loop circuits. In addition, it is not useful from a practical point of view also
considering that at these frequencies circuits usually make use of distributed elements that are difficult
to analytically describe. So the description is strictly related to the network configuration and cannot
be generalized.
3. MMIC Design and Test
Following the above proposed design strategy and making use of the new architecture shown in
Figure4for the AI, a two-cells example filter has been designed, considering for each cell the same
architecture shown in Figure1. However, the core of the proposed work is the AI design and the filter
performance are strictly dependent on the active inductor characteristics. The AI should be applied
also to different filter families (e.g., Butterworth, Chebyshev, etc.) [11] that make use of grounded
inductors. In this example, the filter has been fabricated on a GaAs technology provided by HSRI,
realized and tested for demonstration. The standard PDK from HSRI includes 0.13μm pHEMT devices
that exhibit low noise figure, high gain and high-power density (0.7 W/mm). Varactor diodes are not
currently available in this technology; the design will be updated with inclusion of varactors as soon as
they are available in the future. The proposed design method can be applied with any technology
process and into the millimeter-wave band. It is also important to note that the performances of the
example filter have been designed for the replacement of an existing passive filter used as post selector
in base station unit for mobile communications, and so could be improved further.
The filter acts exactly as a resonator. Its ease of realization represents its effectiveness. More in
detail,C resandL resin Figure1define the resonant frequency, that is the center frequency of the filter.
The quality factor of the filter depends mainly on the quality factors of the components used in the
resonator.C dcandL dcrealize series resonators that have decoupling effects and are helpful to tighten
the filter bandwidth. The same architecture has been widely described in [11–13]. The filter has been
realized replying twice the same cell. Each single cell includes an active inductor that realizesL res.
The embedded AI in each cell has been realized with a transistor, whose dimensions are 6
×25 um,
in common source configuration. A self-gate bias architecture has also been implemented in order to
limit the number of the bias pads and to reduce the temperature dependence of the filter characteristics.
The bias current per transistor is 15 mA, while the total power consumption is 120 mW with a DC
voltage supply of 4 V. It is straightforward to notice that the DC power consumption is not very low;
but in this example this design choice was not critical. In general, it depends on the desired linearity
and dynamic range of the filter, in addition to the available technology. Considering the HAMLA13B
Model Handbook from HSRI, in particular the recommended bias voltages and the IV-curves of the
active devices, a drain voltage of 4 V and a bias current per transistor of 15 mA are suitable choices,
6

22. Electronics2020,9, 1232
considering the required power handling and the connected voltage and current swings. Obviously,
by using different technology processes and considering different design specs power consumption
should be different, but still in the same order of magnitude if you use the same transistor topology.
In addition, it may be reduced also changing the number of cells, so allowing to have a lower shape
factor of the filter.
In Figure6, the complete schematic of the single cell is reported, while in Figure7, the simulated
results of the proposed IC design are shown for a fixed tuning state. The insertion loss is about 6 dB,
while the 3 dB bandwidth is 30 MHz. It is worth noting that given the active nature of the filter there is
no problem in principle to obtain very low attenuation, close to zero, but this was not the aim of this
work since the proposed circuit has been designed for the one-to-one replacement of an existing passive
post-selector filter, and therefore it had to have the same performances. In that application the insertion
loss is not a critical parameter, and has not been improved. However, active filters may reduce the
attenuation to zero or even have amplification, at the expense of stability. Typically, an insertion loss of
0.5 dB can be reached with still a good stability margin. The insertion loss is defined properly balancing
the negative resistance introduced by the active inductor and losses of passive components of filtering
network. So, it is of primary importance the definition of a suitable shape for the input impedance of
the AI that allows to provide low losses, out-of-band rejection and tunability versus an external control
voltage. As shown in Figure7, the shape factor achievable with the proposed solution is typical of
higher-order passive solutions [11], and the quality factor is approximately equal to 90. It is important
to remark that the circuit is stable, as evident from the behavior of the stability factor K and Delta
parameter in the same figure [14]. The stability has been checked not only between the external RF I/O
pads, but also at transistor level in each stage with the approach proposed in [8]. This is necessary due to
the presence of feedback networks (Figure4) that may generate inner instability problems. In particular,
the amplifier in each active inductor is unconditionally stable at all frequencies. Additionally, each cell
is unconditionally stable at all frequencies, because the small negative resistance of the active inductor
is compensated by the losses of the resonating capacitor and of the connecting lines. Therefore, no
oscillations can take place due to reflections between cells. In Figure8, the simulated output power and
attenuation vs. input power are shown for the circuit tuned at 1800 MHz, for a−7 dBm compression
point. In Figure9, the simulated dynamic load lines of the transistor for the same tuning frequency are
also shown for several input power levels, demonstrating class-A operations.
1
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Figure 6.Schematic of the single cell.
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Figure 7.Simulated S-parameters and stability parameters of the two-cell filter for a single frequency.
Figure 8.Simulated compression of the filter tuned at 1800 MHz.
Figure 9.Dynamic load line of the transistor of the filter tuned at 1800 MHz, for different input power
levels up to−9 dBm.
At the considered frequencies, better performance can be achieved by using, for instance,
SAW devices. However, SAW filters [15] have a limited integration capability and cannot be used at
very high frequencies. Additionally, an active chip filter has potential tunability, and smaller size and
cost compared to a SAW filter.
8

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25. Canvas, 11
Carbonising, 12
Carded Union Yarns;
see Union Yarns,
96
Carding Wools; see
Wool,
107
Casement Cloth, 12
Cashmere, 12
Cashmere Double, 12
Cashmere Wool, 12
Castor, 13
Cellular Cloth, 13
Ceylon or Ceylon
Flannel,
13
Challis, 13
Chambray, 13
Charmeuse, 13
Checks, 13
Cheese Cloth, 13
Cheviot, 14
Chiffon, 14
China Grass; see
Ramie,
71
Chinchilla, 14
Chiné, 14
Chinese Customs
Definition of
Nankeen; see
Nankeen,
55
Chintz, 14
Classification of
Samples; see
Sl
74

26. Samples,
Clip Spots, 14
Coated Cotton Cloths,14
Collarette, 15
Coloured, 15
Coloured Crimp Cloth,15
Coloured Lists, 15
Coloured Sateens; see
Printed Sateens,
68
Coloured Woollen and
Worsted Yarns,
15
Combination Twill; see
Twill Weave,
93
Combing Wool; see
Wool,
107
Continuous or Pad-
dyeing Process; see
Dyeing,
25
Corduroy, 15
Corkscrew Twill; see
Twill Weave,
93
Côtelé, 16
Cotton, 16
Cotton, Animalised; see
Animalised Cotton,
2
Cotton Duck, 16
Cotton Flannel, 16
Cotton Plush, 17
Cotton Velvet, Plain;
see Plain Velvet
(Cotton),
62

27. Cotton Yarn, Coarse,
Medium, and Fine;
see Yarn, Cotton,
Grey or Bleached,
111
Cotton Yarn, Grey or
Bleached; see Yarn,
Cotton, Grey or
Bleached,
111
Cotton Yarn Measures,17
Counts, 17
Counts of Spun Silk;
see Silk Yarns,
85
Coutil, 18
Covert, 18
Crabbing, 18
Crape Cloth, Plain, 18
Crape Weave; see
Crape Cloth, Plain,
18
Crash, 19
Cravenette, 19
Crêpe de Chine, 19
Crêpe Meteor, 19
Crepoline, 19
Crépon, 19
Cretonne, 19
Cretonne, Shadow; see
Shadow Cretonne,
82
Crimp Cloth, Plain, or
Crimps,
20
Crinkle, or Seersucker,20
Cross-dyed, 20
Crossover, 20
CtseeWoollenYan109

28. Cut; see Woollen Yarn,109
Cut Goods, 20
Cuttling, 21
 
D.
Damask, 21
Damassé, 21
Delaine, 21
Denim, 21
Derby Rib, 22
Descriptions of
Standard Cloth; see
Market Descriptions
of Standard Cloth,
50
Diagonal, 22
Diaper, 22
Diced; see Diaper, 22
Dimity, 22
Discharge Printing, 22
Dobbie, or Dobby, 22
Domestics, 23
Domet, 23
Dorneck; see Diaper, 22
Double Cloth Weave, 23

29. Double Sole, Heel, and
Toe,
23
Double Warps, 23
Drap d'Été, 23
Dresden, 23
Drill, Pepperell; see
Pepperell Drill,
60
Drills, 23
Drills, Grey; see Grey
Drills,
39
Drillette, 24
Drilling; see White
Drills, or Drilling,
104
Duchesse, 24
Duck, 24
Dungaree, 24
Duplex Prints, 24
Dyeing, 25
Dyed and Printed, 25
Dyed Alpacianos, 25
Dyed Balzarines, 26
Dyed Cambrics, 26
Dyed Corduroys
(Cotton),
26
Dyed Cotton Lastings,26
Dyed Cotton Spanish
Stripes,
26
Dyed Crimp Cloth, 27
Dyed Drills, 27
Dyed Figured Cottons,27
Dyed Figured Cotton
Italians,
27

30. Dyed Figured Cotton
Lastings,
27
Dyed Figured Cotton
Reps,
28
Dyed Figured Ribs, 28
Dyed Fustians, 28
Dyed Imitation Turkey
Reds,
28
Dyed in the Grey; see
Dyed in the Piece,
29
Dyed in the Grey; see
Union Cloth,
95
Dyed in the Piece, or
Piece-dyed,
29
Dyed Lawns, 29
Dyed Lenos, 29
Dyed Leno Brocade, 29
Dyed Muslins, 30
Dyed Plain Cottons, 30
Dyed Plain Cottons; see
White Italian,
104
Dyed Plain Cotton
Italians,
30
Dyed Real Turkey Reds,30
Dyed Reps, 31
Dyed Ribs, 31
Dyed Sheetings, 31
Dyed Shirtings, 31
Dyed T-Cloths, 32
Dyed Velvet Cords
(Cotton),
32
Dyed Velveteen Cords
(Cotton)
32

31. (Cotton),

32.  
E.
Elongated Twill; see
Twill Weave,
93
Embossed Velvet
(Cotton),
32
Embossed Velveteen
(Cotton),
32
Embroideries, 33
End, 33
English Foot, 33
English System of Silk
Cords; see Silk
Yarns,
85
Eolienne, 33
Éponge, 33
Equestrienne Tights,33
Étamine, 33
Extract, 33
Extracted, 33
 
F.
Face-finished
Cashmere; see
Velour,
96
Façonné, 33
Faille, 33
Fancies, 34
Fancy Shirtings; see
White Striped
Shirtings,
106
FancySilkSeal;seeSilk

33. Fancy Silk Seal; see Silk
Seal,
84
Fancy Twill; see Twill
Weave,
93
Fast Pile; see Pile
Weave,
61
Fents, 34
Figured, 34
Figured Cretonne; see
Cretonne,
19
Figured Muslin, 34
Figured Twill; see Twill
Weave,
93
Figure Weaving, 34
Filled Cotton Cloth, 35
Filling, 35
Filling (finishing term),35
Flannel (Woollen), 35
Flannel, Cotton; see
Cotton Flannel,
16
Flannelette, 35
Flat Underwear, 36
Fleece-lined, 36
Flocks; see Waste and
Flocks,
100
Floconné, 36
Florentine Drills, 36
Folded Yarn, 36
Foulard, 37

34. Foundation Muslin; see
White Muslin,
105
French Cambric; see
White Cambric,
103
French Foot, 37
French System of
Cotton Counts; see
Cotton Yarn
Measures,
17
French System of Silk
Counts; see Silk
Yarns,
85
Full Regular, 37
Full-fashioned, 37
Fustian, 37
 
G.
Galatea, 38
Gauge, 38
Gauze Weave, 38
Genoa Plush; see
Cotton Plush,
17
Gingham, 38
Gingham, Madras; see
Madras Gingham,
49
Gingham, Silk; see Silk
Gingham,
84
Glacé, 38
Granité, 39
Grenadine, 39
Grey, in the Grey, or
Grey Cloth,
39
ll

35. Grey Drills, 39
Grey Jeans, 39
Grey Sheeting, 39
Grey Shirting, 40
Grey T-Cloths, 40
Grosgrain, 40
 
H.
Habit Cloth (Woollen),40
Habutai, 41
Hair-cord Muslin, 41
Hand Looms and Power
Looms,
41
Handle, 41
Hank; see Cotton Yarn
Measures,
17
Hank; see Counts, 17
Hard Waste; see Waste
and Flocks,
100
Harvard Shirting, 41
Henrietta, 42
Herring-bone, 42
Hessian, 42
Hog, or Hoggett Wool,42

36. Honeycomb, 42
Huckaback, 42
 
I.
Imitation Oxford; see
Oxford Shirting,
58
Imitation Rabbit Skin,42
Imitation Wright's
Underwear; see
Wright's Underwear,
Imitation,
111
India Lawn; see White
Lawn,
104
India Linon; see White
Lawn,
104
India Mull; see Mull, 54
Indigo Print; see
Printed,
65
Ingrain, 43
Irishes, 43
Irish Cambric, 43
Italian Cloth, 43
Italian Cloth, Figured,
Cotton Warp and
Wool Weft,
43
Italian Cloth, Plain,
Cotton Warp and
Wool Weft,
44
 
J.
Jaconet, 44
Jaconettes; see
44

37. Jaconet,
44
Jacquards, 44
Jaeger, 44
Jean, 45
Jean; see Galatea, 38
Jeanette, 45
Jouy, 45
 
K.
Kerseymere, 45
Khaiki, 45
Khaki, 45
 
L.
Ladies' Cloth, 45
Lamb's Wool; see
Wool,
107
Lappet Weave, 45
Lastings, 46
Lawn; see White Lawn,104
Lawns, Dyed; see Dyed
Lawns,
29
Leas, 46
Leather Cloth, 46
Leno, 46

38. Leno Brocades, Dyed;
see Dyed Leno
Brocade,
29
Liberty, 47
Linen Cambric; see
White Cambric,
103
Linen, Tests for; see
Tests for Linen,
89
Linen Thread; see
Thread,
90
Linen Yarn, 47
Lingerie, 47
Lining, 47
Linon; see White Lawn,104
Lisle Thread, 47
List; see Selvedge, 81
Loading Worsted and
Woollens,
47
Longcloth, 47
Long Ells (Woollen), 48
Long Stick, 48
Loom State; see Grey,39
Louisine, 48
Lustre Dress Fabrics,48
Lustre Orleans; see
Orleans,
57
 
M.
Maco, 49
Madapolams, 49
Madras, 49
MadrasGingham, 49

39. Madras Gingham, 49
Madras Handkerchiefs,49
Make; see Reed and
Pick,
71
Maline, 49
Market Descriptions of
Standard Cloth,
50
Marl, 50
Marquisette, 50
Matelassé, 50
Matt Weave, 50
Medium Cloth
(Woollen),
50
Mélange, 50
Mélanges (Yarns); see
Coloured Woollen
and Worsted Yarns,
15
Melton, 51
Mercerised Cotton, 51
Mercerising, 51
Merino, 51
Mesh Underwear, 52
Messaline, 52
Mexican; see T-Cloth,87
Milled Finish; see
Schreiner Finish,
80
Millerayes; see
Grosgrain,
40
Mixed Cloths; see
Union Cloth,
95

40. Mixed Dyeing; see
Cross-dyed,
20
Mixture Yarn, 52
Mixtures (Yarns); see
Coloured Woollen
and Worsted Yarns,
15
Mock Leno, 52
Mock Seam, 52
Mohair, 52
Mohair Beaver Plush,52
Mohair Brilliantine, 52
Mohair Coney Seal, 53
Mohair Sicilian, 53
Moiré, 53
Moleskin, 53
Mottles, 53
Mousseline de Soie, 53
Mule-twist Yarn, 53
Mull, 54
Mungo and Shoddy, 54
Muslin; see White
Muslin,
105
 
N.
Nainsook, 54
Nankeen, 55
Nankeen; see Galatea,38
Nankeen, Chinese
Customs Definition
of,
56
Native Cotton Cloth;
seeNankeen,
55

41. see Nankeen,
Native Cotton Cloth;
see Unclassed Native
Cotton Cloth (China),
94
Net Silk Yarn; see Silk
Yarns,
85
Noils, 57
Nominal; see Actual, 1
 
O.
Ombré, 57
Opera Hose, 57
Organzine, 57
Orleans, 57
Ottoman, 57
Outsize, 57
Oxford, 58
Oxford Shirting, 58
 
P.
Padded Back Linings,58
Pad-dyeing, 58
Panne, 59
Panung, 59
Panama Canvas, 59

42. Papoon, 59
Paramatta, 59
Pastel, 59
Pastille, 59
Peau de Cygne, 59
Peau de Soie, 59
Pekiné, or Pekin Stripes,60
Pepperell Drill, 60
Pepperell Drill; see Grey
Drills,
39
Percale, 60
Percaline, 60
Persian Cord, 60
Pick, 60
Piece Goods, 60
Pile Fabrics, 60
Pile Weave, 61
Piqué, 61
"P.K.", 61
Plain, 62
Plain Velvet (Cotton),62
Plain Velveteen (Cotton),62
Plain (or Homespun)
Weave,
62
Plated, 62
Plissé, 62
Plumetis, 63
Plumety; see Plumetis,63
Plush, 63
Plush of Silk mixed with
other Fibres,
63
PlushVelveteen 63

43. Plush Velveteen, 63
Pointillé, 63
Pompadour, 63
Poncho Cloth, 64
Pongee, 64
Pony Skin, 64
Poplin, 64
Print Cloth; see Printers,70
Printed, 65
Printed Balzarines, 65
Printed Calico, 65
Printed Cambrics, 65
Printed Chintzes, 66
Printed Cotton Drill, 66
Printed Cotton Italians,66
Printed Cotton Lastings,66
Printed Crapes, 67
Printed Crimp Cloth,67
Printed Furnitures, 67
Printed Lawns, 67
Printed Leno, 67
Printed Muslin, 68
Printed Oxford; see
Oxford Shirting,
58
Printed Reps, 68

44. Printed Sateens, 68
Printed Satinets, 68
Printed Sheetings, 68
Printed Shirtings, 69
Printed T-Cloth, 69
Printed Turkey Reds, 69
Printed Twills, 69
Printed Velvet (Cotton),69
Printed Velveteen
(Cotton),
69
Printed Warp; see Warp
Print,
99
Printers, 70
Pure Silk Plush, 70
Pure Silk Velvet, 70
 
R.
Raised Back Cloths, 70
Raised Cotton Cloth,70
Ramie, Rhea, China
Grass,
71
Ratine, 71
Rattine; see Ratine, 71
Rattinet; see Ratine, 71
Rayé, 71
Reed and Pick, 71
Regatta Twill; see
Galatea,
38
Regular Twill; see Twill
Weave,
93
Rembrandt Rib, 72
Remnant;seeFents 34

45. Remnant; see Fents, 34
Rep, 72
Resist or Reserve
Printing,
72
Reversible Cretonnes,72
Rhea; see Ramie, 71
Rib, 73
Rib Crape Effect, 73
Richelieu Rib, 73
Right and Wrong Side of
Fabrics,
73
Ring-spun Yarn, 73
Robes, 74
Russian Cloth (Woollen),74
Russian Prints, 74
 
S.
Samples and their
Classification,
74
Sateens, 79
Satin, 79
Satin Drill, 80
Satin Weave, 80
Satinet, or Satinette, 80
Satin faced Velvet; see
Panne,
59
Schreiner Finish, 80
Scribbled, 81

46. Seamless, 81
Seamless Bags, 81
Seersucker; see
Crinkle, or
Seersucker,
20
Selvedge, 81
Serge (Cotton), 82
Sett; see Reed and
Pick,
71
Sewing Thread; see
Thread,
90
Shadow Cretonne, 82
Shantung, 82
Sheeting, 82
Sheetings, American;
see American
Sheetings,
2
Sheetings, Dyed; see
Dyed Sheetings,
31
Sheetings, Grey; see
Grey Sheeting,
39
Sheetings, White; see
White Sheetings,
105
Shirtings, 83
Shirtings, Dyed; see
Dyed Shirtings,
31
Shirtings, Grey; see
Grey Shirting,
40
Shirtings, White; see
White Shirtings,
105
Short Stick, 83
Shot, 83
ShotSilks;seeGlacé 38

47. Shot Silks; see Glacé,38
Sicilienne, 83
Sifting Cloth; see
Étamine,
33
Silence Cloth, 83
Silesia, 83
Silk Beaver, 83
Silk Gingham, 84
Silk Mull, 84
Silk Plush; see Pure Silk
Plush,
70
Silk Pongee, 84
Silk Seal (Cotton Back),84
Silk Velvet; see Pure
Silk Velvet,
70
Silk Yarns, 85
Silver Seal; see Mohair
Coney Seal,
53
Singles; see Yarn,
Cotton, Grey or
Bleached,
111
Sliver, 85
Soft Waste; see Waste
and Flocks,
100
Spanish Stripes,
Cotton,
86
Spanish Stripes,
Woollen,
86
Spanish Stripes, Wool
and Cotton,
86
Split Foot, 86

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