Salt aktif süzgeçler
Active only filters
Yazar: HACER ATAR YILDIZ
Danışman: PROF. DR. ALİ TOKER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Elektronik Mühendisliği Bilim Dalı
Derece: Doktora, 2015
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

Özet:
Bugüne kadar "salt aktif süzgeçler" başlığı altında yapılan birçok devre, kompanze
edilmiş işlemsel kuvvetlendirici ve OTA elemanları kullanılarak gerçekleştirilmiştir.
İşlemsel kuvvetlendiricinin kompanzasyonu için kullanılan kapasitenin pasif bir
eleman olması nedeniyle, şimdiye kadar literatürde sunulan devrelerin "salt aktif"
tanımına tam olarak uygun oldukları söylenemez. Bu çalışmada harici veya tümdevre
kapasitelerinin hiçbirisi kullanılmadan sadece aktif elemanların iç kapasiteleri
kullanılarak süzgeç devrelerinin nasıl gerçekleneceği ortaya konulmuştur.
Temel analog işaret işleme yapı taşlarından olan aktif süzgeçlerin tümdevre
gerçekleştirilmesindeki en önemli sorunlardan biri, tümdevre kapasitelerin kırmık
üzerinde kapladığı alandır. Bu olumsuz durum daha büyük zaman sabitli, daha büyük
değerli kapasite kullanımını gerektiren alçak frekans süzgeçlerinde daha da kritik
hale gelmektedir.
MOS transistorun geçit kapasitesinin kapasite yoğunluğu, poli arası veya poli metal
arası tümdevre kapasitelerinin yoğunluğuna göre daha büyük olmaktadır. Ayrıca
gene MOS geçit kapasitesi, tümdevre kapasiteleri kadar doğrusal davranışa sahiptir.
Bu tezde, tümdevre süzgeçlerinin kırmık üzerinde daha düşük alan kaplayarak
gerçeklenmesi amacıyla, bunların tümdevre kapasiteleri yerine MOS geçit
kapasiteleri kullanılarak nasıl gerçeklenebileceği ve bu gerçeklemelerin getireceği
avantajlar ortaya konulmuştur. Bu doğrultuda harici pasif eleman kullanmadan
istenilen süzgeç fonksiyonunu gerçekleyen salt aktif süzgeçlerin gerçeklenmesine
yönelik yeni devre topolojileri önerilmiştir. Bu elde edilen devrelerin, harici pasif
elemanlar ile gerçekleştirilen devrelere göre tümdevre üzerinde daha düşük alan
kapladığı görülmüştür.
Öte yandan, tezde verilen salt aktif süzgeçlerin sentezinde MOS transistorun en
büyük iç kapasitesi olan geçit kapasitesi kulllanılmış olduğundan, dinamik
davranışları parazitik kapasitelerin etkilerden daha az etkilenmekte, bunlar klasik
süzgeçlere göre yüksek frekanslı çalışmaya çok daha uygun olmaktadırlar.
Tezin ikinci bölümünde, düşük frekanslı süzgeçlerin tümdevre üzerinde kapladığı
alanı düşürmek amacıyla dört farklı devre tasarım teknikleri önerilmiş, ve
tümleştirilebilen düşük frekanslı süzgeç devreleri elde edilmiştir.
Bu doğrultuda çok geniş bir frekans bölgesinde ayarlanabilen temel süzgeç
fonksiyonlarını gerçekleyen devreler elde edilmiştir. Önerilen yöntemler sayesinde
büyük boyutlu transistorlar kullanmaya ihtiyaç duymadan, 1.8MHz'lik integratör
tabanlı bant geçiren salt CCCII süzgeç devresi, 3MHz'lik birinci derece salt
MOSFET tümgeçiren devre ve 24MHz'lik ikinci derece bant geçiren süzgeç
devreleri elde edilmiştir. Benzetim sonuçlarıyla da bu devrelerin uygulanabilirliği
gösterilmiştir.
Önerilen devre tasarım teknikleri kullanılarak gerçekleştirilen salt aktif süzgeçlerin 
etkin kullanım alanına sahip olduğunu göstermek için, 4MHz'lik birinci derece
tümgeçiren süzgeç devresi önce harici kapasiteler kullanılarak MOSFET-C süzgeci
olarak, daha sonra tezde önerilen yöntemlere uygun olarak salt MOSFET süzgeci
olarak gerçeklenmiştir. Devrelerin serimleri çizilmiş ve önerilen yöntem sayesinde
%81 oranında bir alan tasarrufu sağlandığı gösterilmiştir.
Sadece düşük frekanslı çalışma için kullanılan yöntem sayesinde değil, salt aktif
yapıdaki devrelerin kullanılmasıyla da alan tasarrufu sağlanmıştır. 37MHz'lik kesim
frekansındaki devre için de %40'lık bir alan tasarrufu sağlanmıştır.

Abstract:
Active filters have always received attention as an essential building block of many
analog signal processing applications. One of the important factors in realization of
active filters is the passive elements used in filter design. From this point of view, in
the filter circuits called as active-C and active-R, the compansated opamp transfer
function is used as an ideal integrator circuit. In the large part of active-C filter, filter
parameters can be adjusted by using dc voltage or current values. One of the most
important restrictions in this type of filter circuits is that passive elements occupy too
much space on the chip area. On the other hand, active filter topologies are obtained
also by using resistive voltage divider in the feedback paths of active-R filter. As it is
known that, the important restriction in active-R filter is that circuit parameters can
not be set electronically.
The first introduced active-only filters in the literature are based on using opamp as
an integrator such as active-R filters. Voltage divider function is aimed to realize by
using tansconductance element (OTA) instead of using resistances in the feedback
paths. In this way, it is possible to adjust circuit parameters electronically by
transconductance gains of OTAs in active only filters.
On the other hand, it should be also noted that, the compansation capacitance of
opamp used in active only filters is a passive element and the integration design
realized by using this capacitance is based on Miller theory. Therefore, these circuits
should not be defined as active only filters actually. These circuits, which should be
considered as pseudo active-ony filters entail the basic restrictions, e.g. limited highfrequency
performance, large chip area, limitations in slew rate capability.
In this thesis, in order to tackle these problems, a "real" active-only integrator and a
"real" active-only filter based on this integrator are presented. The integrator pole
comes from the intrinsic capacitances and resistances of a current controlled current
conveyor (CCCII), although the active element could be replaced with any
transconductance amplifiers offering electronically tunable parameter.
This type of filters offers two obvious advantages over the conventional active-R
filters: i) The filter is free from slew-rate limitation, hence offers better highfrequency
performance compared to the conventional active-only filters which
employs opamps. ii) The removal of external capacitors significantly reduces the
chip area occupied by the filter.
However, this approach also entails some practical implementation issues: i) the time
constants turn out to be very large, making the filter design challenging at relatively
lower frequencies, ii) some of the intrinsic capacitances due to involved active
devices suffer from large tolerances, iii) some of the intrinsic capacitances are
nonlinear.
In order to address these issues, we considered and discussed possible circuit design 
techniques, which, in turn, have lead us to a new active-only integrator capable of
operating at high-frequencies and providing electronically adjustable time constant
with wide tuning range.
The integration frequency of the proposed integrator is determined by the intrinsic xterminal
resistance and z-terminal capacitor of a current controlled current conveyor
(CCCII), the multiplication factor of a capacitance multiplier and the loss factor of a
voltage divider. To illustrate the usefulness of the proposed integrator, a secondorder
filter based on the well-known two-integrator loop filter topology is considered
and simulation results using SPECTRE in the CADENCE design tool verifying the
proper operation of the circuit are provided.
In this thesis, filters called as MOS-only filters, which do not employ any external
passive components, neither capacitors nor inductors, but rather which exploit the
intrinsic capacitors of the MOS transistors are also studied. These circuits provide
very useful advantages from IC realization viewpoint such as: i)low occupied chip
area as a result of using as reactive component MOS capacitances with higher
capacitance density compared to those of intentional, external capacitors. ii) these
filters are capable of operating at high frequencies since most significant parasitic
capacitances are taken into account during the synthesis procedure. iii) electronic
tuning property of the important filter parameters, since the design of these circuits
relies on the device transconductances which can be controlled by bias currents.
On the other hand, allpass filters are very useful blocks for realizing phase shifters,
phase equalizers, high-Q bandpass filters, quadratic oscillators with improved
frequency stability and even for implementing arbitrary magnitude filters designed
with classical approximations such as Butterworth, Chebyshev and Elliptic
characteristics. While many active RC allpass filters are proposed in the literature, to
the best of author's knowledge, only one single MOS-only allpass filter realization
exists in the literature. However, this circuit realizes only first-order transfer
functions, thus lacks the possibility to realize complex poles and zeros
In this thesis, a simple filter topology that can be used to implement both first- and
second-order MOS-only allpass filters is proposed. The filters derived from this
topology provide all the advantages mentioned above. Unlike to the other MOS-only
allpass filter, the proposed first- and second-order filters can also be considered as
building blocks for the realization of nth-order allpass filters, since filters of any
order can be realized by cascading first- and second-order stages. Moreover, the
proposed MOS-only allpass filters offer inherently very accurate magnitude and
phase characteristics at very high frequencies.
Simulation results performed using Spectre simulator in Cadence design environment
and experimental results verifying the proper operations of the allpass circuits are
provided. The second-order effects, as well as some remedies for these are also
discussed.
In this thesis, a simple MOS-only second-order filter which simultaneously realizes
bandpass and lowpass type characteristics is also proposed. The filter is based on a
general RLC prototype circuit and provides all the advantages mentioned above.
The main nonidealities of the filter are studied and its proper operation is verified
trough Spectre simulation results.
However, MOS-only active filters suffer from an inherent low frequency limitation.
This fact can be intuitively justified by noting that filters' natural frequencies are 
proportional to gm/Cgs, where gm is the device transconductance and Cgs is the gate
source capacitance. Therefore, for achieving low natural frequencies, either the value
of gm, i.e. MOS biasing current should be decreased or the value of Cgs should be
increased. However, MOS biasing current cannot be decreased below a specific
value at which the transistor enters the subthreshold regions where filter suffers from
large distortion due to the governing transistor's exponential nonlinearity. On the
other hand, to increase the value of Cgs implies the use of large devices that increase
the chip area occupied by the circuits.
In order to address this issue, two modification techniques allowing the derivation of
MOS-only filter which allow extension of the operating frequency towards lower
frequency region are proposed. The first method, based on using cross coupled MOS
transistor pairs, while the second method relies on modifying the given filter by
using capacitance multipliers.
Detailed simulations results of the filters modified according to the proposed
techniques are also provided in order to verify the usefulness of the theoretical
approach.
Finally, in order to demonstrate the usefullness of the approach, a 4MHz first-order
allpass filter is first realized using a classical MOSFET-C filter topology with
integrated capacitors and then using a MOSFET-only filter, that is obtained
according the proposed methods. From the filters' layouts, it is found that an area saving of 80% is achieved using the proposed technique.