Alçak geçiren ve band geçiren aktif OTA-c filtrelerinin quad ve kaskad yöntemi ile tasarımı
Design of lowpass and bandpass active OTA-c filters using quad and cascade methods
- Tez No: 66585
- Danışmanlar: PROF. DR. ALİ NUR GÖNÜLEREN
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Filtreler, Kaskadlar, OTA, Filters, Cascades, Operational transconductance amplifier
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Elektronik ve Haberleşme Mühendisliği Bilim Dalı
- Sayfa Sayısı: Belirtilmemiş.
Özet
OTA (Operational Transconductance Amplifier) monolitik tümleştirme tekniği ile kolayca gerçeklenebilir, elektronik olarak ayarlanabilir ve tasarım kolaylığı sağlar. Yüksek frekans performansları işlemsel kuvvetlendiricilerden çok daha iyidir. OTA elemanı ile oluşturulan filtrelerde OTA iletkenlik kazancı tasarım parametresi olarak kullanılabilir. Ayrıca OTA, CMOS teknolojisine uygun bir elemandır. Bir ucu topraklı kapasite elemanı da CMOS teknolojisi ile kolayca gerçeklenebilir ve OTA ile beraber uyumlu bir eleman çifti oluşturur. Filtre tasarımında,son yıllarda OTA ve kapasite elemanları sayılan bu nedenlerden dolayı, işlemsel kuvvetlendirici ve RC elemanlarından çok daha tercih edilir duruma gelmiştir. Bu çalışmada, sadece OTA ve kapasite elemanları kullanılarak, quad ve kaskad tasarım yöntemiyle, yüksek dereceden aktif filtre tasarımı amaçlanmıştır. Filtreler ve yaklaşıklık tipleri kısaca ele alındıktan sonra alçak geçiren ve band geçiren filtre transfer fonksiyonları Butterworth, Chebyshev ve Eliptik yaklaşıklık tipleri için ayrı ayrı elde edilmiştir. Daha sonra quad yöntemi genel bir biçimde anlatılmıştır. Genel quad yöntemi yardımıyla, alçak geçiren ve band geçiren filtreler için quad ve kaskad denklemlerinin bulunması ayrıntılı bir biçimde ele alındıktan sonra OTA-C elemanlarıyla oluşturulan biquadratik devreler incelenerek, kullanılan alt devrelere ilişkin kazanç değerleri devrenin dinamik davranışını iyileştirecek biçimde belirlenmektedir. Ayrıca tasarlanan OTA-C filtrelerinin girişine uygulanabilecek maksimum gerilim değerinin hesaplanması için izlenecek yol anlatılmıştır. Ek A' da çeşitli tasarım örnekleri ve bu örneklerde elde edilen filtreler için frekans cevabı karakteristikleri Micro Cap analiz programı yardımıyla verilmektedir. Ek B'de ise alçak geçiren ve band geçiren filtrelerin tasarımını quad ve kaskad yöntemi ile gerçekleştiren bir bilgisayar programı verilmektedir.
Özet (Çeviri)
In electronic circuits, filters are widely used. Filters are circuits which select the electrical signals according to their frequencies. At the beginning of this century, filters were realized using resistors, inductors and capacitors as basic components. In filter realization, inductors caused a lot of problems. These problems is that inductors are very large components and their production and tuning are difficult. In the 1950s, active networks began to take the place of inductors. So, designers begun to use the active-RC filters. Operational amplifiers have been used in the active filter design for many years, because they are developed and cheap circuit components. The operational amplifiers have not a good frequency performances. This is caused to come out more suitable gain devices such as OTAs. High frequency behaviour of Operational Transconductance Amplifiers (OTAs) is better than operational amplifiers (OPAMPs). Furthermore, OTAs provide linear electronic tunability of its transfer gain. For this reason, filter circuits that are realized by using OTAs are more useful than operational amplifiers. The use of circuits constructed with operational transconductance amplifiers and capacitors is potentially advantageous for the realization of high-frequency continuous-time monolithic analogue linear and nonlinear systems. OTA and grounded capacitors are easy to implement in all IC technologies. Grounded capacitors are natural for the simplest single-polynomial process and can absorb many XIcapacitive shunt parasitics. Grounded capacitors are the cheapest linear capacitor in integrated circuits. A grounded capacitor can be implemented as input capacitance of MOS tranzistor. Several different design methods for high order active filters have been reported in literature to realize the transfer function of the form bms +bm,sm~l + +b,s + b0 T(S) = -m- S=L- ! 1 <n (1) v ' sn+anlsn"'+ +a,s + a0 v ' Those methods can be classified into five categories. 1- The direct method 2- Cascade realization 3- Inductance simulation 4- Frequency dependent negative resistor (FDNR) 5- Multiloop feedback topologies (MF) The sensitivity behaviour of the direct method is not good. The obtained circuits are very sensitive to component variations. Cascade and MF topologies are widely used in filter design. Cascade design is commonly used in industry because of the simplicity of the design and ease of tuning. The sensitivity performance of the cascade design is good in stop band, but poor in the pass band. MF topologies utilize subsection of biquad blocks and have lower sensitivity over the pass band than those of cascade design Inductance simulation method is expensive and the realized circuits are not modular. In other words, different designs required very different circuit structures. The main aim of inductance simulation and FDNR method is to realize inductorless filter circuits. The sensitivity performance of these designs depend on the quality of the operational amplifiers used. xiiIn this study, design procedures for high order lowpass and bandpass OTA-C filters are presented using the configuration of quad. Quad configuration, which is a special application of Generalized Multiloop-feedback Filters, has many advantages. Filter circuits that are realized using quad configuration are less sensitive than ones that are realized using the other methods. Quad configuration is general and can be applied to high order symmetrical or unsymmetrical filters. It is easy to tune. It is economic and modular. The realization of quad configuration is easier than all other methods except the cascade method. It does not require feedforward and summation circuits. Using the low sensitivity performance of the quad configuration and the advantages of the OTA-C devices yield suitable filters for many applications. In the thesis, design of lowpass and bandpass active OTA-C filters using quad and cascade method is realized for Butterworth, Chebyshev, Elliptic approximations. OTA-C cascade realizations can be easily obtained using the same procedure, because the cascade realization is a special case of the quad configuration. In section 2, filter classifications and filter approximations types are examined. Transfer functions of lowpass and bandpass filters are obtained for every filter approximation. While this work is realized, firstly the transfer function of prototype lowpas filter is found by using the given properties and then frequency transformations according to the filter type are made. In section 3, quad method are generally considered. Basic quad topology contain two second order biquadratic blocks and a feedback path as shown in Fig. 1. The transfer function of Fig. 1 can be expressed as, t f\ - Tı(s)T2(s) m ^-l + fT^sVT^s) K) where. Xlllk.^+Cw^QJs + w2,) iW (s2+(wpı/Qpı)s+w2pı),i=l,2 (3) TQ(s).s*-»& -f v0 V, T,(s) T2(s) V0 Fig 1. Quad topology In section 4, the method which should be followed to obtain quad and cascade equations for lowpass and bandpass filter whose transfer functions are determined in section 2 is given in details. The resulting T(s) filter transfer function is factored into 4th order transfer functions. With the assumption that radial frequencies and quality factors are equal to each other biquadratic transfer functions and feedback coefficients are determined by using the equation (3) In section 5, OTA component and its models are considered. OTA is basically a voltage controlled current source as seen from Figure 2. 4, ic y+C Jo gn oV0 ^gn^-V) Figure 2. OTA a) Circuit symbol b) Equivalent circuit of ideal OTA The transconductance gain, gm, is assumed proportional to Icnti. The proportionality constant k is dependent on temperature, device geometry and the process. The output current is given by, Io=gm(V+-V) (4) XIVThe filter may not be operate properly because many practical OTA have some problems. The problems are finite input and output impedance's. Bipolar OTAs can not operate linearly for the input voltages greater than certain values. In other words, they have limited dynamic range. Bipolar and the symmetrical CMOS-OTAs are also given in section 5. Apart from OTA models, four different biquadratic circuit structures is given by comparing with each other. In section 6, each quad blocks are realized by using the known dynamic range consideration of quad filters. Pole-zero pairing and ordering of quad blocks have significant effect on the dynamic range of a high order filter. Determination and distribution of gain factors of the biquads are also very important to maximize the dynamic range. Therefore, gain factors of each biquadratic subcircuits and feedback factors are determined in the way to improve the dynamic behaviour of the active filter. In addition to those, the values of OTA and capacitor components that will be used in the filter design are calculated with the aid of the resulting design equations. The maximum input voltage level is very important to not causing clipping and slew- rate limiting. The output voltage and current of any OTA should not exceed the saturation values for the linear operation of the OTA-C filter. In section 7, the maximum input voltage levels of lowpass and bandpass filters will be determined considering this point. In the Appendix A, Examples of lowpass and bandpass filters and frequency characteristics are given using Micro Cap Analysis program. In the Appendix B, a computer program that uses QUICKBASIC language is given. This program realizes the design of lowpass and bandpass active OTA-C filters by using one of the three approximation. XV
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