Band geçiren aktif OTA-C filtrelerinin quad ve kaskad yöntemi kullanılarak tasarımı ve duyarlılık analizi
Design of bandpass active OTA-C filter using cascade and quad methods and sensitivity analysis
- Tez No: 68905
- Danışmanlar: PROF. DR. ALİ NUR GÖNÜLEREN
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 139
Özet
Bu çalışmanın amacı, sadece OTA (Operational Transconductance Amplifier, İşlemsel Geçiş Kuvvetlendiricisi) ve kapasite elemanları kullanılarak, quad ve kaskad tasarım yöntemleri ile yüksek dereceden aktif filtre tasarımı ve quad ve kaskad yöntemleri ile tasarlanan bu filtrelerin duyarlık açısından karşılaştırılmasının yapılmasıdır. Literatürde OTA ve kapasite elemanları ile oluşturulmuş çeşitli biquadlar bulunmaktadır.OTA tümleşik devre teknolojisine uygun olması, iletkenlik değerinin kolaylıkla ayarlanabilmesi, yüksek frekans davranışının iyi olması nedenlerinden dolayı aktif filtre tasarımı için avantajlı bir eleman niteliğindedir. Filtre tasarımında, son yıllarda OTA ve kapasite elemanları, işlemsel kuvvetlendirici ve RC elemanlarından çok daha tercih edilir duruma gelmiştir. Filtreler ve yaklaşıklık tipleri kısaca ele alındıktan sonra, tasarım yöntemlerinden kaskad ve quad tasarım yöntemleri açıklanmış ve band geçiren filtre fonksiyonunun elde edilmesi ve elde edilen transfer fonksiyonu ile quad ve kaskad tasarım denklemlerinin bulunması ele alındıktan sonra OTA elemanı tanıtılmakta, OTA'ya ilişkin ideal ve pratik modeller verilmekte ve 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. Daha sonra duyarlık konusunda temel kavramlar ve devreleri duyarlıklarına göre karşılaştırmak için bazı duyarlık ölçüleri verilmiştir. Duyarlık analizinde, devre parametrelerinin istatiksel özelliklerini içeren, çok parametreli duyarlık ölçüsünden yararlanılmıştır. Buna göre, OTA-C tabanlı kaskad ve quad tasarım yöntemleri kullanılarak gerçeklenen filtrelerin duyarlık analizi yapılmıştır. Ek A'da filtrelerin duyarlık hesaplamalarının yapıldığı çeşitli örnekler, Ek B'de ise duyarlık hesaplamaları için, bir bilgisayar programı QBASIC dili kullanılarak geliştirilmiştir. vı
Özet (Çeviri)
In electronic circuits, filters are widely used. Filtering in the general sense is a selection process. The output of a filter is then a selected subset of the input. In electrical filtering, the object is to perform frequency-selective transmisson. When a signal is applied to the input of a filter network, a certain band of frequencies is emphasized at the output and another band or bands of frequencies are highly attenuated. Filters are typically categorized according to the functions they perform, e.g., low-pass, high pass, band-pass, band-reject and all-pass. From 1920 to the latter 1960s the majority of voice-frequency filters were realized as discrete RLC networks. However, it was was understood that size and eventual cost reductions could potentially be archived by replacing the large costly inductors with active networks. Then designers started to use the active-RC networks,which were composed of operational amplifiers.Opamps have been used in the active filter design for many years, because they are developed and cheap circuit elements.But the opamps have not a good high frequency performance and this caused to come out more suitable gain devices such as OTAs(Operational Transconductance Amplifier) In filtering applications, it is desirable to have a circuit which presents orthogonal tunability of its important parameters. In addition, it is also advantageous that such circuits should be realizable in a standart monolithic technology. With the introduction of OTA-C circuits, using OTA as the active device, along with capacitors, a class of circuits has become available for fabrication in MOS technology and simultaneously present wide range electronic tunability of its parameters. In such filters, the transconductance gain (gm) is linearly tuneable with bias voltage/current over many decades, which lends electronic tunability to circuit parameters.The high frequency performance of OTAs is better than Opamps.lt seems that the use of circuits composed of OTAs and grounded capacitors in the high frequency continuous-time monolithic analog filters is extremely advantages. Several different design methods for high order active filters have been reported in the literature to realize the transfer function of the form; VllThese 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 direct method is not advisable to realize the transfer function H(s) because it isn't a practical method and leads to poor sensitivity In the cascade realization, a high order filter is realized by cascading two or more active biquadratic sections. This method is widely used in industry because cascade filters are relatively straightforward to design and tune. The sensitivity performance of the cascade design is good in the stopband, but poor in the passband. In the inductance simulation approach, an inductance is simulated by an active-RC network such as a capacitor-loaded gyrator; thus, classical lossless passive-ladder filter realizations can be transformed directly into active filter realizations. The sensitivity behaviour of these circuits depend on the quality of the opamps used. The aim of the FDNR method is to realize inductorless filter circuits as same as the inductance simulation. Multiloop feedback approach is similiar to the cascade method and splits the T(s) into second-order biquads.Its most advantageous side is that it provides high- order filter realizations which have better passband sensitivity compared to those realized with the cascade method. In this thesis, design of high order OTA-C filters are presented using the quad configuration. This is a special application of Generalized Multiloop-feedback filters, and has many advantages. It is modular, economic and easy to tune. Filter circuits that are realized by the quad method are less sensitive than ones that are realized using the other methods.lt can be applied to symmetrical or unsymmetrical filters. In the study, design of bandpass active OTA-C filters using quad and cascade method is realized for Butterworth, Chebyshev and Elliptic approximations. In section 2, filter classifications and techniques for approximating ideal filter transmission characteristics are considered.Firstly the transfer function of lowpass filter is found by using the given properties and then the frequency transformations are made according to the filter type and that is examined in section 3. In section 4, cascade and quad method are generally considered. Figure 1. shows the schematic for a cascqde of N noninteracting filter sections with transfer functions Tj. viaR« ÖT. ı--------a- VP *2.__ __\ o. il z z ol i: o2 S3 Z¦ V“7Tn_,»1N & *L «N”» -cN. Figure 1. Schematic for a cascade of N noninteracting filter sections with transfer functions Tj The transfer function of a cascade realization is; v N V; (2) ' 7 = 1 Thus, the transfer function for a cascade of sections Tj is simply the product of the individual section transfer functions. Basic quad topology contain two second order biquadratic blocks and a feedback path as shown figure 2. V: -f TQ(s) -o = O©- V0 V, T,(s) T2(s) -o V, u Figure 2. Basic Quad Topology The transfer function of the circuit shown in figure 2 can be written as; Tö(s) = T|(s).T2(s) l + /.T,(s).T2(s) where,,. b.2 s*“ +b.i s + b/0 T,.(s) = -^--------,J-------'¦*-,i=l,2 s”+ a,, s+a/0 (3) (4) IXTo realize a high order transfer function given with the equation (1), it is split into 4th order transfer functions of the form (3).Then, these 4th order quadratic functions are factored into two biquadratic transfer functions given with the equation (4)-[17] In section 5, the calculation of the quad and cascade design equations for bandpass filters are examined according to the given bandpass spesificationş using Butterworth, Chebyshev and Elliptic approximations. In section 6, OTA component and its models are considered. OTA is basically a voltage controlled current source as seen from Figure 3. L-jJi,1“ 8”» V*' i V ^gm(V*-V) Figure 2. OTA a) Circuit Symbol b) Equivalent circuit of ideal OTA The transconductance gain, gm, is assumed proportional to Icmi. The proportionality constant k is dependent on temperature, device geometry and the process.The output current is given by, iQ = smiv+-y~) (5) In section 7, the well-known dynamic range consideration of quad filters is applied to bandpass OTA-C Quad filters. Determination and distribution of gain factors of the biquads are also very important to maximize the dynamic range.And new feedback factors are calculated. The maximum input voltage level for bandpass filters is determined in section 8.This is important to not causing clipping and slew- rate limiting. Section 9, gives the various definitions of sensitivity as used in the literature. Over the years, a number of sensitivity measures have been employed. Among these, the statistical multiparameter sensitivity measure, is particularly useful as it realistically accounts for the element tolerances and the correlation between elements and the purpose of this thesis is, to give a general sensitivity analysis for OTA-C Quad filters are examined using statistical multiparameter sensitivity measure. In the Appendix A, some examples are given about sensitivity calculation and these calculations are made by the computer program, which was evaluated using Quickbasic language and this program is given in the Appendix B.
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