Akım Taşıyıcılar Ve Akım Taşıyıcı Tabanlı Aktif Elemanlarla Transfer Fonksiyonlarının Gerçekleştirilmesi

Abstract

Son zamanlarda, akım taşıyıcılar ve akım taşıyıcı tabanlı aktif elemanlarla ilgili araştırmalar sürdürülmektedir. Bu tezde, işaret akış diyagramlarından yararlanılarak, akım taşıyıcılar veya akım taşıyıcı tabanlı aktif elemanlarla gerilim ya da akım transfer fonksiyonlarının gerçekleştirilmesi konuları ele alınmıştır. Akım veya gerilim transfer fonksiyonlarının akım taşıyıcılar, CFCCII'ler ve birim kazançlı elemanlarla gerçekleştirilmesine ilişkin sentez yöntemleri önerilmiştir. Ele alınan gerilim veya akım transfer fonksiyonlarına ait uygun işaret akış diyagramlarının elde edilmesine ve bu diyagramlardan da aktif-RC devrelerine geçişe dayanan bu yöntemler uyarınca alçak duyarlıklı devreler gerçekleştirilmiştir. Yöntem uyarınca, gerçekleştirilen devrelerin eleman değerleri transfer fonksiyonlarının katsayılarınca belirlenmektedir. Ayrıca, önerilen bu genel yöntemlerle yüksek dereceli filtrelerin gerçekleştirilmesi de mümkün olmaktadır.

Recently, in active circuit design the current conveyors and current conveyor-based active elements attracted certain attention and a great deal of work has been reported on the synthesis of the voltage and current transfer functions (from nowon voltage and current transfer functions will be named transfer function for the sake of briefness) realized with these elements. However, until now no general way of synthesis has been proposed. Moreover, almost all of the work done deals with second order transfer functions. In this thesis, a general synthesis method based on signal flow graphs is given. This method also works for higher order functions. The first generation current conveyor (CCI) was introduced by Smith and Sedra in 1968. At that it wasn't clear what advantages the current conveyor offered over the operational amplifier. Moreover, the electronics industry was just beginning to focus its efforts on the creation and application of generation of monolithic operational amplifiers. Without clearly stated advantages, the electronics industry lacked the motivation to develop a monolithic current conveyor realization. Now the analog designers are discovering that the current conveyor offers several advantages over the operational amplifiers. CCI had distortion and accuracy limitations due to base current errors and output impedance restrictions. So, in 1970 Sedra and Smith presented a more useful element which was named second generation current conveyor (CCII). The second generation current conveyor whose circuit symbol is given in Fig. 1 can be defined by the following constitutive relations; I, In this equation, (+) sign refers to positive current conveyor that is denoted by CCII+, whereas (-) sign refers to negative one denoted by CCII-. XI Fig. 1 Second generation current conveyor Terminal y exhibits an infinite input impedance. The voltage at x follows that applied to y, thus x exhibits a zero input impedance. The current supplied to x is conveyed to the high-impedance output terminal z. CCIIs have wide application areas such as the realisation of controlled sources, impedance converters, impedance inverters, gyrators, oscillators, and various analog computation elements like current amplifier, current differentiator, current integrator, current summer and weighted current summer. A great deal of work has been reported on the realisation of the voltage-mode and current-mode filters. A pair of five terminal active current conveyor (CFCCII) which contains current follower attached to plus type second generation current conveyor was introduced by Ikeda and Tomita in 1992. CFCCII, whose circuit symbol is given in Fig.2 can be defined by the following constitutive relations; I 0 0 1 0 0 k, 0 ±k, vx<^ Vv 0- x z CFCCII y o ^-oV, -o v0 Fig.2 CFCCII In this equation, (+) sign refers to positive-type CFCCII that is denoted by CFCCIIP, whereas (-) sign refers to negative-type CFCCII that is denoted by CFCCIIn. ki is the current conversion factor. Xll X t z y "X" £> Fig. 3 Unity-gain cell As the unity-gain cells obtained further importance since they are appropriate to high frequency applications, in this thesis the method will also be given for these. If Y terminal of the current conveyor is grounded, in this case it behaves like a unity-gain current follower. When a unity-gain voltage buffer attached to a current follower is named unity-gain cell. In this thesis, synthesis of the transfer function which contains CCII or CCII based active elements such as CFCCIIs and unity-gain cells have been examined. A signal flow graph is composed of nodes and directional branches which are related to linear, algebric and independant equation system. In the signal flow graph method the following steps are followed;. Subnetworks are chosen. Analyzing the chosen subnetworks, the subgraph are obtained.. Transformation rules are determined from the subnetworks and subgraphs.. A signal flow graph which is composed of the subgraphs as obtained before is drawn from the given transfer function.. Active circuit is obtained from this signal flow graph using the transformation rules. Due to the method proposed the element values are expressed in terms of the transfer function coefficients. In this thesis in the second section, the reasons of introducing current conveyor concepts, their historical progress, the constitutive relations of the first and second generation current conveyors, advantages of the second generation current conveyors Xlll over the OAs and OTAs, nonidealities of the CCII and the physical realisations of it are given. In the third section, signal flow graph method for the realisation of voltage-mode and current-mode transfer functions using current conveyors are given. First, signal flow graph method is applied for realizing voltage transfer functions using only plus-type current conveyors, and a circuit that realized the general nth-order voltage transfer function is given. As an example third order Butterworth type lowpass transfer function is realized using equal valued capacitors with this method. Sensitivity analysis is carried out. Efects of the nonidealities of CCIIs are examined. The amplitude characteristic of this filter is obtained using SPICE simulation program. And the limitations of the input signal level is examined for this example. Then, signal flow graph method is applied for realising current transfer function using current conveyors, and a circuit that realized the general nth-order current transfer function is given. As an example third order highpass current filter is realized. Sensitivity analysis is carried out. Efects of the nonidealities of the CCII are examined. The amplitude characteristic of this filter is obtained using SPICE simulation program. In the fourth section, a pair of four terminal active current conveyor (CFCCII) which contains current follower attached to a plus-type second generation current conveyor is introduced. Signal flow graph method is applied for the realisation of lowpass filters and a circuit which realized nth-order current-mode lowpass filter was given. As an example third order lowpass current filter using equal valued capacitors is realized. The sensitivity analysis is carried out. The amplitude characteristic is obtained using SPICE simulation program. Then, giving aditional subnetworks and modifiying the subnetworks which are given before for the realization of the lowpass transfer function, the method generalised to the realisation of current-mode transfer functions. As an example third order allpass transfer function using equal valued capacitors is realized. The sensitivity analysis is carried out and the amplitude and phase characteristic of this filter is obtained using SPICE simulation program. Furthermore, a second order universal current-mode filter which realizes lowpass, bandpass, highpass filters simultaneously on the same structure is proposed using only three CFCCIIP. The notch filter can simply be realized by modifiying the circuit, it does not require additional active elements. Sensitiviy analysis of this circuit is carried out. The amplitude characterisics of the realized filters are obtained using SPICE simulation program. In the fifth section, signal flow graph method is applied for the realisation of voltage- mode and current-mode transfer functions using unity-gain cells and two circuits xiv which realized general second-order voltage-mode and current-mode transfer functions are given. Sensitivity analysis of these circuits are carried out. If a unity-gain cell is composed of the plus-type current conveyor, it is realized with a commercially available component namely AD844. Then, two signal flow graph for the relisation of the allpass voltage transfer functions are presented and the circuits that realizes nth-order allpass (also, realization is possible for lowpass, bandpass and highpass) voltage transfer function by using commecially active components (AD844) are given. As an example, third order allpass voltage transfer function is realized. Sensitivity analsis of this circuit is carried out. The amplitude and phase characteristics of this circuit is obtained using SPICE simulation program.