Akım taşıyıcılı devrelerin analizi ve sentezi

Abstract

Bu tezde,, işaret akış diyagramlarından yararlanarak, ikinci kuşak akım taşıyıcı elemanları içeren devrelerin, gerilim transfer fonksiyonlarının bulunması ve ger çekleştirilmesi konuları ele alınmıştır. Bu tür elemanların bulunduğu aktif RC-devrelerinin, devreye bakılarak, doğrudan doğruya işaret-akış diyagramlarının çizilmesine, bu diyagramlardan da devre fonksiyonlarının bulunmasına dayanan bir analiz yöntemi verilmiştir. Ayrıca, gerilim transfer fonksiyonlarının akım taşıyıcılarla gerçekleştirilmesine ilişkin bir sentez yön temi sunulmuştur. Ele alınan gerilim transfer fonksiyonlarına ilişkin uygun işaret-akış diyagramlarının elde edilmesine ve bu diyagramlardan da akım taşıyıcılı aktif- RC devrelerine geçişe dayanan bu yöntem uyarınca alçak duyarlıklı devreler gerçekleştirilmiştir. Yöntem uyarınca gerçekleştirilen bir devrenin eleman değerleri uygunlaştırılarak, SPICE analizi yardımıyla, pratiğe uygun devrelerin elde edilmesine çalışılmıştır.

The current conveyor is functionally flexible and versatile active building block. The first-generation current conveyor (CCI) was introduced by Smith and Sedra in 1968. In 1970, Sedra and Smith presented a more useful circuit concept which was named second-generation current conveyor (CCII). The applications of the current conveyors have emerged in recent years, because, at the time of the introduction of the current conveyor, it wasn't clear what advantages the current conveyor offered over the other active elements. Now, it is known that the current conveyor circuit can provide a higher voltage-gain and larger bandwidth than the corresponding operational amplifier circuit, in effect a higher gain-bandwidth- product. Besides, current conveyors (CCII) are an alternative to OTAs (Operational Transconductance Amplifier) in filter applications. Due to absence of resistors in circuit, The filter desig using OTAs is the most suited one for integration purposes, but the performance limitations of OTAs such as poor bandwidths and poor output drive capabilities, restrict the circuit operating performance. CCI Is have higher bandwidths and improved current drive capabilities. The second-generation current conveyor is shown by the block diagram in Fig. 1. Fig. 1 Second-generation current conveyorAnd it is defined by the following terminal relationship. 0 0 0 10 0 0 ±1 0 Terminal y exhibits an infinite input impedance because, the current of terminal y is zero. Voltage of input terminal y is equal to voltage of terminal x also, current of input terminal x is equal to current of output terminal z. Positive and negative signs refer to positive and negative polarity current conveyors (CCII+ and CCII-) respectively. CCIIs are first widely used in application areas such as the relization of controlled sources, impedance converters, impedance inverters, gyrators and various analog computation elements like current amplifier, current differentiator, current integrator, current summer and weighted current summer. A number of circuit topologies have been presented for the current-mode circuits. A great deal of work has been reported on the realization of the voltage transfer functions that are using second generation current conveyors. One of the first works on the realization of the voltage transfer functions using current conveyors is Soliman's circuit that realize the second-order all-pass function with single current conveyor (1973). In 1974, Aronhime has demonstrated the generality of the current conveyor approach for any voltage transfer function using single current conveyor and RC elements. But these circuits haven't offered high input impedance. Then Soliman has presented two realizations of band-pass functions in 1977. Nandi has proposed a third-order low-pass Butterworth filter using equal-valued elements in 1978. Salawu has realized Soliman's first circuit with only four passive components (1980). (vii)In 1982, Pal and Singh have presented a multiple current conveyor all-pass filter structure. This circuit offered high input impedance and controllable voltage gain. Naqshibendi and Sharma ' s improved two band-pass filters which offered high input impedance and adjustable u, Q and gain that are independent of each other (1983). In 1985, Senani has presented a work about high- order filter design based on simulations of FDNR (Frequency Dependant Negative Resistor ) and lossy inductance. Nawrocki and Klein's implementation which realized second-order universal filter with OTAs, has been modified by Toumazou and Lidgey who replaced all the operational transconductance amplifiers by current conveyors and resistors in 1986. In late 1986 Chong and Smith have introduced current conveyor theme which included voltage inversion between the input terminals. These have been named CCII ±2 type current conveyors. The purpose of the voltage inversion was to realize low-pass, high-pass and band-pass filters with independently controllable cj and Q, using single current conveyor. In 1989, Anday and Tek, using signal flow- graphs, have realized general second-order voltage transfer function. In late 1990, Singh and Senani have presented a multifunction active filter configuration employing current conveyors. They have realized second-order low-pass, band-pass, all-pass and notch filters on the same structure. In this thesis, using signal flow graphs, analysis and synthesis of the circuits which consist second-generation current conveyors have been examined. Using the defining equation for the second- generation current conveyor, it can be shown that the subgraph in Fig. 2b correspond to the subnetwork in Fig. 2a. In symbolic representation (+), (or(-)) signs of current conveyors correspond to the signs (+) (or(-) ) of the transmittances in the subgraph shown in Fig. 2b, respectively. (viii)V,o^ CCI1 © ML 1 o V"., "Fi V"°- CCI1 M '.F^ î (o) V> _1-Yn., (b) Fig. 2 (a) CCII subnetwork (b) Associated subgraph According to analysis method, the signal-flow graph can be obtained directly from given circuit by the aid of Fig. 2, and the voltage transfer function can be easily found from this, using Mason's gain formula. Besides, if nth-order transfer function is represented by a suitable signal-flow graph composed of subgraphs in the form given in Fig. 2b, the corresponding circuit realization can be easily found by the use of Fig. 2. The general nth-order voltage transfer function can be given as. n n-i V. a s + a. s +...+ a, s + a o n n-1 1 o V. sn + b,sn + + b,s + b i n-1 1 o This transfer function can be represented by the signal flow graph which is suitable for the realization procedure shown in Fig. 3a. (ix)(a) Î- ıs k ecu © % ecu © [w z -i CClI JT ® $ ecu © 2 25 ecu © Ql/b, l" '" (b) Fig. 3(a) Signal-flow graph of the general nth-order voltage transfer function (b) CCII circuit which realize the general nth-order voltage transfer function It should be noted that this circuit contains at most (3n-2) current conveyors, (n+1) capacitors (n of them being equal) and (3n-l) resistors (n-1 of them being equal). All capacitors are grounded. Furthermore, since the coefficients are directly proportional to conductances and inversely proportional to capacitances, the coefficient sensitivities due to any conductance or capacitance are not greater than one in magnitude. It should be noted that the method can be also applied to the synthesis of transfer functions in which some of the coefficients of the numerator polynomial have negative values. Also, another CCII filter configurations which are different from this can be derived in similar way using different signal flow-graph models. (x)In this thesis, why the current conveyor concepts are introduced, their historical progress, the defining equations and applications of the first and second generation current conveyors, advantages of the second- generation current conveyors over the OTAs and OAs were given in the second section. In the third section, subnetwork and subgraph were given which are used for analysis and synthesis of the circuits that consist current conveyors. Using signal-flow graphs, analysis of the circuits were explained, By the aid of this the voltage transfer function was found for a given circuit. In the fourth section, the suitable signal-flow graph of the general nth-order transfer function was given and corresponding circuit was realized. Also, third- order high-pass filter was realized by the aid of above and sensitivity analysis of this filter was made. Besides, the circuit which realized low-pass and band-pass filters on the same structure with the equal-valued elements was given and sensitivity analysis was made. In the fifth section, the circuit models of negative and positive current conveyors were given which are used for SPICE analysis. The element values of the third-order high-pass filter that is realized in the fourth section were changed to suit practical values, also SPICE analysis was made for this circuit.