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... our method, operational amplifiers are used as nullor. If op-amp is used as nullor, the circuit around the op-amp (nullor) determines the output of op-amp in such a way that its difference input is forced to zero. That means nullor output can take any value so that its difference input equals zero. Fig.1 shows fixators and fig.2 shows nullators, norators, nullor and nullor model of op-amp [1,3]. ...
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A new method for the biasing design of analog
circuits is presented in this article. In this method, the
properties of operational amplifiers are well exploited, and it is
useful for the biasing design of circuits containing non-linear
components like diodes, BJTs, FETs etc. The method uses a
combination of fixators, norators and nullators, where
o...
Citations
... A complicated source transformation steps may required for reducing the number of DC sources, which is time consuming. Later, Hashemian [10,11] proposed a new design tool called Fixator Norator Pair (FNP), which is a combination of nullor and sources [12][13][14]. A fixator fixes a port parameter at the design; the pairing norator defines the corresponding supporting component to hold the fixator. ...
... A fixator fixes a port parameter at the design; the pairing norator defines the corresponding supporting component to hold the fixator. Applications of FNPs are wide [10][11][12][13][14]. ...
A method for the modification/correction of analog circuits whose response is deviated from the actual one due to component replacement or ageing is presented. The emphasis is to go after the problem causing component and apply proper sets of fixator-norator pairs until the problem is solved. This approach fixes biasing bugs by redesigning some of bias supporting components without altering the basic circuit configuration. For eliminating the errors in frequency response, reactive elements are redefined. For some odd cases, extra sub circuit may be added to retain the original frequency response.
... To overcome the above mentioned computational difficulties, some authors [15][16][17][18][19][20][21][22] have proposed a new approach to the biasing design by using local biasing. The main idea of this technique is to start biasing by adding supply sources to each port of nonlinear components. ...
... Every norator is replaced with a DC supply if it is placed in a location designated for a source, or otherwise with a power conducting component or an active load. In [21,22], the authors suggested the use of operational amplifiers instead of theoretical components, fixators and norators. ...
The analog circuit design approach based on local biasing is shown to be very attractive as it removes the nonlinearity in the biasing procedure. Based on this design approach, we offer a new technique for the sizing of analog integrated circuits. The proposed technique is based on the relations that exist between linear elements of a cut-set or a loop when the voltages and currents in the remaining elements are held fixed. These relations enable the designer to fix a circuit variable (biasing current or voltage of a transistor) in exchange for a set of interrelated element values that can be independently changed. The proposed procedure allows us to directly change the element values or the DC parameter values for the active loads without being concerned about the DC biasing. Therefore, the circuit designer is able to manage tradeoffs in the design by comparing multiple solutions that meet the desired criteria. Moreover, multiple circuit simulations are not necessary in the case when any of the calculated element values is not realistic or workable.
... A fixator fixes one critical parameter at the design; its pairing norator helps to find the corresponding bias supporting component. Recently, FNPs finds applications in design of active loads [1], biasing design, source allocation [15] and in design for bandwidth [16]. FNPs can be modeled with the help of controlled sources with very high gain or using op-amps [17]. ...
Feedback is an integral part of many analog circuits. This paper presents a method for the design of feedback networks for analog amplifiers based on Fixator–Norator Pair (FNP). The design process for required transfer function includes inserting proper FNPs to the equivalent small signal model of the target circuit, with norators lying along the feedback path, and helps to design the feedback network components. Care must be taken to ensure that the added feedback should not alter the original DC biasing of the circuit. A number of examples are worked out in this paper using the proposed method and the results are verified. The FNP approach gives a one-step solution for the design problems which otherwise require tedious analysis and calculations. Although the scope of this paper is limited to design of feedback for amplifiers, a skillful designer can extend the proposed method to other areas of analog circuits.
... As the existing methods make no separation between linear and non-linear components, circuit design becomes complex as the number of elements increases. [2][3][4][5]. Further, large amount of calculations along with the trial and error method add to the complexity in the field of circuit design. The proposed method treats the nonlinear devices differently. ...
... A fixator is a nullor plus source(s). Use of op-amp as fixator and applications of opamp fixators such as biasing design, source allocation, source transformation etc. are extensively studied in literature [3][4][5]. The use of nullor elements in analog design and analysis is becoming getting popular [10,11]. ...
This paper presents a novel method for the design of analog integrated circuit, making use of fixator-norator pairs for the performance design and biasing design. Fixators are the distinctive tools for setting a critical design parameter at a desired value whereas the pairing norator renders these critical parameters into adequate supporting components, mainly resistors. For analog ICs, active loads and current mirrors serve as supporting components. Hence, the use of fixator-norator pairs may abbreviate as defining the dynamic and static resistance of active loads and current mirrors that should be affirmative with a given design. The proposed methodology is illustrated by the use of a common emitter amplifier, a BJT differential amplifier, a MOS operational amplifier and a three-stage CMOS operational amplifier.
... Controlled sources with very high gain are used to mimic the pair. The uses of op-amp as a fixator and applications of op-amp fixators are extensively studied in literature [5][6][7] . ...
This paper presents a novel approach to the accurate time domain analysis and design of analog circuits containing storage elements by making use of ‘companion models’. The emphasis is given to the design using fixator-norator pair, which is now ingenious in analog circuit design. The Backward Euler method can render a storage element to an equivalent circuit, containing only linear components viz. current source or voltage source and resistance. This distinctive feature allows us to generate equivalent companion models of the storage elements for every time step, whereby persuading the application of fixator-norator pairs in such circuits containing reactive components. This paper briefly explains the construction of equivalent circuits at desired time steps and provides a detailed explanation on the design of the gain of an op-amp differentiator for a given input by exploiting the fixator-norator method. The proposed method reveals to be much reliable and accurate in the design of circuits containing reactive elements.
In this paper, the method for the design automation of a narrow band-pass amplifier, and hence the amplifier tuned oscillator is discussed. A fixator approach is utilized in this method to design the narrow band-pass amplifiers and a reference circuit is required for this process. The fixator–norator pair helps to generate an extra sub-circuit, generally the feedback network; the addition of this sub-circuit in the actual amplifier circuit will modify the frequency response of the amplifier. The amplifier now behaves like an active narrow band-pass filter, which exactly follows the frequency response of the model circuit. This can be turned into an oscillator by providing positive feedback. Such a circuit possesses independent frequency and amplitude control. Hence, the re-designed circuit can be employed as an active filter or an oscillator at the selected center frequency. In addition to the technical merits, the proposed method has pedagogical importance. Few case studies are worked out in this paper to demonstrate the method.
