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Practical Biasing Design for Analog Circuits
Abstract and Figures
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
operational amplifiers are used as nullator plus norator (or
simply nullor). As examples, a diode circuit, a BJT circuit and
a JFET circuit are shown which are designed using the
proposed method for some given critical specs. Application of
current mirror as a current source, and its design using the
proposed method are also discussed in this paper.
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... 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]. ...
... Vladimir Filaretov and Konstantin Gorshkov [15] proposed symbolic analysis of networks based on nullor approach. Circuit designing method, which is an extended version of [3,4] is presenting in this paper. This procedure is helpful for the design of integrated circuits, which deals with active loads and current mirrors. ...
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.
... The design of analog circuit consists of AC performance design and DC biasing design. AC design defines the circuit characteristics like frequency response, bandwidth, input and output impedance etc, whereas the aim of DC biasing design is to fix the operating points of non-linear devices at the desired level [2][3][4]. It seems to be a difficult part in circuit design because of the time consuming iterations required to get the targeted design. ...
... Operational amplifiers (op-amps) can work as a nullor, i.e., combination of nullator and norator. Hence, it is possible to model fixators using op-amps for practical purposes [1,3]. ...
... Nullor: They are theoretical two port network with a nullator at its input port and norator at its output port [1][2][3]. Ideal op-amp is a perfect nullor. ...
... 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.
... Fixators and norators [4][5][6][7] are the emerging tools in circuit analysis. They are always used in pairs. ...
... Nullor is the combination of norator and nullator. Ideal operational amplifiers are the examples of nullors and therefore in practical cases, operational amplifiers are used to model fixator-norator pairs 5,6 . Circuit simulators cannot directly model fixator-norator pairs, so ideal controlled sources with very high gain can be used to mimic the pair. ...
Network theorems or circuit theorems are special aids, which can reduce the amount of effort involved in circuit analysis to a considerable degree. For linear networks, there exists interdependence between various network theorems. Thus, by careful analysis, one theorem can verify in terms of another theorem and it is advantageous for pedagogical reasons. A scheme for analogue circuit analysis is presented in this paper. Here piece-by-piece or part-by-part analyzing strategy is employed which can reduce the complexity associated with analyzing or biasing design of large analogue circuits. Fixatornorator pair plays the key role in this methodology. Hybrid equivalent circuit, an alternative for Thevenin’s or Norton’s equivalent model is realized with fixator-norator pair, and is seen to be more dynamic and flexible since it contains both voltage source and current source. Thevenin’s theorem, compensation theorem and maximum power transfer theorem are analyzed in terms of fixator norator pairs, and the study indicates the importance and capabilities of fixator-norator pair and hence hybrid equivalent circuit in analogue circuit design and analysis.
... 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.
Design of analog integrated circuits is discussed in this paper. The emphasis is on the biasing design of ICs using Fixator-norator pairs. Fixators are used to keep the driver transistors biased at the desirable operating points while the pairing norators are used to allocate and specify the bias-supporting components. A bias-supporting component is shown to be one of the two categories: 1) a DC voltage source or a DC current source/sink or 2) a power-conducting component. A power-conducting component is typically a resistor in lumped circuits but an active load or current mirror in an analog IC. Three types of active loads are introduced and their design is also discussed in this paper. Two examples, one in bipolar and one in CMOS technology, demonstrate the analog IC design procedure.
Although local biasing of components used in an analog circuit is shown to be a very attractive design methodology, significantly simplifying the design procedure [3], it makes the DC supplies distributed and often not in desire locations in the circuit. In response to this problem a new technique is developed that in conjunction with the local biasing it handles the DC supply sources very smoothly and transfers them to the designated locations in the circuit, specified for global biasing. The technique utilizes nullator-norator pairs to do the required source transformation. Overall, the technique totally avoids nonlinearity in the operation due to a novel nullator modeling that is presented for locally biased components. For the lack of space, the method is only applied to MOS transistors here, but it can simply be extended to BJTs as well. As an example, a two stage amplifier with feedback is used to demonstrate the methodology.
A new biasing technique called ldquolocal biasingrdquo of transistors is used to design analog integrated circuit amplifiers, or any other analog ICs. The technique is based on designing the circuit without any external source but only the sources that are used to locally bias the transistors [12, 13]. Later these sources are transferred to appropriate locations in the circuit which leads the circuit to a new topology and configuration that makes it possible to replace the local biasing sources with final current mirrors and one or two conventional power supplies. Local biasing is revisited, and an OTA design example is provided to clarify the methodology and demonstrate the procedure.
A new biasing technique is introduced for complex analog circuits. The technique is gradual, controllable and fast converging. The technique offers the circuit designers to initially and directly choose the devices operating points first and later proceed for linear designing. The technique is based on a local biasing method that removes all DC supplies from the circuit and replaces them with sources augmented to the devices so that the devices ports are DC-nullified. It is shown that when the local biasing is done in steps the additivity property, used in linear circuits, can be implemented. Finally, the local biasing makes the nonlinear devices to respond to an AC signal, at selected operating points, just like other linear elements without any need of externally bias them.
- D C Nn Bhargav
- S C Kulshreshtha
- Gupta
NN Bhargav, DC Kulshreshtha and SC Gupta, Basic Electronics
And Linear Circuits, Tata McGrew-Hill Publishing Company
Limited,42nd reprint 2006.