Fixator–Norator Pairs Versus Direct Analytical Tools in Performing Analog Circuit Designs

Abstract

Two analog circuit design approaches are introduced and compared. They are used for partial designs with certain given design criteria. The first approach, which is called direct analytical, works through the circuit conductance matrix, and it needs linearity to perform. The second approach uses fixator-norator pairs (FNPs), changing an analysis into a design problem. The two methods are shown to be theoretically identical, except that they use different tools to get the results. The advantage of using FNP over the direct analytical method is that it can simply handle nonlinearities, as it is done in a circuit analysis or simulation. The drawback, however, is the lack of fixator and norator components in a typical simulator; although, the closest components replacing them can be the controlled sources with very high gains.

Identification of Circuit Parameters for the Specified or Measured Performances

“…A controlling voltage or current is a difference between the specified and the calculated one. It has been demonstrated, on benchmark example, that such adjoint circuit is practically identical with a circuit obtained from the FNPs method [4]. These two methods differ only in character of an element that produces the controlling variable, but this character is meaningless for the intended PSpice simulation.…”

“…It should be emphasized, that in the proposed adjoint circuit approach, character of the selected controlled source is absolutely arbitrary, what allows to break a loop of voltage sources or a cutset of current sources, as described in Section IV. In the FNPs method, some moderate difficulties when selecting controlled source other than VCCS may be encountered [4].…”

“…Consider the circuit in Fig. 4a [4]. The transimpedance For the assumed I 1 =1 mA, the specified performance is F * =U o * =10 V. Other circuit parameters are as follows:…”

“…4b, obtained from the adjoint circuit method, originally described in 1982 [2]. The only difference is in character of element added to produce the controlling voltage: arbitrary resistance in FNPs method [4], zero current source in adjoint circuit method [2]. The character of this element is meaningless for the intended simulation and this is practically the only original finding of the FNPs method if compared with the adjoint circuit method.…”

Using Nullors to Modify Linear Model Parameters of Transistors in an Analog Circuit

“…The crucial components that are used for such operations are nullors, which are special types of fixator-norator pairs (FNP) [4][5][6][7][8][9][10]. Nullors are among pathological elements that although not ideally available in physical form but have very unique properties particularly for circuit designs [8,9]. Briefly, a nullor consists of a pair of elements, a nullator and a norator.…”