Article

Iterative solutions of the generalized diode equation

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Abstract

For original paper `Approximate analytical solution of generalized diode equation' by T.A. Fjeldy et al. see ibid., vol.38, no.8, p.1976-7, Aug. 1991. The authors significantly enhanced the efficiency with which one may solve the generalized diode equation in numerical circuit simulation programs. This study concluded that Newton-Raphson iteration is relatively ill-suited for this task. To the contrary, the commenter finds that Newton's method is comparable to that of Fjeldly et al. and discusses the merits of an alternative cubic step and two Newton steps

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... VER since the publication of Shockley's seminal research on p-n junction diodes [1], general diode equation (GDE) has become the de-facto basis of device modeling and circuit simulations [2] enabled over computer simulation program with integrated circuit emphasis (SPICE). Unfortunately, the proposed solutions of this equation are mostly approximate [3][4][5][6][7]. Since an exact solution of the GDE has remained a challenge, most of the research on diode circuit modeling have focused on finding a solution of this equation [3][4][5][6][7]. ...
... Unfortunately, the proposed solutions of this equation are mostly approximate [3][4][5][6][7]. Since an exact solution of the GDE has remained a challenge, most of the research on diode circuit modeling have focused on finding a solution of this equation [3][4][5][6][7]. So, research on verifying or improving the accuracy of the equation in prediction of practical IV characteristics have been very limited. ...
... If i and v are respective current and voltage of a device then an exact solution of its IV equation should be expressible in the form of i = f(v) without any deliberation; therefore, as the exact solution claimed in [6] is not expressible in this form, it is not exact solution with respect to the sense mentioned here; [8] deliberately uses a Lambert W-function such that the basic structure of the GDE gets changed. Since, so far, the solution of GDE takes the form of i = f(v,i), a solution of GDE still remains approximate in nature [3][4][5][6][7]. GDE does have an exact solution in terms of an unknown voltage, i.e. v = f(i) where voltage across a diode may be obtained using an estimated current through it. ...
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The general diode equation or the non-ideal diode equation is the foundation of circuit models of active devices for the past several decades. Apart from the effect of p-n junction, this equation also accounts for the series bulk resistance of a diode. Despite a reasonable agreement of the equation with measured IV characteristics, it is shown here that the equation is incompatible with basic theories of circuits and systems. Therefore, a modification in the equation is proposed to remove this incompatibility. This modified equation leads to a compact model of a p-n junction diode that has an excellent agreement with the measured IV characteristics.
... VER since the publication of Shockley's seminal research on p-n junction diodes [1], general diode equation (GDE) has become the de-facto basis of device modeling and circuit simulations [2] enabled over computer simulation program with integrated circuit emphasis (SPICE). Unfortunately, the proposed solutions of this equation are mostly approximate [3][4][5]. Since an exact solution of the GDE has remained a challenge, most of the research on diode circuit modeling have focused on finding a solution of this equation. So, research on verifying or improving the accuracy of the equation in prediction of practical VI characteristics have been very limited. ...
... Since, so far, the solution of GDE takes the form of i = f(v).f(i), a true solution of GDE still remains approximate in nature [3][4][5]. However, if i and v are current and voltage respectively, GDE does have an exact solution in terms of an unknown voltage, i.e. v = f(i) where voltage across a diode may be obtained using an estimated current through it. ...
Preprint
The general diode equation or the non-ideal diode equation is the foundation of circuit models of active devices for the past several decades. Apart from the effect of p-n junction, this equation also accounts for the series bulk resistance of a diode. Despite a reasonable agreement of the equation with measured VI characteristics, it is shown here that the equation is incompatible with basic theories of circuits and systems. Therefore, a modification in the equation is proposed to remove this incompatibility. This modified equation has an excellent agreement with the measured VI characteristics.
... The authors (Pimbley et al., 1992) used Newton's method provides an accurate solution for negative values of normalized tension, but the precision of the solution is less acceptable for very large values of the normalized tension. Moreover, this method induced a lot of computing time. ...
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