I am looking for an approach on how to apply Kirchhoff current / voltage law in the infinitely long diode ladder network. Can anyone help me with this ?
I am looking for 1D differential equation or an implicit equation.
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engineer
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Which model are you using for the diodes? – Alfred Centauri Aug 24 '14 at 22:25
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I aim to model the lateral current injection with a lumped resistor/diode ladder circuit or with a 1D differential equation. Can you help me how to identify diode current in any of the branch ? – Tanmay Bhargava Aug 25 '14 at 12:58
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Related: http://physics.stackexchange.com/q/10615/2451 , http://physics.stackexchange.com/q/73713/2451 and links therein. – Qmechanic Jun 17 '15 at 08:33
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@engineer: FYI, the [tag:semiconductor-physics] tag was added as a consequence of being a synonym for the [tag:diodes] tag. But you are welcome to remove it if you think that is better. – Qmechanic Jun 17 '15 at 08:44
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The admittance looking into the network "$Y_{net}$" can be expresed as:
$$Y_{net} = \dfrac{1}{R + \dfrac{1}{Y_{net} + Y_{diode}}} $$
Rearranging as a quadratic and solving:
$$Y_{net}^2R + Y_{net}Y_{diode} - Y_{diode} = 0$$
$$Y_{net} = \dfrac{\sqrt{Y_{diode}}\sqrt{4R +Y_{diode}}}{2R}$$
Where
$$Y_{diode} = \frac{nV_t}{I_s}e^{-\frac{V_f - I_fR}{V_t}}$$
Then
$$I_f = V_f\dfrac{\sqrt{Y_{diode}}\sqrt{4R +Y_{diode}}}{2R}.$$
I think this implicit equation could then be solved for $I_f$. Once you know the first forward current you can plug $V_f - I_fR$ into the diode equation to find the current in the first diode in the string, then iterate using the above and the implicit equation to find the current in any diode.
MattyZ
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