Question

Algebra Question for Electrical Engineers

Solve for x.

1= x+ (3 * 10^-13 ) * $e^{\frac{x}{(26*10^{-3})}}$

Here, x represents the Voltage across Diode.

The answer should be in ln(something..). It looks simply but hope you can help me. I really need a step by step explanation.

Please do not use Matlab!!  

The answer I got from Matlab was 0.718.

Answer 1

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1 = x + (3 times 10^- 13) e^x/26 times 10^- 3 (1 - x) = (3 times 10^- 13) e^x/e^26 times 10^- 3 rightarrow ln (1 - x) = ln (3 times 10^- 3) + x/26 times 10^- 3 rightarrow ln (1 - x) = -28.834 + 10^3/26 x rightarrow ln (1 - x) = -28.834 + 38.46 x Now using Newton Rapson take, f(x) = 38.46 x - ln (1 - x) - 28.834 f'(x) = 38.46 + 1/1 - x Now take the point x_n = 0 x_n + 1 = x_n - f(x)/f'(x) = 0 - f(0)/f'(0) = 0 - (- 28.834/39.46) = 0.730 (Ans)