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The latter approximation assumes that the bias current I is large enough so that the factor of 1 in the parentheses of the Shockley Equation can be ignored. This approximation is fairly common in nonlinear circuit analysis.
Noting that <math>\frac {dI} {dV}</math> corresponds to the instantaneous conductivity of the diode, the small signal resistance <math>r</math> is the negative reciprocal of this quantity:
<math>r=\frac{1}{I}\frac{kT} {q} </math>
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