Diode Dynamic Resistance

A diode is a non-ohmic device, so its useful resistance for small signals is the dynamic (or AC) resistance, defined as the ratio of a small change in forward voltage to the corresponding change in forward current: (r_d = \Delta V / \Delta I). This is the reciprocal of the local slope of the steeply rising forward characteristic, and it differs from the static ratio (V/I), which would wrongly include the large fixed knee voltage and overstate the resistance. The dynamic value matters because in practical circuits a diode usually carries a steady bias current with a small alternating signal superimposed, and it is this slope resistance that governs how the signal voltage and signal current relate. Because the forward curve grows steeper as current increases, the dynamic resistance also falls at higher operating currents, so the value quoted is meaningful only for the stated 10-to-20 mA window. Here the voltage change is (\Delta V = 0.75 - 0.70 = 0.05,\text{V}) and the current change is (\Delta I = 20 - 10 = 10,\text{mA} = 0.01,\text{A}). Therefore (r_d = 0.05 / 0.01 = 5,\Omega). The value 2.5 halves the result by mistakenly using twice the current change. The value 50 comes from using current in milliamperes without converting to amperes. The value 70 confuses the static resistance (V/I) with the dynamic definition. As a plausibility check, a few ohms is the expected order of magnitude for a forward-biased diode operating well past its knee voltage, where the characteristic is very steep.