to Vt. This circuit approximates the cut-in voltage present in real diodes. The combined I-V characteristic of this circuit is shown below: The Shockley diode model can be used to predict the approximate value of . Using and : Typical values of the saturation current at room temperature are: for silicon diodes; for germanium diodes. As the variation of goes with the logarithm of the ratio , its value varies very little for a big variation of the ratio. The use of base 10 logarithms makes it easier to think in orders of magnitude. For a current of 1.0mA: for silicon diodes (9 orders of magnitude); for germanium diodes (3 orders of magnitude). For a current of 100mA: for silicon diodes (11 orders of magnitude); for germanium diodes (5 orders of magnitude). Values of 0.6 or 0.7 volts are commonly used for silicon diodes. Diode with voltage source and current-limiting resistor The last thing needed is a resistor to limit the current, as shown below: The I-V characteristic of the final circuit looks like this: The real diode now can be replaced with the combined ideal diode, voltage source and resistor and the circuit then is modelled using just linear elements. If the sloped-line segment is tangent to the real diode curve at the Q-point, this approximate circuit has the same small-signal circuit at the Q-point as the real diode. Dual PWL-diodes or 3-Line PWL model When more accuracy is desired in modelling the diode's turn-on characteristic, the model can be enhanced by doubling-up the standard PWL-model. This model uses two piecewise-linear diodes in parallel, as a way to model a single diode more accurately. Small-signal modelling Resistance Using the Shockley equation, the small-signal diode resistance of the diode can be derived about some operating point (Q-point) where the DC bias current is and the Q-point applied voltage is . To begin, the diode small-signal conductance is found, that is, the change in current in the diode caused by a small change in voltage across the diode, divided by this voltage change, namely: . The latter approximation assumes that the bias current is large enough so that the factor of 1 in the parentheses of the Shockley diode equation can be ignored. This approximation is accurate even at rather small voltages, because the thermal voltage at 300K, so tends to be large, meaning that the exponential is very large. Noting