11.6 : Small-signal Diode Model

In analyzing the behavior of diodes in circuits, the relationship between the current through a diode and the voltage across it is of particular interest, especially when considering the effect of a direct current (DC) bias voltage. When applied, this DC bias influences the diode's operating point, known as the Q point, around which the current-voltage (I-V) characteristic of the diode exhibits exponential behavior. Introducing a small, time-varying signal on top of this bias aids in examining the diode's response to fluctuations around this Q point.

When the amplitude of this additional signal voltage remains considerably smaller than the diode's thermal voltage (V_T), the diode's response can be approximated as linear over a short segment of its characteristic curve. This scenario, termed the small-signal approximation, simplifies the complex exponential relationship into a more manageable linear one, allowing the total instantaneous diode current (i_D) to be seen as a sum of both the constant bias current i_D(DC) and the varying signal current i_D(AC)

The measure that connects the signal current to the signal voltage is expressed in terms of conductance, measured in mhos, and is referred to as the diode small-signal conductance. It is the slope of the tangent to the I-V curve at the Q point. Conversely, the diode's small-signal or incremental resistance (r_d) is the inverse of its conductance. It measures the diode's resistance to small changes in current and is calculated by dividing the thermal voltage by the bias current.

These parameters are crucial for designing and analyzing circuits involving diodes, especially in applications requiring precise control over signal amplification or attenuation.