11.6:
Small-signal Diode Model
In a diode circuit, a DC bias voltage drives the diode current through a resistor, exhibiting exponential behavior in the current-voltage characteristic curve.
When a small, time-varying signal is introduced, it combines with the DC bias voltage centered around the Q point.
The exponential term in the total instantaneous diode current contributes to both the bias current and the signal current.
If the amplitude of the signal voltage is significantly smaller than the thermal voltage, the diode operates within a short, nearly linear segment of the characteristic curve.
Under this small-signal approximation, the exponential term simplifies.
As a result, the diode current becomes the sum of the DC bias current and the signal current.
The diode small-signal conductance is defined as the ratio of the small signal current to the small signal voltage, which is determined by the slope of the tangent to the I–V curve at the Q point.
The inverse of the diode small-signal conductance, called the diode small-signal resistance or incremental resistance, equals the thermal voltage divided by the bias current.
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 (VT), 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 (iD) to be seen as a sum of both the constant bias current iD(DC) and the varying signal current iD(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 (rd) 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.