Piecewise Linear Model of a Diode
Piece-wise linear model
The piece-wise linear model, as the name suggests, is a model in which the characteristics of diode is approximated by “piece-wise linear” line segments. The graph given below shows piece-wise linear characteristics of diode along with the its model.
In the graph shown on left, the actual characteristics of diode is superimposed by piece-wise linear characteristics (shown in amber color). It is clear that the piece-wise linear characteristics do not exactly represent the characteristics of diode, especially near the knee of the curve. However it provides a good first approximation to the actual characteristics of the diode. Piece-wise linear characteristics can be obtained by replacing the diode in the circuit with a resistor, a battery and an ideal diode.This is shown in the right side of the above figure. Lets see the logic behind the three components being used to approximate the diode in piece-wise linear way.
- Consider the horizontal line from (0 to 0.7 V) in the piece-wise characteristic curve. The horizontal line indicates that the current flowing through diode is zero for voltages between 0 and 0.7 V. To model this behavior, we put a battery of 0.7 V in the equivalent diode model. This does not mean that diodes are a source of voltage. When you measure the voltage across an isolated diode, the instrument will show zero value. The battery simply indicates that it opposes the flow of current in forward direction until 0.7 V. As the voltage becomes larger than 0.7 V, the current starts flowing in forward direction.
- An ideal diode is also connected in series with the battery which indicates that no current flows in the circuit in reverse biased condition.
- Now consider the (almost) vertical line in the piece-wise linear characteristics. This straight line indicates constant slope. Slope in the V-I graph indicates resistance. So we add a resistor in the diode model. The value of resistance can be found from the graph. We can see from the graph that the diode current changes from 0 to 15 mA for a voltage change from 0.7 to 0.8 V. Thus the average value of resistance is (0.8 V-0.7 V)/(15 mA-0 mA) = 6.67 Ω. Thus the value of resistance in the equivalent model is approximately 6.67 Ω.