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Using the Nonlinear Model

For more accuracy, let's consider the nonlinear model for the diode, Section 7.2.1, which relates the diode current i and voltage v.

The circuit also relates i and v, since by KVL, we have

V_S = i R + v

so that

$$i = \frac{V_S-v}{R}$$ (75)

From equations (74) and (75) we can eliminate i to obtain the following nonlinear equation for the diode voltage v:

$$\frac{V_S-v}{R} = I_s [ \exp ( \frac{q v}{kT} ) -1 ]$$ (76)

It is not possible to solve this equation exactly in closed-form, but we can solve it approximately via an iterative scheme. Maple can be used to do this:

solve( (5-v)/1000 = 0.07*10^(-12)*( exp(v/0.026) -1), v  );
		0.6461929

This gives v=0.6461929 V, and

$$i = \frac{V_S-v}{R} = \frac{5-0.65}{1000} = 4.35 \ {\rm mA}$$

These calculations are illustrated in Figure 78. The operating point Q of the device corresponds to the values v=V_Q=0.65 V and i=I_Q=4.35 mA just calculated.

  

Figure 78: Diode biasing circuit analysis showing nonlinear diode characteristic and load line.

Figure 78 provides an alternative and commonly used method for determining the operating point Q. The circuit connected to the diode determines a straight line (corresponding to equation (75)), called the load line.   The operating point is seen to be the point of intersection of the load line and the diode characteristic, so if one has available a graph of the diode characteristic (instead of an equation), say from a data sheet, then draw the load line and determine Q.

This procedure is characteristic of circuits with active devices, making use of

• device characteristics, and
• circuit equations.

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