Question 9.4: Analysis of a Zener-Diode Regulator with a Load Consider the...

First, consider the circuit as redrawn in Figure 9.12(b), in which we have grouped the linear elements together on the left-hand side of the diode. Next, we find the Thévenin equivalent for the linear portion of the circuit. The Thévenin voltage is the open-circuit voltage (i.e., the voltage across R_L with the diode replaced by an open circuit), which is given by

V_T=V_{SS}\frac{R_L}{R+R_L}=20 \text{ V}

The Thévenin resistance can be found by zeroing the voltage source and looking back into the circuit from the diode terminals. This is accomplished by reducing V_{SS} to zero so that the voltage source becomes a short circuit. Then, we have R and R_L in parallel, so the Thévenin resistance is

R_T=\frac{RR_L}{R+R_L} =1 \text{ k}\Omega

The resulting equivalent circuit is shown in Figure 9.12(c).
Now, we can use Kirchhoff’s voltage law to write the load-line equation from the equivalent circuit as

V_T+R_Ti_D+v_D=0

Using the values found for V_T \text{ and } R_T, we can construct the load line shown in Figure 9.13 and locate the operating point. This yields v_L = -v_D = 10.0 \text{ V}.
Once vL is known, we can find the voltages and currents in the original circuit.
For example, using the output voltage value of 10.0 V in the original circuit of Figure 9.12(a), we find that I_S = (V_{SS} – v_L)/R = 11.67 \text{ mA}.