Problem 65-7   Source:  Problem elaborated by the author of the site.

Given the circuit shown in the Figure 65-07.1, calculate the output voltage V_o , assuming that the input voltage is given by V_i = 20 sin 500 t. Sketch a graph with the circuit transfer characteristic. Consider the voltage on the conducting diode as V_D = 0.7 V, V_Z1 = 6.8 V and V_Z2 = 3.9 V.

Solution of the Problem 65-7   

When the input voltage V_i begins to grow in the direction of the positive peak, the zener diode Z ₁ will act as a zener and the zener diode Z₂ will act as a common diode. In this way, for the positive cycle of the sinusoidal function, the diodes will only conduction when V_i = V_Z1 + 0.7 = 6.8 + 0.7 = 7.5 V.

On the other hand, when V_i starts the negative cycle, the zener diode Z₂ will act as a zener and the zener diode Z₁ will act as a common diode. In this way, for the negative cycle of the sine function, the diodes will only conduction when V_i = - (V_Z2 + 0.7 ) = - (3.9 + 0.7 ) = - 4.6V.

After these initial considerations we are able to determine the output voltage as a function of the input voltage. So for the positive cycle of the sinusoid we have:

And for the sinusoid negative cycle, we have:

In the Figure 65-07.2 the graph with the circuit transfer characteristic is represented. Note that by changing the slope of the line, we smooth the curve, approaching the real behavior of a zener diode.