Problem 64-4    Source:   Problem elaborated by the author of the site.

Be the circuit shown in the Figure 64-04.1. Assume that Vi = 24 volts with ΔV = 6 volts and V_Z = 12 volts. The current consumed by the load varies from 30 mA to 100 mA. Determine the values of R_Smax and R_Smin and what the power in the zener.

Solution of the Problem 64-4   

Note that the input voltage is variable and the load is also variable. Therefore, we should apply the case 4 studied in the Zener Diode Circuit Design item (Here!!). Since the model of the zener to be used was not provided, we must start by stipulating a maximum current for the zener. Since the load consumes 100 mA, we will stipulate a maximum current for the zener of, say, I_Zmax = 200 mA. In this case, the power in the zener will be:

Commercially there is no zener for this power. The closest is 5 watts. So let's assume that the zener is 5 watts. We can calculate the maximum current that zener can support, or:

Then, I_Zmin will be:

With these two values, it is possible to calculate R_Smin and R_Smax using the two equations studied. See below:

Recalling that in this problem, V_i(min) = V_i - (ΔV/2) = 24 - 3 = 21 volts and to find the maximum, V_i(max) = V_i + (ΔV/2) = 24 + 3 = 27 volts. Then:

And in turn:

Note that R_Smax > R_Smin enabling the project. We can choose to the series resistor the average value of the calculated values. Like this, R_S = 48.6 ohms. A commercial value that can be used is R_S = 47 ohms.

Note that the current through R_S is not constant. Depends on variations in input voltage. So we have I_Smax = (V_i(max) - V_Z) / R_S = 0.32 A . In this way, the maximum current flowing through the zener is when the load consumes the lowest current, or I_Lmin = 0.03 A .  So, I_Zmax = (I_Smax - I_Lmin) = 0.29 A . Therefore, zener supports this current without problems. The power dissipated by it will be:

Thus, the zener of 5 watts used in the design fully meets the needs of the circuit. Case I_L = 0 A (load problems), the maximum current flowing through the zener is I_Zmax = I_Smax = 0.32 A. This current is perfectly supported by zener.