Zener Diode In A Voltage Regulator Circuit

Strings (SiPjAjk) = S7P7A72     Base Sequence = 12735     String Sequence = 12735 - 7 - 72

Expressions Of Pj Problems
Zener Diode In A Voltage Regulator Circuit
Math Zener diodes (symbol in 121.10(a)) are voltage regulator devices. They help to keep the rectifier DC voltage output constant. They are deliberately designed to operate in the reverse-breakdown region.

The voltage regulator circuit of figure 121.10(b) has the following characteristics:
Constant reverse breakdown Zener voltage, VZ = 8.2 V.
Allowable range of operational Zener current: 75 mA≤ iZ ≤1 A.
Load resistance, RL = 9 Ω

Size Rs so that vL = Vz = 8.2 V is maintained while Vs varies by + 10% from its nominal value of 12 V.

The strings: S7P7A72 (Dynamic Equilibrium).

The math:
Pj Problem of Interest is of type equilibrium (dynamic equilibrium). The objective of a Zener diode voltage regulator circuit is to maintain a stable (constant) voltage across a load. The two most important characteristics of a Zener diode are the Zener voltage and the rated power dissipation. Zener diode behaves like any other reverse-biased diode for variable DC Vs ≤ reverse breakdown voltage Vz. When Vs is > Vz (occurrence of avalanche voltage), Zener diode will conduct current. This transition point is called the avalanche point. Zener voltage is kept constant at and beyond the avalanche point. So, load connected in parallel to the Zener diode will have a constant load voltage equal to Vz as long as Vs is > Vz.

Now, by Ohm's law
iL = vL/RL = Vz/RL = 8.2/9 = 0.911 A

By KVL
Rs = (Vs - VZ)/(iL + iZ)
So, sizing Rs for max iZ and max Vs, we have:
Rs = [(1.1)(12) - 8.2]/(1 + 0.911) = 2.62 Ω

Now, for iZ at min Vs, given Rs = 2.62 Ω we have:
iZ = [(minVs - VZ)/ Rs] - iL = [((0.9)(12) - 8.2)/2.62] - 0.911 = 81.3 mA
So, since iZ ≥ 75 mA, Rs = 2.62 Ω maintains
vL = Vz = 8.2 V while Vs varies by + 10% from its nominal value of 12 V. The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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