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Suppose the components of the Zener diode voltage regulator circuit of figure 121.11(b) have the following values:
Vs = 24 V; VZ = 12 V; Rs = 50 Ω; RL = 250 Ω;
(a) Determine the minimum acceptable power rating of the Zener diode.
Now suppose the values are changed as follows:
Vs = 50 V; VZ = 14 V; Rs = 30 Ω; PZ = 5 W.
(b) Determine the range of load resistances, RL such that the diode power rating is not exceeded.
S7P7A72 (Dynamic Equilibrium).
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. Even though we are calculating pwer and resistances, the basic objective of stability remains.
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.
(a) Now, by Ohm's law
is = (Vs - VZ)/ Rs = (24 -12)/50 = 0.24 A
iL = vL/RL = Vz/RL = 12/250 = 0.048 A
So, Zener current, iz = is - iL = 0.24 - 0.048 = 0.192 A
So, PZ = izVz = 12(0.192) = 2.304 W
However, this is not PZmax.
PZmax is calculated by envisioning the worst-case scenario in which all source current is channeled through the Zener diode. For example if the load is suddenly disconnected (accidentally or deliberately) from the circuit.
In this case, izmax = is = 0.24 A
So, PZmax = izmax VZ = 12(0.24) = 2.88 W.
So, a 3-W Zener diode will be a safe power rating for the circuit.
(b) is = (Vs - VZ)/ Rs = 50-14/30 = 36/30.
RLmin is the case when all current is channeled to the load.
So, RLmin = VZ/is = 14(30)/36 = 11.7 Ω
RLmax is the case when maximum current (taking into account maximum diode current) flows through RL
So, RLmax = VZ/(ismax - iZmax)
ismax = (Vs - VZ)/ Rs = (50-14)/30 = 1.2 A
iZmax = PZ/VZmax = 5/14 = 0.357 A
So,RLmax = VZ/(ismax - iZmax) = 14/0.843 = 16.6 Ω
So, range of allowable resistance is 11.7 Ω ≤ RL ≤ 16.6 Ω.
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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