EXAMPLE 88 Determining the Power Rating of a Zener Diode

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We wish to design a regulator similar to the one depicted in Figure 853(a) Determine the minimum acceptable power rating of the Zener diode

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Known Quantities: vS = 24 V; VZ = 12 V; RS = 50

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; RL = 250

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Find: The maximum power dissipated by the Zener diode under worst-case conditions Assumptions: Use the piecewise linear Zener diode model (Fig 852) with rZ = 0 Analysis: When the regulator operates according to the intended design speci cations,

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Semiconductors and Diodes

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ie, with a 250iS =

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load, the source and load currents may be computed as follows:

vS V Z 12 = = 024 A RS 50 VZ 12 = 0048 A = RL 250

iL =

Thus, the Zener current would be: iZ = iS iL = 0192 A corresponding to a nominal power dissipation PZ = iZ VZ = 0192 12 = 2304 W However, if the load were accidentally (or intentionally) disconnected from the circuit, all of the load current would be diverted to ow through the Zener diode Thus, the worst-case Zener current is actually equal to the source current, since the Zener diode would sink all of the source current for an open-circuit load: iZ max = iS = vS VZ 12 = = 024 A RS 50

Therefore the maximum power dissipation that the Zener diode must sustain is: PZ max = iZ max VZ = 288 W

Comments: A safe design would exceed the value of PZ max computed above For example, one might select a 3-W Zener diode

EXAMPLE 89 Calculation of Allowed Load Resistances for a Given Zener Regulator

Problem

10 20 +

Calculate the allowable range of load resistances for the Zener regulator of Figure 854 such that the diode power rating is not exceeded

vL _

Solution

Known Quantities: VS = 50 V; VZ = 14 V; PZ = 5 W Find: The smallest and largest values of RL for which load voltage regulation to 14 V is achieved, and which do not cause the diode power rating to be exceeded Assumptions: Use the piecewise linear Zener diode model (Fig 852) with rZ = 0 Analysis:

1 Determining the minimum acceptable load resistance To determine the minimum acceptable load, we observe that the regulator can at most supply the load with the amount of current that can be provided by the source Thus, the minimum theoretical resistance can be computed by assuming that all the source current goes to the load, and that the load voltage is regulated at the nominal value: RL min = 14 VZ VZ = = 117 = VS V Z 36 iS 30 30

Part II

Electronics

If the load required any more current, the source would not be able to supply it Note that for this value of the load, the Zener diode dissipates zero power, because the Zener current is zero 2 Determining the maximum acceptable load resistance The second constraint we need to invoke is the power rating of the diode For the stated 5-W rating, the maximum Zener current is: PZ 5 = 0357 A iZ max = = VZ 14 Since the source can generate 50 14 VS VZ = = 12 A 30 30 the load must not require any less than 12 0357 = 0843 A; if it required any less current (ie, if the resistance were too large), the Zener diode would be forced to sink more current than its power rating permits From this requirement we can compute the maximum allowable load resistance: VZ 14 = 166 = RL min = iS max iZ max 0843 iS max = Finally, the range of allowable load resistance is 117 RL 166

Comments: Note that this regulator cannot operate with an open-circuit load!

EXAMPLE 810 Effect of Nonzero Zener Resistance in a Regulator

Problem

Calculate the amplitude of the ripple present in the output voltage of the regulator of Figure 855 The unregulated supply voltage is depicted in Figure 856

RS + Vs + vripple + _ VZ RL

VS(t) 14 V

100 mV

Solution

RL = 150

Known Quantities: vS = 14 V; vripple = 100 mV; VZ = 8 V; rZ = 10

; RS = 50

Find: Amplitude of ripple component in load voltage Assumptions: Use the piecewise linear Zener diode model (Fig 852)