Zener Regulator

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This model can be used in the design of simple Zener (shunt) voltage regulators. When using the model to calculate the power dissipation of the resistor and Zener , be sure to exercise the circuit over the full range of input voltage variations and load currents. (The Zener power dissipation is maximum at zero load current IL.) If the Zener resistance Rz is not known exactly, it can be assumed to be very small (e.g. 0.1 Ohm) for normal Zener diodes.

The model is valid only if the input voltage Ein is greater than the Zener voltage Vz and if the load current IL drawn from the output is less than the resistor current Ir. If you attempt to force IL to be equal to or greater than Ir, then the Zener current Iz will go zero or negative and the model is no longer valid.

In the example variable sheet shown below, a Zener regulator that derives a nominal 15 volt output from a 20 volt input is tested. The results show that with the resistor specified, the load current would be limited to about 16 mA (Ir). A Zener with a power dissipation of greater than 2.5 watts is required and a resistor with a power dissipation of greater than 0.8 watt is needed. 

Variable Sheet
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St Input     Name    Output    Unit      Comment
   20        Ein               volts     Input voltage (volts, mV)
             Eout    15.016667 volts     Output voltage (volts, mV)
   0         IL                Amps      Load current (Amps,mA,ľA)
   15        Vz                volts     Zener voltage (volts, mV)
   30        R                 ohms      Resistor value (Ohms,KOhms,MOhms)
             Iz      .16666667 Amps      Zener current (Amps,mA,ľA)
             Er      5.016667  volts     Voltage across resistor (volts, mV)
             Ir      .16666667 Amps      Current through resistor (Amps,mA,ľA)
             Pr      .83333333 watts     Power dissipated by resistor (watts, mW)
             Pz      2.5       watts     Power dissipated by Zener (watts, mW)
   .1        Rz                ohms      Dynamic resistance of Zener (ohms)

Rule Sheet
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S Rule
* Pz=Iz*Vz       "Joules Law for Zener
* Er=Ir*R        "Ohms Law for resistor
* Ir=Iz+IL       "Kirchoffs Law for current
* Er=Ein-Eout    "Kirchoffs Law for voltage
* Pr=Er*Ir       "Joules Law for resistor
* Eout=Vz+Iz*Rz  "Ohm's Law for Zener