**2. (a) Explain with V-I characteristics the working of Zener diode as a voltage regulator. [6M]**

i) Zener Diodes are widely used as Shunt Voltage Regulators to regulate voltage across small loads.

ii) Zener Diodes have a sharp reverse breakdown voltage and breakdown voltage will be constant for a wide rang of currents.

iii) Thus we will connect the zener diode parallel to the load such that the applied voltage will reverse bias it. Thus if the reverse bias voltage across the zener diode exceeds the knee voltage, the voltage across the load will be constant.

iv) In the above circuit diagram excess voltage (V_{in} – V_{z} ) will drop across R_{s} thus by limiting the current through Zener. For the proper designing of the regulator we should know,

- Unregulated Input Voltage Range
- Required Output Voltage
- Max Load Current Required

v) The value of resistance R_{s} should satisfy the following conditions,

- The value of R
_{s}must be small enough to keep the Zener Diode in reverse breakdown region. The minimum current required for a Zener Diode to keep it in reverse breakdown region - The value of R
_{s}must be large enough that the current through the zener diode should not destroy it. That is the maximum power dissipation P_{max}should be less than I_{z}V_{z}.

Thus we should find R_{s min} and R_{s max.} To find the value of R_{s min} we should consider the extreme condition that Vin is minimum and load current is maximum.

$latex I_s\;=\;I_{z\;min}\;+\;I_{L\;max}$

$latex I_{z\;min}\;=\;Please\;Refer\;Datasheet$

$latex V_{s}= V_{in min}-V_{z}$

$latex R_{s\;min}\;=\;V_s/I_s$

To find the value of R_{s max} we should consider the extreme condition that V_{in} is maximum and load current is minimum (ie, no load connected).

$latex I_s\;=\;I_{Zmin}\;+\;I_{Lmax}\;$

$latex I_{Zmax}\;=\;P_{max}/V_z\;$

$latex V_{s}= V_{in min}-V_{z}$

$latex R_{s\;max}\;=\;V_s/I_s$

If α = 0.98, Calculate value of β. [6M]

**ALPHA (α):** It is a large signal current gain in common base configuration. It is the ratio of collector current (output current) to the emitter current (input current).

$latex \begin{array}{l}\alpha=\frac{Collector\;current}{Emitter\;current}\\\\\alpha=\frac{I_C}{I_E}\end{array}$

It is a current gain in CB amplifier and it indicates that the amount of emitter current reaching to collector. Its value is unity ideally and practically less than unity.

**Beta (β):** It is a current gain factor in the common emitter configuration. It is the ratio of collector current (output current) to base current (output current).

$latex beta\;\left(\beta\right)=\frac{I_C}{I_B}$

normally Its value is greater than 100.

**Relation between α and β in a transistor:**

$latex \begin{array}{l}\begin{array}{l}\alpha=\frac{I_C}{I_E}\;\;and\;\;\beta=\frac{I_C}{I_B}\\\\I_E=I_B+I_C\end{array}\\\\\frac{I_C}\alpha=\frac{I_C}\beta+I_C\\\\\therefore\alpha=\frac\beta{\beta+1}\;\;or\;\;\;\beta=\frac\alpha{1-\alpha}\\\end{array}$

Given value of α= 0.98

To calculate: beta(β)

By using relation of α and β

β=α/1-α

By substituting given value of α= 0.98

beta(β)= 49.

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