**2. (a) In a centre tapped FWR, the rms half secondary voltage is 10 V. Assuming ideal diodes and load resistance of 2 kΩ, find DC load current, ripple factor and efficiency of rectification. [6M]**

Given:- Centre tapped FWR

V_{rms}= 10 V ; R_{L}= 2 kΩ

i) I_{m} = $latex \frac{V_m}{R_L}$

Now,

$latex V_m=\sqrt2\;V_{rms}=14.14\;V$

$latex I_m=\frac{14.14}2=7.07\;mA\;\;\;\;\;\leftarrow\left(peak\;current\right)$

$latex I_{dc}=\frac{2I_m}\pi=\frac{2\times7.07}\pi=4.5\;mA.$

ii) Ripple factor = $latex \sqrt{\left(\frac{I_{rms}}{I_{oc}}\right)^2-1}$

$latex I_{rms}=\frac{I_m}{\sqrt2}=\frac{7.07}{\sqrt2}=4.99\;mA.$

Ripple factor = $latex \sqrt{\left(\frac{4.99}{4.5}\right)^2-1}$

Ripple factor = 0.4839

iii) Efficiency of rectification:-(η)

$latex \begin{array}{l}P_{DC}=\;I_{DC}^2\;\cdot R_L\\\\\;\;\;\;\;\;\;=4.5^2\times2\times10^3\\\\\;\;\;\;\;\;\;=40.5\;mW\\\\\end{array}$

$latex \begin{array}{l}P_{AC}=\;I_{rms}^2\;\cdot R_L\\\\\;\;\;\;\;\;\;=4.99^2\times2\times10^3\\\\\;\;\;\;\;\;\;=49.8\;mW\end{array}$

$latex \begin{array}{l}\%\eta\;=\;\frac{P_{DC}}{P_{AC}}\times100\\\\\;\;\;\;\;\;\;=\frac{40.5}{49.8}\times100\\\\\;\boxed{\%\eta=81.32\%}\\\end{array}$

**(b) Draw and explain drain and transfer, characteristics of enhancement type P-channel MOSFET. [6M]**

i) Following figure shows the drain characteristics of p-channel enhancement type MOSFET.

ii) If no voltage is applied to the gate terminal (i.e.V_{GS}=0) we can say that there are two back to back diodes between source and drain region. Thus current flowing is zero even if V_{DS} is applied.

iii) Now if we increase the V_{GS} in negative direction, the concentration of holes near the SiO_{2} surface i.e. between source and drain starts increasing. This is known as induced p-channel.

iv) At particular value of V_{GS}, there are a sufficient number holes get induced to form conducting channel and there is a measurable current flow between drain and source. This value of V_{GS} is called as threshold voltage denoted as V_{T}. The value of V_{T} is negative for p-channel MOSFET.

v) Drain characteristics for n channel enhancement type MOSFET is shown in the figure. It clearly indicates that current I_{D} is zero for |V_{GS}|<|V_{T}|. The region is known as cut-off region.

vi) Consider any constant value of V_{GS }and assume that V_{DS} is increasing in negative direction from 0V. For small values of V_{DS} current I_{D} increases linearly with increase in the voltage V_{DS}. This region is known as ohmic region.

vii) As V_{DS} is further increased(in negative direction), the channel starts tapering at drain end because of voltage drop across the length of channel. The current I_{D} no longer increases linearly. At particular value of V_{DS}, channel becomes pinched-off at drain end and current remains constant for further increase in V_{DS}. i.e. becomes saturated. This region is known as saturation region.

viii) Transfer characteristics is shown below.

ix) Transfer characteristics is a relation between I_{D} and V_{GS} for constant is shown in the figure. For PMOS device it is in the negative V_{GS} region and the current I_{D} is zero till V_{GS}=V_{T}.

x) For the | V_{GS} |>| V_{T} |, i.e. more negative than threshold voltage, relation between drain current I_{D} and V_{GS} is given by following non-linear relation:

I_{D}=k (V_{GS}-V_{T})^{2}

where k is constant and function of the geometry of the device.

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