What is the voltage gain for the circuit given below?

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Question

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DFCCIL Executive S&T 2018 Official Paper

Answer 1

In AC model analysis all DC sources will be shorted.

For M₂ MOSFET-

So gate and source of M₂ are shorted.

F1 Neha B Shraddha 05.05.2021. D2

V_GS = 0

So output resistance \({R_{out}} = \dfrac{{{V_x}}}{{{I_x}}} = {r_{02}}\)

So M₂ will act as a resistor with resistance r_o2.

F23 Neha B 17-3-2021 Swati D3

Here M₂ will act as a Resistor whose Resistance will be \({r_{{0_2}}}\)

F23 Neha B 17-3-2021 Swati D4

Replacing M₁ with small-signal model.

F23 Neha B 17-3-2021 Swati D5

\({V_0} = \left( {{r_{{0_1}}}\parallel {r_{{0_2}}}} \right) \times (- g_{m_1}\;Vgs)\)

V_in = Vgs

\(\frac{{{V_{out}}}}{{{V_{in}}}} = - g_{m_1}\left( {{r_{{0_1}}}\parallel {r_{{0_2}}}} \right)\)