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GATE 2016 EC (EC3) – Question 51

Analog Circuits · BJT and MOSFET Amplifiers · 2 marks · Multiple choice

All transistors in the shown circuit operate in saturation, have nonzero channel-length modulation and negligible body effect. Its small-signal voltage gain $V_O/V_{in}$ is

Diagram for GATE 2016 EC (EC3) question 51
  1. $-g_{m1}(r_{o1}\parallel r_{o2}\parallel r_{o3})$
  2. $-g_{m1}(r_{o1}\parallel g_{m3}^{-1}\parallel r_{o3})$
  3. $-g_{m1}[r_{o1}\parallel(g_{m2}^{-1}\parallel r_{o2})\parallel r_{o3}]$
  4. $-g_{m1}[r_{o1}\parallel(g_{m3}^{-1}\parallel r_{o3})\parallel r_{o2}]$

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Correct answer: (C) $-g_{m1}[r_{o1}\parallel(g_{m2}^{-1}\parallel r_{o2})\parallel r_{o3}]$

Explanation

M1 supplies the common-source transconductance current $g_{m1}v_{in}$ and output resistance ro1. M3 has its gate and source at AC ground, so it contributes ro3 without a transconductance shunt.

M2's gate and drain are both at AC ground. Looking into its source gives conductance $g_{m2}+1/r_{o2}$, equivalent to $(1/g_{m2})\parallel r_{o2}$.

These three loads are parallel. Multiplying their equivalent resistance by −gm1 gives **C**.

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