In the circuit shown in the figure, the channel length modulation of all transistors is non-zero $$\left( {\lambda \ne 0} \right)$$. Also all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain $$\left( {{V_0}/{V_{in}}} \right)$$ of the circuit is

A voltage V_G is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for V_G = 0.8 V is $$2\,\, \times \,\,{10^{11}}\,\,\,\,\,\,c{m^{ - 2}}$$ . For $${V_G}\,\, = \,\,1.3\,\,V,$$ the inversion carrier density is $$4\,\,\, \times \,\,\,{10^{11}}\,\,\,\,c{m^{ - 2}}.$$ What is the value of the inversion carrier density for V_G = 1.8 V?

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of V_GS and V_DS. Given,
g_m = 0.5$$\mu {\rm A}/V$$ for V_DS = 50 m V and V_GS = 2V,
g_d = $$8\mu {\rm A}/V$$ for V_GS = 2 V and V_DS = 0 V,
Where g_m =$${{\partial {{\rm I}_D}} \over {\partial {V_{GS}}}}\,\,and\,\,{g_d}\,\, = \,{{\partial {{\rm I}_D}} \over {\partial {V_{DS}}}}$$

The threshold voltage (in volts) of the transistor is

In the circuit shown, both the enhancement mode NMOS transistors have the following characteristics: k_n = $${\mu _n}{C_{ox}}(W/L) = 1m{\rm A}/{V^2}$$ ; V_TN = 1V. Asuume that the channel length modulation parameter $$\lambda $$ is zero and body is shorted to source. The minimum supply voltage V_DD (in volts) needed to ensure that transistor M₁ operates in saturation mode of operation is _____