Question

2. (25 pts) An NMOS transistor operating in the linearregion with VDs 50mV is measured to have a drain current of 25μΑ for VGs* IV (Case I) and 50μΑ for VGs* 1.5V (Case II). a. (5 pts) Calculate the threshold voltage ofthe NMOS transistor b. (5 pts) Calculate the resistance between drain and source for each case c. (5 pts) Calculate the device aspect ratio W/L iKn_ 50μΑ/. d. (5 pts) Calculate the drain current of the NMOS transistor if VDS=0.1V and Vos=2V. e. (5 pts) Calculate the Vos value and corresponding drain current when the pinch-off starts at VGs 2V

Answer 1

N - MOS in saturation region I_D = 1/2 mu_n Cox W/L (V_GS - V_T)^2 (1 + lambda V_DS) neglect channel length modulation lambda = 0 I_D = -1/2 mu Cox w/L (V_GS - V_T)^2 25 times 10^-6 = 1/2 k_n(1 - V_T)^2 equation (1) 50 times 10^-6 = 1/2 k_n(1.5 - V_T)^2 equation (2) (2)/(1) implies 2 = (1 - 5V_T)^2/)(1 - V_T)^2 squareroot 2 = 1.5 - V_T/1 - V_T squareroot 2 - squareroot 2 V_T = 1.5 - V_T 1.41 - 1.5 = 1.41 V_T - V_T -0.09 = 0.41 V_T V_T = 0.09/0.41 = -0.2 V \r\n 1st case V_DS = 50 mV R_ds = V_DS/I_D = 50 mV/25 mu A R_ds = 2 times 10^3 = 2k ohm 2nd case V_DS = 50 mV R_ds = 50 mV/50 mu A implies 1 k ohm \r\n mu_n Cox = k_n^� 50 = 1/2 k_n^�(w/L)(1.3)^2 50 = 1/2(50) (w/L)(1.3)^2 2 = (w/L)(1.7) W/L = 2/1.7 = 20/17 I_D = 1/2 mu_n Cox W/L(V_GS - V_T)^2