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Amplification modeHere we derive the impedances as seen looking into the terminals of a MOS device connected in amplification mode. The setup is as follows:Gate ImpedanceThe DC impedance looking into the gate is practically infinite since the gate leakage is very smallDrain ImpedanceThe small signal circuit to derive the drain impedance is as follows:We can write the KVL from the test source to ground through Rs and from gate to ground through Rs we have the following 3 equations: $$(I_1g_mV_1g_{mb}V_{BS})r_o+I_xR_S=V_x$$ $$V_1+I_xR_S=0$$ $$V_{BS} = I_xR_S$$ Eliminating $V_1$ and $V_{BS}$ and solving for $V_x/I_x$ we have$$Z_D = r_o+R_S(1+r_o(g_m+g_{mb}))$$ Special Cases:
Source ImpedanceThe small signal circuit to derive the source impedance is as follows:Again writing the KVL from $V_x$ to the gate and to the drain we have the following equations:$$V_x = V_1$$ $$V_x=V_{BS}$$ $$(I_x+g_mV_1+g_{mb}V_{BS})r_o+I_xR_D=V_x$$ Eliminating $V_1$ and $V_{BS}$ and solving for $V_x/I_x$ we have$$Z_S = {r_o+R_D}/{1+r_o(g_m+g_{mb})}$$ Special CasesIf$R_D=0$ then$$Z_S = r_o∥{1/{g_m+g_{mb}} }$$ Diode Connected ModeHere we derive the impedances as seen looking into the terminals of a MOS device connected as a diode. The setup is as follows:GateDrain ImpedanceThe small signal circuit to derive the GateDrain impedance is as follows:Writing the KVL through the $V_1$ loop and through the $r_o$ we have the following equations:$$V_x=I_xR_S+V_1$$ $$V_{BS}=I_xR_S$$ $$(I_xg_mV_1g_{mb}V_{BS})r_o+I_xR_S=V_x$$ Eliminating $V_1$ and $V_{BS}$ and solving for $V_x/I_x$ we have$$Z_D = {r_o+R_S(1+r_o(g_m+g_{mb}))}/{1+g_mr_o}$$ Special Cases
Source ImpedanceThe small signal circuit to derive the Source impedance is as follows:Writing the KVL through the $V_1$ loop and through the $r_o$ we have the following equations:$$V_x+V_1=I_xR_D$$ $$V_{BS}=V_x$$ $$(I_x+g_mV_1+g_{mb}V_{BS})r_o+I_xR_D=V_x$$ Eliminating $V_1$ and $V_{BS}$ and solving for $V_x/I_x$ we have$$Z_S = {r_o+R_D+r_og_mR_D}/{1+(g_m+g_{mb})r_o}$$ Special Cases
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Copyright 2018 Milind Gupta 