Question 4.3: Check the validity of the assumption of ω0Cdg << gm fo...
Check the validity of the assumption of \omega_0 C_{dg}\ll g_m for a typical 0.13 micron NMOS transistor operating in the velocity saturation regime.
The operating frequency of the amplifier is 3 GHz.
Under velocity saturation (which is the case for a 0.13 micron transistor, as shown in Chapter 1), the transconductance is g_{m(v-sat)} = kWC_{ox}v_{sat} and the drain–gate capacitance C_{dg}=W\times CDGW.
Therefore,
\frac{\omega_0C_{dg}}{g_m}=\frac{\omega_0\times CDGW}{C_{ox}v_{sat}}which is independent of the gate width.
The related parameter values for this 0.13 micron technology are TOX = 2.3\times 10^{-9} [m] (which corresponds to C_{ox}= 15\times 10^{-3} f/m²), and CDGW = 5.18\times 10^{-10} [f/m].
The saturation velocity of electrons in the channel was given in Chapter 1 as 6.5\times 10^4 [m/s]. Therefore
\frac{\omega_0C_{dg}}{g_m}=\frac{2\pi \times (3\times 10^9)\times (5.18\times 10^{-10})}{(15\times 10^{-3})\times (6.5\times 10^4)}\cong 10^{-2}which corresponds to an error of 1% on the magnitude of the gain and an excess phase
shift of only 0.57º.