can you give me example problems?

The MOSFET Unity-Gain Frequency (fy) A figure of merit for the high-frequency operation of the MOSFET as an amplifier is the unity-gain frequency, /r, also known as the transition frequency, which gives rise to the subscript 7. This is defined as the frequency at which the short-circuit current gain of the common-source configuration becomes unity. Figure 10.5 shows the MOSFET hybrid-x model with the source as the common terminal between the input and output ports. To determine the short-circuit current gain, the input is fed with a current-source signal /; and the output terminals are short-circuited. We can see that the current in the short circuit is given by 10 = 8m Vgs - SCgd Vgs = (8m - SCgd) Vgs (10.6) From Fig. 10.5, we see that Coo appears in parallel with Cos and thus we can express Ves in terms of the input current I; as (10.7) Vgs s (Cas + Cgd) Equations (10.6) and (10.7) can be combined to obtain the short-circuit current gain, 8m - SCed (10.8) 1; s( C s + C ed) For physical frequencies s = jo, the magnitude of the current gain is where we have neglected Cgo relative to gm. The gain magnitude becomes one at the frequency WT = 8m/(Cgs + Cgd) Thus the unity-gain frequency fr = wy/2x is 8m (10.9) fr = 27 ( Cqs + Cgd) Since fy is proportional to go, which determines the midband gain, and inversely proportional to the MOSFET internal capacitances, which limit the amplifier bandwidth, the higher the value of fy, the more effective the MOSFET becomes as an amplifier. Substituting for gm using Eq. (7.41), we can express fr in terms of the bias current Ip (see Problem 10.3). Alternatively, we can substitute for gm from Eq. (7.40) to express fy in terms of the overdrive voltage Vor (see Problem 10.4). Both expressions give us additional insight into the high-frequency operation of the MOSFET. Also refer to Appendix G for a further discussion of fT