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Problem 2. [50 pts] Frequency response 2- Cascode amplifier M3 VDD=3.3V 10ux VIN M2 ID2 C2 M4 VE RIN MI Vel The circuit above is similar to the one in Problem 2 with: An additional transistor M4 that have the same size with M1. 。 Bias voltage VB is constant. The Body of M4 is connected to GND, as drawn in the schematic. o Cdb4 = Csb4 = 20 fF, Cgd4 = 10 fF, Cgs4 = 40 fF. • Ignore body effect for M4. All other parameters are the same as in Problem 2. Assume all transistors in saturation. Ignore the channel-length modulation when calculating transistor DC currents but consider channel length modulation in calculations of the transistor output resistances, the gain and time-constant calculations. a. Draw the complete small-signal model of the amplifier with all device capacitors mentioned above. b. Find the low-frequency gain, Av = |Vo/Vsig, in dB, of the amplifier. c. Use the Miller's Theorem and OCTC methods to find the time-constant, t₁, at the Gate of Mi. (Hint: note that the gain from the input to voi is different than that in Problem 2) d. Use the Miller's Theorem and OCTC methods to find the time-constant, t2, at the Drain of Mi (i.e., Vol). (Hint: note that the gain from the input to vol is different than that in Problem 2) e. Use the OCTC method to find the time-constant, t3, at the Drain of M4 (i.e., v.). f. Based on (b), (c), (d) find the 3-dB frequency, fi, in Hz of the amplifier. g. Find the frequency of the zero, fz, in Hz of the amplifier. h. Based on the above analysis, this amplifier has three poles and one zero. Please use piecewise linear method to sketch the magnitude and phase of amplifier on a Bode plot (a semi-log plot). i. In your Bode plot, highlight fu, fz, and 20-logio(Av(joo)) at both f→0 and fz. Also, highlight the slopes of non-horizontal piecewise linear lines. Hint: for (h) and (i), please assume the two poles are almost at the same frequency (i.e., fH) if "max[11,12]/min[11,12] <4”.

Fig: 1