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Problem 1. [50 pts] Frequency response 1-CS amplifier VDD=3.3V M3 HCM2 ID2 Vol RIN 7 C2 M1 Rol 10uA VIN Given an amplifier circuit shown above and the following parameters: - - - PMOS: Vt,p = -0.62 V, μp Cox = 36 UA/V², 1p=0.019 [1/V] NMOS: Vt,n = 0.48 V, Cox = 90 UA/V², 1=0.025 [1/V] Resistor RIN = 20 k (W/L)2=20(W/L)3 (W/L)₁ = 20 Cgd1=Cgd2 = 10 fF. Assume: - All transistors in saturation. - Cgs1 = 40 fF. - Cdb1 = Cdb2 = 20 fF. C2 = 500 FF. - All transistors have the Body shorted to the Source, i.e. you can ignore CSB. 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 M1. d. Use the Miller's Theorem and OCTC methods to find the time-constant, t2, at the Drain of M₁ (i.e., Vol). e. Based on (c) and (d), find the 3-dB frequency, fн, in Hz of the amplifier. f. Find the frequency of the zero, fz, in Hz of the amplifier. g. Based on the above analysis, this amplifier has two poles and one zero. Please use piecewise linear method to sketch the magnitude of the Bode plot (a log-log plot). h. In your Bode plot, highlight fH, fz, and 20-log10(Av(jo)) at both f→0 and fz. Also, highlight the slopes of non-horizontal piecewise linear lines. Hint: for (g) and (h), please assume the two poles are almost at the same frequency (i.e.,

Fig: 1