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The MOS transistors have the following characteristics: Vtn = |Vtp| = 0.5 V, Kn’ = 400 µA/V2 and Kn’ = 100 µA/V2. Assume VDD = 3 V and Q2 and Q3 are matched. The required gm of the amplifying transistor (Q1) is 1000 µA/V and the output voltage (VOUT ) should be allowed to swing to within 0.2 V of VDD. (a) Find the (W/L) ratio of all transistors and the resistor R. For this part you may assume there is no channel length modulation. (b) Show a clean and labeled small signal equivalent circuit with the values (gm and ra) shown. Assume all transistors have |λ| = 0.02 V-1 (c) Find both an expression and the numerical value for the small signal gain v0/vsig, and Rout. (d) What is the range of the output voltage swing.
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Answer the following questions on the circuit shown in Fig. 3. The n-type MOS transistors M1 and M2 have the same characteristics, and the small-signal equivalent circuit of each transistor is shown in Fig. 4. Here, gm, ro, and v are the transconductance, the drain resistance, and the input voltage of the MOS transistor, respectively. RD and RS are the resistances in the circuit. VDD is a positive constant voltage. Note that v1, v2, v3, and v4 represent small-signal components of the voltages V1, V2, V3, and V4, respectively. (1) The small-signal components vin and vout represent the difference of two input signals v1 - v2 and the difference of two output signals v3 - v4, respectively. Find the voltage amplification factor A = vout/vin. (2) The small-signal components vin’ and vout’ represent the sum of two input signals v1 + v2 and the sum of two output signals v3 + v4, respectively. Find the voltage amplification factor A’ = vout’/vin’. (3) Describe in a few lines the function of the circuit in Fig. 3, based on the results of Parts (1) and (2). Assume ro → ∞ and RS ≫ gm-1.

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(a) The MOS capacitor in Fig. 4.1 has VTN = 1 V and VG = 2 V. To what region of operation does this bias condition correspond? (b) Repeat for VG = -2 V. (c) Repeat for VG = 0.5 V. Figure 4.1 MOS capacitor structure on p-type silicon.
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