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Question 1. Cascode Amplifier In the circuit below, assume μnCox(W/L)1 = μnCox(W/L)2 = 1 mA/V2, ID1 = ID2 = 0.55 mA, VDD = 3.1 V, Vth = 1 V, λ = 0.1, and RD = 2 kΩ (neglect body effect) (a) Calculate VB and VIN such that M1 is exactly at saturation (VDS = VGS−Vth) (b) Draw small signal model and calculate small signal gain vout/vin Figure 1. Cascode Amplifier

Question 1. Cascode Amplifier In the circuit below, assume μnCox(W/L)1 = μnCox(W/L)2 = 1 mA/V2, ID1 = ID2 = 0.55 mA, VDD = 3.1 V, Vth = 1 V, λ = 0.1, and RD = 2 kΩ (neglect body effect) (a) Calculate VB and VIN such that M1 is exactly at saturation (VDS = VGS−Vth) (b) Draw small signal model and calculate small signal gain vout/vin Figure 1. Cascode Amplifier

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Question 1. Cascode Amplifier In the circuit below, assume μ n C o x ( W L ) 1 = μ n C o x ( W L ) 2 = 1 m A / V 2 , I D 1 = I D 2 = 0.55 m A , V D D = 3.1 V, V th = 1 V , λ = 0.1 , and R D = 2 k Ω (neglect body effect) (a) Calculate V B and V I N such that M 1 is exactly at saturation ( V D S = V G S − V t h ) (b) Draw small signal model and calculate small signal gain v out v in Figure 1. Cascode Amplifier

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(a) Choose VB such that M1 is 300mV away from the triode region (VDS1 = VGS1-VTH1+300mV; M1 and M2 operate in Saturation region). (b) Calculate the small-signal voltage gain (VOUT/VIN). (c) Assume VB = 1.43 V, calculate the maximum output voltage swing to keep all transistors in saturation. Neglect channel length modulation. (d) Assume the maximum output swing is VOUT = 2.23 VPP, Calculate the swing at node X. In Fig. 2, assume (W/L)1 = 12 μm/0.18 μm, (W/L)2 = 24 μm/0.36 μm, ID1 = ID2 = 0.5 mA, and RD = 2 kΩ, VTH,N = 0.5 V, μnCox = 150 μA/V2, VDD = 3.3 V, λn = 0.1 V-1. Neglect body effect. Neglect channel length modulation except doing output impedance calculation.
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In this question, we will study the source follower cascaded by a CS stage. Neglect body effect and channel length modulation. (a) First we carry out a dc analysis on the CS stage. In the CS stage circuit shown in Figure 1, assume μnCox(W/L)1 = μpCox(W/L)2 = 1mA/V2, VTN = 0.7V, VTP = −1V, VDD = 2.5V. Calculate I1 and VOUT such that M1 operates in saturation with VGS1 = 0.8 V. What is VIN if M1 is at the edge of saturation? (b) Then we do small signal analysis on the CS stage. In the circuit shown in Figure 1, derive the small signal voltage gain Av = vout/vin. What is the maximum dc level of Vin for which M1 remains saturated? Express VIN by VDD, gate-source voltages and threshold voltages of M1 and M2. (c) To accommodate an input de level close to VDD, we further cascade it with a source follower as shown in Figure 2. Derive the small signal gain vout/vin. If VIN = VDD, what relationship between the gate-source voltages of M2 and M3 guarantees that M1 is saturated?
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Q1: (a) Choose VB such that M1 is 200mV away from the triode (linear) region. Assume Vtn = 0.5 V, unCox = 200 uA/V2, and VDD = 2.5 V ID1 = ID2 = 0.5 mA,( W/L)1 = 80u/5u, (W/L)2 = 40u/5u, and Rd = 1 kohm hint: gm = 2unCox(W/L)ID = 2ID/VGS-Vth Q1: (b) Calculate the small signal voltage gain Assumptions remain the same as Q1(a) Q1: (c) Using the value of VB from part (a), calculate the maximum output voltage swing that keeps both transistors in saturation. Assumptions remain the same as Q1(a).Choose VB such that M1 is 200 mV away from the triode (linear) region. Assume Vtn = 0.5 V, μnCox = 200 μA/V2, and VDD = 2.5V ID1 = ID2 = 0.5 mA, (W/L)1 = 80u/5u, (W/L)2 = 40u/5u, and Rd = 1 kΩ
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