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Q6. An amplifier circuit using an n-MOSFET is shown in Fig. Q6. The n-MOSFET has the following parameters: Kn = 1 mA/V2 and λ = 0.02 V−1. vin is a small signal AC voltage source. Fig. Q6 (a) Calculate the DC gate voltage, VG. (b) Assuming that the n-MOSFET is operating in the saturation region and neglecting channel length modulation, calculate the threshold voltage, VTHN, given that the voltage drop across the dc current source, IBUS, has been designed to be approximately 0 V. Verify that the n-MOSFET is operating in the saturation region. (c) Find the values of small signal parameters gm and ro of the n-MOSFET. (d) What is the configuration of the amplifier circuit? (e) Draw the small signal ac equivalent circuit of Fig. Q6. You may assume that in the small signal ac equivalent circuit, all the coupling capacitors behave like short circuits. (f) Calculate the input resistance, Rin, and output resistance, Rout . (g) Calculate the voltage gain, vout/vin.

Q6. An amplifier circuit using an n-MOSFET is shown in Fig. Q6. The n-MOSFET has the following parameters: Kn = 1 mA/V2 and λ = 0.02 V−1. vin is a small signal AC voltage source. Fig. Q6 (a) Calculate the DC gate voltage, VG. (b) Assuming that the n-MOSFET is operating in the saturation region and neglecting channel length modulation, calculate the threshold voltage, VTHN, given that the voltage drop across the dc current source, IBUS, has been designed to be approximately 0 V. Verify that the n-MOSFET is operating in the saturation region. (c) Find the values of small signal parameters gm and ro of the n-MOSFET. (d) What is the configuration of the amplifier circuit? (e) Draw the small signal ac equivalent circuit of Fig. Q6. You may assume that in the small signal ac equivalent circuit, all the coupling capacitors behave like short circuits. (f) Calculate the input resistance, Rin, and output resistance, Rout . (g) Calculate the voltage gain, vout/vin.

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Q6. An amplifier circuit using an n-MOSFET is shown in Fig. Q6. The n-MOSFET has the following parameters: K n = 1 m A / V 2 and λ = 0.02 V − 1 . v m is a small signal A C voltage source. Fig. Q6 (a) Calculate the DC gate voltage, V G . (b) Assuming that the n-MOSFET is operating in the saturation region and neglecting channel length modulation, calculate the threshold voltage, V T H N , given that the voltage drop across the dc current source, IBUS, has been designed to be approximately 0 V . Verify that the n-MOSFET is operating in the saturation region. (c) Find the values of small signal parameters g m and r o of the n-MOSFET. (d) What is the configuration of the amplifier circuit? (e) Draw the small signal ac equivalent circuit of Fig. Q6. You may assume that in the small signal ac equivalent circuit, all the coupling capacitors behave like short circuits. (f) Calculate the input resistance, R i n , and output resistance, R out . (g) Calculate the voltage gain, v our / v i n .

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Q6. For the amplifier circuit shown in Fig. Q6, the MOS Transistor Ml has the following parameters: Kn = 1 mAV−2, and VTHN = 1 V. MOS transistors M2 and M3 are identical and have the following parameters: Kp = 1 mAV−2, and VTHP = −1 V. Fig. Q6 (a) Perform the DC analysis of the amplifier circuit shown in Fig. Q6, and show that the DC gate voltage of Ml is 5 V. You need to explain briefly your answer. (b) Calculate the value of RS such that the drain current of MI is 4 mA. Verify that the Ml is operating in the saturation region. [ Ans: Rs = 0.5 kΩ] (c) Calculate the parameters, gm and ro, of the small-signal model of the transistor Ml. [Ans: gm, M1 = 4 mAV−1, and ro, M1 = ∞ ] (d) What is the configuration of this amplifier? (e) Calculate the values of Rin , and Rout . [Ans: Rin = 5 kΩ and Rout = 2 kΩ ] (f) Estimate the voltage gain, Av( = vout /vin ). [ Ans: AV = −1.78]

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Consider MOSFET-based current source circuits shown below. Assume that the n-type MOSFET transistors follow the long-channel model with μnCox = 100 μA/V2 and Vth,n = 0.5 V. All the transistors have a fixed channel length L = 0.25 μm. The bias voltage VB1 is at 0.8 V. Assume that all transistors have no back-bias effect. (1) (2) (a) For a basic current source in Fig. (1), size the NMOS transistor M1's width ( = W1) so that it conducts a current of 1 mA when it operates in saturation region. You may assume λn = 0. (b) What is the minimum value of Vout for this circuit that keeps M1 in saturation region? (c) For a cascode current source in Fig. (2), assume that the transistor M2 has the same width with M1 you determined from part (a). Determine the value of VB2 that yields the lowest minimum VOUT keeping both M1 and M2 in saturation regions. (d) Now, let's assume that the transistors M1 and M2 have a finite output resistance with λn = 0.1 V−1. Compute the value of the output resistance (Rout) of this cascode current source when M1 and M2 are in the saturation region. (Hint: Calculate the output impedance in a small signal equivalent circuit.)
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For the amplifier below, following design information is provided: VDD = 3.3 V, R = 2.4 kΩ, ISS = 1.8 mA, k1 = k2 = 5 mA/V2, VTH,1 = VTH,2 = 0.5 V, λ = 0.1 V−1, γ = 0, ki′ = μ0Cox, ki = μ0 Cox(W L)i. Assume that both transistors are identical and in the saturation region. Finally, NMOS and PMOS bulk terminals are connected to the ground and VDD, respectively. a) What is the DC bias voltage for M1 and M2 given that the voltage drop across ISS is 0.4 V ? You can neglect the channel length modulation, here. Check that the transistors are in the correct operation-mode. b) The resistors will be realized using identical PMOS transistors M3 and M4. If the transistors to be used will have k3 = k4 = 1.5 mA/V2, what will be their overdrive voltages? Check that the transistors are in the correct operation-mode. c) What is the differential voltage gain AV,diff = Vout/Vid in dB ? d) ISS will be realized as a cascode current source. Assume that the voltage drop of 0.4 V is equally shared by the two transistors, M5 and M6 having k5′ = k6′ = 0.5 mA/V2 and VTH, 5 = VTH, 6 = 0.5 V. Assuming the gate voltages of both transistors are 1 V, find the W/L ratios of each device. Once again, you can neglect the channel length modulation here. e) Considering (d), how would the W/L ratios qualitatively change (increase/decrease/stays the same), if γ > 0 ? Explain your reasoning analytically, i. e. , using appropriate equations. f) Using the cascode current source, calculate the common-mode gain of the circuit AV, CM = Vout /Vin in dB, where Vin . s applied to the gates of both M1 and M2. Assume λ = 0.1 V−1 for M5 and M6. g) Calculate the CMRR of the circuit in dB.
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