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In the following feedback amplifier, assume that M1, M2, and M3 are all biased to be in the saturation region. Consider λ = 0 (30 points). a. Find the polarity of the feedback. b. Identify the type of feedback. c. Derive the expression for the open-loop voltage gain (AV,OL = Vout /Vin ), including the loading effects of the feedback. d. Determine the value of the feedback factor K and derive the expression for the closed-loop voltage gain (Av,CL = Vout/Vin). e. Derive the expression for the closed-loop output resistance Rout,CL.

In the following feedback amplifier, assume that M1, M2, and M3 are all biased to be in the saturation region. Consider λ = 0 (30 points). a. Find the polarity of the feedback. b. Identify the type of feedback. c. Derive the expression for the open-loop voltage gain (AV,OL = Vout /Vin ), including the loading effects of the feedback. d. Determine the value of the feedback factor K and derive the expression for the closed-loop voltage gain (Av,CL = Vout/Vin). e. Derive the expression for the closed-loop output resistance Rout,CL.

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In the following feedback amplifier, assume that M1, M2, and M3 are all biased to be in the saturation region. Consider λ = 0 (30 points). a. Find the polarity of the feedback. b. Identify the type of feedback. c. Derive the expression for the open-loop voltage gain (AV,OL = Vout /Vin ), including the loading effects of the feedback. d. Determine the value of the feedback factor K and derive the expression for the closed-loop voltage gain (Av,CL = Vout/Vin). e. Derive the expression for the closed-loop output resistance Rout,CL.

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Consider the following amplifier operating at 300 K. The transistor M1 has μnCox = 250 μA/V2 and Vth = 0.4V. You may assume that M1 operates in saturation region and neglect its channel length modulation (λ = 0). The supply voltage VDD is 1.8V. (a) Find the expression for the input resistance (Rin) assuming that M1 has the transconductance of gm in saturation region. (b) Find the expression for the voltage gain AV=Vout /vin. (c) Explain the phase relationship between the vin and Vout signals. In other words, are they in phase or out of phase? Explain the reason why. (d) If this amplifier stage must provide an output resistance of 500 Ω, what is the maximum allowable value for ID of M1 that keeps M1 in saturation? (e) For the ID value obtained from (d), calculate the required value of W/L that makes the voltage gain Av equal to 10. (f) Calculate the maximum load capacitance (Cout ) that the amplifier can drive at its output while keeping its −3dB bandwidth above 100 MHz.
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For all circuits, do not consider channel length modulation for calculating bias points. Unless otherwise specified, channel length modulation effect needs to be considered for small-signal analysis. All answers should be given to the second decimal place. Circuit and device parameters are: Vdd = 5 V;VTn = VTp = 1 V; μnCox = 50 μA/V2; μpCox = 25 μA/V2; λn = λp = 0.01 V−1; Lmin = 1 μm Figure 1 (for problems 1-3) Figure 2 (for problems 5-9) Figure 1: Transistor M1 has (W/L) = (160 μm/2 μm) and a bias current Iout = 2 mA. We desire M1 to be in saturation. You should assume λn = 0 for problems (1)-(3). Determine the ratio R1 /R2 required. 1 point Let VTn increase by 10% to 1.1 V. What is the new value of Iout in mA ? 1 point Let μnCox increase by 10% to 55 μA/V2. What is the new value of Iout in mA ? 1 point Figure 2: The circuit has Iref = 2 mA and Vp = 4 V. Transistors M1, M2 and M3 have (W/L) = (80 μm/1 μm). Determine the value of vx. (in volts) 1 point Determine the minimum allowable value of Vb (in volts) such that all devices are in saturation. 1 point Determine the maximum allowable value of Vb (in volts) such that all devices are in saturation. 1 point Determine Vb (in volts) such that vX = VY. 1 point determine the output resistance of this circuit ∂Vp/∂Iout in MΩ. 1 point Description for questions 9-10: An NMOS device with ID = 1 mA must operate in saturation with drain-source voltages as low as 0.5 V. The minimum required small-signal output impedance is 400 kQ. {Hint: You need to use the relations: rout = 1 /(λ⋅ID); λ⋅L = constant; and expression for VDS, sat = VGS−VT} Determine the length of the device in μm. 1 point Determine the width of the device in μm. 1 point

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For all circuits, do not consider channel length modulation for calculating bias points. Unless otherwise specified, channel length modulation effect needs to be considered for small-signal analysis. All answers should be given to the second decimal place. Circuit and device parameters are: Vdd = 5 V; VTnn = VTp = 1 V; μnCox = 50 μA/V2; μpCox = 25 μA/V2; λn = λp = 0.01 V−1; Lmin = 1 μm Figure 1 (for problems 1-3) Figure 2 (for problems 5-9) Figure 1: Transistor M1 has (W/L) = (160 μm/2 μm) and a bias current Iout = 2 mA. We desire M1 to be in saturation. You should assume λn = 0 for problems (1)-(3). Determine the ratio R1 /R2 required. 1 point Let VTn increase by 10% to 1.1 V. What is the new value of Iout in mA ? 1 point Let μnCox increase by 10% to 55 μA/V2. What is the new value of Iout in mA ? 1 point Figure 2: The circuit has Iref = 2 mA and VP = 4 V. Transistors M1, M2 and M3 have (W/L) = (80 μm/1 μm). Determine the value of vx. (in volts) 1 point Determine the minimum allowable value of Vb (in volts) such that all devices are in saturation. 1 point Determine the maximum allowable value of Vb (in volts) such that all devices are in saturation. 1 point Determine Vb (in volts) such that VX = VY. 1 point determine the output resistance of this circuit ∂Vp/Iout in MQ. 1 point Description for questions 9-10: An NMOS device with ID = 1 mA must operate in saturation with drain-source voltages as low as 0.5 V. The minimum required small-signal output impedance is 400 kΩ. {Hint: You need to use the relations: rout = 1 /(λ⋅ID); λ⋅L = constant; and expression for VDS, sat = VGS−VT }Determine the length of the device in μm. 1 point Determine the width of the device in μm. 1 point

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