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The circuit below is a model of a MOS common drain amplifier where vs is the input voltage and vo is the output. a) Find the differential equation for vo.(3 pt) b) if vo(0) = 0 and if vs(t) = 1 V for t > 0, what is the solution for vo(t) for t > 0. (Consider R, C, g are known; note that Vs is not known) (2 pt)

The circuit below is a model of a MOS common drain amplifier where vs is the input voltage and vo is the output. a) Find the differential equation for vo.(3 pt) b) if vo(0) = 0 and if vs(t) = 1 V for t > 0, what is the solution for vo(t) for t > 0. (Consider R, C, g are known; note that Vs is not known) (2 pt)

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The circuit below is a model of a MOS common drain amplifier where vs is the input voltage and vo is the output. a) Find the differential equation for vo.(3 pt) b) if vo(0) = 0 and if vs(t) = 1 V for t > 0, what is the solution for vo(t) for t > 0. (Consider R, C, g are known; note that Vs is not known) (2 pt)

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Assume that the MOSFET has the following parameters: Vt = 1 V, K = 0.4 mA/V2 VA = 40 V. It is connected as an amplifier as shown in Figure Q4 and vs is an AC input voltage and vo is the AC output voltage. The DC drain voltage VD is set to be 0 V. Further assume that all the capacitors in the circuit are very large. Figure Q7. (a) Which type of amplifier configuration does the above circuit (3 marks) belong to? What are the electrical properties of this type of amplifier configuration? (b) Show that the MOS transistor operates in the saturation mode. (3 marks) State one electrical characteristic of a saturated MOS transistor. (c) Determine the drain current ID. (10 marks) (d) Design the load resistance RL such that the AC voltage gain vo/vs of (10 marks) the MOSFET amplifier equals -10 . (e) Suppose the amplitude of AC input vs is 0.2 V and the AC voltage (4 marks) gain of the amplifier equals -10. Do we have a distorted AC output waveform?

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All the capacitors in the circuit shown below have large values, i.e. can be considered short circuits at low frequencies. The threshold voltage of the NMOS transistor in the common source amplifier circuit is 1 V and the kn' (W/L) = 1 mA/V2.a) Find the required DC value of the Vas that would establish a dc bias current of 1) = 2 mA; b) Find the required values for the resistances RG1 and Rg2 so both the value of VGS from part (a) can be assured and the value of the input resistance (Rin) of this amplifier to be equal or higher than 3 M22; c) Determine a value for R, so the open circuit voltage gain of this amplifier A, to be -10. NOTE: Use the small signal model discussed in lecture notes.
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In this question, you are asked to find the effective transconductance (Gm) and the resistance into the drain (Rx) of a common-source amplifier with source degeneration. Based on the results, the voltage gain of a common-source amplifier with source degeneration will be evaluated a) The figures shown below are a circuit to find the effective transconductance (G) of the NMOSEFT with source degeneration (left) and its corresponding small-signal circuit (right). It is noted that the output is shorted to VDD (ac grounded) since the definition of effective transconductance is the ratio between the short-circuit output current and the input signal voltage. Prove that Gm is given by Gm = id/vin = gm/1+gmRs In this calculation, the current passing through ro can be neglected since, in general, ro is very large when the NMOSFET operates in saturation region and so this current is very small. Thus, the indication of id is the current of the voltage-controlled current source (gmvgs) only. b) The figure shown below is the method to evaluate the resistance looking into the drain (i.e. Rx) of a source-degenerated NMOSFET. The circuit is shown on the left while the equivalent small-signal modeling is shown on the right. It is noted that the bias condition (VBiAS) is set so that the values of gm and ro, can be defined. Moreover, there is no input signal (i.e. Vin = 0) since we would like to see the value of Rx which is due to the circuit only but not due to the external effect. Based on the above small-signal model, prove that RX = ro(1 + gmRS) The complete common-source amplifier with source degeneration is shown below. c) The complete common-source amplifier with source degeneration is shown below. Prove that the voltage gain of this amplifier is given by v. Vin Explain the reason(s) why the voltage gain is negative. What is the physical meaning of negative voltage gain?

In this question, you are asked to find the effective transconductance (Gm) and the resistance into the drain (Rx) of a common-source amplifier with source degeneration. Based on the results, the voltage gain of a common-source amplifier with source degeneration will be evaluated a) The figures shown below are a circuit to find the effective transconductance (G) of the NMOSEFT with source degeneration (left) and its corresponding small-signal circuit (right). It is noted that the output is shorted to VDD (ac grounded) since the definition of effective transconductance is the ratio between the short-circuit output current and the input signal voltage. Prove that Gm is given by Gm = id/vin = gm/1+gmRs In this calculation, the current passing through ro can be neglected since, in general, ro is very large when the NMOSFET operates in saturation region and so this current is very small. Thus, the indication of id is the current of the voltage-controlled current source (gmvgs) only. b) The figure shown below is the method to evaluate the resistance looking into the drain (i.e. Rx) of a source-degenerated NMOSFET. The circuit is shown on the left while the equivalent small-signal modeling is shown on the right. It is noted that the bias condition (VBiAS) is set so that the values of gm and ro, can be defined. Moreover, there is no input signal (i.e. Vin = 0) since we would like to see the value of Rx which is due to the circuit only but not due to the external effect. Based on the above small-signal model, prove that RX = ro(1 + gmRS) The complete common-source amplifier with source degeneration is shown below. c) The complete common-source amplifier with source degeneration is shown below. Prove that the voltage gain of this amplifier is given by v. Vin Explain the reason(s) why the voltage gain is negative. What is the physical meaning of negative voltage gain?

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