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The current entering an element between 0 and 5 ms is shown below. What is the total charges entering this element in μC? 9 −9 8.5 7.5

The current entering an element between 0 and 5 ms is shown below. What is the total charges entering this element in μC? 9 −9 8.5 7.5

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The current entering an element between 0 and 5 ms is shown below. What is the total charges entering this element in μ C ? 9 − 9 8.5 7.5

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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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a) Your job is to design the following circuit, using 2 mA of bias current and achieve a gain of at least 3.5 V/V. You realize that you can bias an amplifier using degeneration resistance using the circuit topology shown below. Calculate values for RS to get 2 mA of current, and RL to get the gain you need. For large signal calculations, you may assume lambda = 0. What is the problem with this amplifier? b) You suggest replacing the load resistance RL with a current source that has a very large output impedance, as shown below. The current source requires a headroom of at least 0.5 V. What is the gain of the amplifier? How does this fix the problem from the previous part? 1 Debugging Amplifiers Suppose you are given an NMOS transistor with the following parameters: In addition, VDD = 5 V.

a) Your job is to design the following circuit, using 2 mA of bias current and achieve a gain of at least 3.5 V/V. You realize that you can bias an amplifier using degeneration resistance using the circuit topology shown below. Calculate values for RS to get 2 mA of current, and RL to get the gain you need. For large signal calculations, you may assume lambda = 0. What is the problem with this amplifier? b) You suggest replacing the load resistance RL with a current source that has a very large output impedance, as shown below. The current source requires a headroom of at least 0.5 V. What is the gain of the amplifier? How does this fix the problem from the previous part? 1 Debugging Amplifiers Suppose you are given an NMOS transistor with the following parameters: In addition, VDD = 5 V.

a) Your job is to design the following circuit, using 2 mA of bias current and achieve a gain of at least 3.5 V/V. You realize that you can bias an amplifier using degeneration resistance using the circuit topology shown below. Calculate values for RS to get 2 mA of current, and RL to get the gain you need. For large signal calculations, you may assume lambda = 0. What is the problem with this amplifier? b) You suggest replacing the load resistance RL with a current source that has a very large output impedance, as shown below. The current source requires a headroom of at least 0.5 V. What is the gain of the amplifier? How does this fix the problem from the previous part? 1 Debugging Amplifiers Suppose you are given an NMOS transistor with the following parameters: In addition, VDD = 5 V.
Solution
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Consider the amplifier circuit shown in the figure below. MOSFET channel length modulation can be neglected, VDD = 5 V, Vtn = 0.7 V, and kn = 1 mA/V2. Find VOV, ID, RD and RG to obtain voltage gain equal to −25 V/V and an input resistance of 0.5 MΩ. What is the maximum allowable input signal, vi? Tip: during small signal analysis you can assume that current through resistor RG is much smaller than gmvGS current and check if this is satisfied later. (Ans. 0.319 V; 50.7μA; 78.5kΩ; 13MΩ; 27mV)
Solution
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