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A negative feedback amplifier is shown below. The small signal equivalent circuit of the open-loop amplifier is shown next to the amplifier schematic. a) Which negative feedback topology is implemented by the amplifier circuit? b) What is the voltage gain Vo/Vsig ? c) What is the input resistance Rin diagrammed in the amplifier schematic?

A negative feedback amplifier is shown below. The small signal equivalent circuit of the open-loop amplifier is shown next to the amplifier schematic. a) Which negative feedback topology is implemented by the amplifier circuit? b) What is the voltage gain Vo/Vsig ? c) What is the input resistance Rin diagrammed in the amplifier schematic?

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A negative feedback amplifier is shown below. The small signal equivalent circuit of the open-loop amplifier is shown next to the amplifier schematic. a) Which negative feedback topology is implemented by the amplifier circuit? b) What is the voltage gain V o / V sig ? c) What is the input resistance Rin diagrammed in the amplifier schematic?

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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.

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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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1. (18 points total) In the circuit shown below, the PMOS transistor has Vtp = −0.8 V, VA = −28 V, and operates with VD = 3 V. Note the 22 MΩ gate resistor, which is another way to bias a CS stage, used here in addition to the current source. You may assume that any channel length modulation does not appreciably affect the DC biasing. (a) Draw the small-signal equivalent circuit for this transistor amplifier. Be sure to label the input and output voltages as well as the source, gate and drain locations on the schematic. Calculate all parameters/component values used in your equivalent circuit that were not given in the problem. (6 points) (b) What is the input resistance of the amplifier? What is the output resistance? (6 points) (c) What is the voltage gain Av = vo/vi? How much does your calculation change if you assume RG → ∞? (6 points)
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