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a) Compute differential-mode gain (Adm), for output taken differentially. Assume there is no body/bulk effect and ro is ∞. (10 pts) b) Convert the circuit into a common-mode half circuit. (5 pts) c) Compute common-mode gain (Acm), for output taken differentially. Assume there is no body/bulk effect and ro is ∞. (5 pts)

a) Compute differential-mode gain (Adm), for output taken differentially. Assume there is no body/bulk effect and ro is ∞. (10 pts) b) Convert the circuit into a common-mode half circuit. (5 pts) c) Compute common-mode gain (Acm), for output taken differentially. Assume there is no body/bulk effect and ro is ∞. (5 pts)

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a) Compute differential-mode gain ( A d m ) , for output taken differentially. Assume there is no body/bulk effect and r 0 is ∞ . (10 pts) b) Convert the circuit into a common-mode half circuit. (5 pts) c) Compute common-mode gain ( A c m ) , for output taken differentially. Assume there is no body/bulk effect and r o is ∞ . (5 pts)

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a) Compute differential-mode gain (Adm), for output taken differentially. Assume there is no body/bulk effect and r0 is ∞. (5 pts) b) Convert the circuit into a common-mode half circuit. (5 pts) c) Compute common-mode gain (Acm), for output taken differentially. Assume there is no body/bulk effect and r0 is ∞. (2 pts Bonus)
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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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In the following circuit, assume that λ = γ = 0, VDD = 3 V, |VTH| = 0.5 V, μPCox = 20 μA/V2. Furthermore, assume that vin is a small signal source and Vbias1 = 1.5 V and the DC level of Vout1 and Vout2 are all equal to 0.5 V and 1.5 V, respectively. Also, assume that the bias current of M1 is twice that of M2. (Hint: ID = 1/2μpCOX(W/L) (|VGS| − |VTH|)^2, in saturation) (1) What is the region of operation of M1 and M2? (10 points) (2) If the overall power consumption is 3 mW, find R1, R2, (W/L)1, (W/L)2. (15 points) (3) What is the small signal gain of the circuit (vout2/vin)? Assume there is no parasitic effect and gm1 = gm2 = 4/3 mV/V. (15points)
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