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Based on the common source amplifier circuit shown in Fig. Q3a, suppose a limited voltage supply VDD is imposed such that only a single load is allowed to insert between VOUT and ground, (i) suggest the type of load required to have a fairly constant DC current while achieving a reasonably high voltage gain. (ii) draw the small signal model circuit based on Q3a)i), assuming λ ≠ 0 and γ = 0

Based on the common source amplifier circuit shown in Fig. Q3a, suppose a limited voltage supply VDD is imposed such that only a single load is allowed to insert between VOUT and ground, (i) suggest the type of load required to have a fairly constant DC current while achieving a reasonably high voltage gain. (ii) draw the small signal model circuit based on Q3a)i), assuming λ ≠ 0 and γ = 0

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Based on the common source amplifier circuit shown in Fig. Q3a, suppose a limited voltage supply VDD is imposed such that only a single load is allowed to insert between VOUT and ground, (i) suggest the type of load required to have a fairly constant DC current while achieving a reasonably high voltage gain. (ii) draw the small signal model circuit based on Q3a)i), assuming λ ≠ 0 and γ = 0

Explanation & Steps

For common-source amplifier, load resistance needs to be connected at drain terminal. This load resistor affects the amplifier's voltage gain and DC operating point. An active load, such as a constant current source or a current mirror can be used in place of passive resistance to bias the circuit at reasonably constant DC current and to provide high voltage gain.

(i) Constant current source:

An active load formed with NMOS transistor, applied with constant DC voltage can be used to provide fairly constant DC current in the circuit. The current in the circuit is decided by the gate-to-source voltage of NMOS load transistor. Since gate-to-source voltage of NMOS load transistor is fixed, then the current in both transistors will be a constant value. Regardless of changes in the input signal or the transistor's settings, a reasonably constant DC current is guaranteed when a constant current source is used as the load.

(ii) Small-signal equivalent model:

Channel length modulation needs to be considered and body bias effect needs to be neglected while drawing the small-signal equivalent model of the circuit. DC voltage sources are to be short circuited to ground potential. Replace by individual transistor with it’s own small-signal model. Voltage gain can also be calculated by solving equivalent small-signal equivalent circuit.

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Based on the common source amplifier circuit shown in Fig. Q3a, suppose a limited voltage supply VDD is imposed such that only a single load is allowed to insert between VDD and VOUT. (i) Choose the type of load such that the small signal voltage gain is a weak function of PVT. (2 Marks) (ii) Sketch the small signal model circuit based on Q3a)(i), assuming λ = 0. (3 Marks) (iii) Deduce an equation representing the voltage gain based on Q3a)(ii). (3 Marks) (iv) Identify the design trade-offs of the circuit. (6 Marks)
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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?

Solution
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