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For the given CMOS logic circuit, identify and describe (graphically, mathematically or using an equivalent circuit) a suitable model of each transistor type for analysis, assuming that each of the input signals A, B and C are equal to 0 V or VDD. Hence or otherwise, determine the states of conduction of each transistor (in terms of ON and OFF) for all combinations of the input signals A, B and C. Hence, deduce the logic function, F, performed by the circuit, including indicative equivalent circuit examples of how the output voltage is determined for a low and a high output (at least one example each).

For the given CMOS logic circuit, identify and describe (graphically, mathematically or using an equivalent circuit) a suitable model of each transistor type for analysis, assuming that each of the input signals A, B and C are equal to 0 V or VDD. Hence or otherwise, determine the states of conduction of each transistor (in terms of ON and OFF) for all combinations of the input signals A, B and C. Hence, deduce the logic function, F, performed by the circuit, including indicative equivalent circuit examples of how the output voltage is determined for a low and a high output (at least one example each).

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For the given CMOS logic circuit, identify and describe (graphically, mathematically or using an equivalent circuit) a suitable model of each transistor type for analysis, assuming that each of the input signals A, B and C are equal to 0 V or VDD. Hence or otherwise, determine the states of conduction of each transistor (in terms of ON and OFF) for all combinations of the input signals A, B and C. Hence, deduce the logic function, F, performed by the circuit, including indicative equivalent circuit examples of how the output voltage is determined for a low and a high output (at least one example each).

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For the given CMOS logic circuit, identify and describe (graphically, mathematically or using an equivalent circuit) a suitable model of each transistor type for analysis, assuming that each of the input signals A, B, C and D are equal to 0 V or VDD. Hence or otherwise, determine the states of conduction of each transistor (in terms of ON and OFF) for all combinations of the input signals A, B, C and D. Hence, deduce the logic function, F, performed by the circuit, including indicative equivalent circuit examples of how the output voltage is determined for a low and a high output (at least one example each).
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Assumptions for all problems (unless specified otherwise, give answers to 10% ): VDD(V) VT0( V) Body effect γ(V 0.5 ) VDSAT( V) k’ (A/V 2) λ(V -1 ) NMOS 2.0 0.4 0 0.5 500×10-6 0 PMOS -0.4 0 -0.5 -200×10-6 0 1. All transistors have the minimum length (Lunit = 250 nm) 2. Ignore body effect and channel length modulation 3. A transistor's intrinsic capacitance (cap) and gate cap are equal, i.e., Cint = Cg, γ = 1 4. The unit-sized transistor has Wunit = Lunit and intrinsic cap Cint = Cg = Cdb = Csb = 1.0fF. 5. For the unit sized inverter, β = (W/L)P / (W/L N = WP/WN = 2, WN = L = 250 nm 6. The unit sized transmission gate has a resistance Req,tr = 10kΩ and all caps of 1.0fF. a) (6 pts) How does the following circuit operate? In a few words/charts, describe what it does Sketch the waveforms of nodes X and Q given the inputs shown below. Initial state of signals X and Q are unknown (mark with xxx as needed) until the impact of the input signals propagate. X Q b) (4 pts) How would you size each transistor? Match the 2:1 inverter (including the clock). Draw the sizing next to the schematic. Calculate the switch model equivalent resistance(s) (note the equation given at the front of the exam for Req, switch model capacitance(s) (based on your sizing), and worst-case propagation delay through the circuit, max(tpLH,tpLH), where output is taken from Q and inputs are IN1 and IN2. c) (4 pts) Calculate the energy consumption from the VDD power supply of this circuit for the input pattern and time duration given in the timing diagram (previous page). Ignore the energy consumption related to driving IN1, IN2, and CLK. State any assumptions you need to make to determine a numerical value.

Assumptions for all problems (unless specified otherwise, give answers to 10% ): VDD(V) VT0( V) Body effect γ(V 0.5 ) VDSAT( V) k’ (A/V 2) λ(V -1 ) NMOS 2.0 0.4 0 0.5 500×10-6 0 PMOS -0.4 0 -0.5 -200×10-6 0 1. All transistors have the minimum length (Lunit = 250 nm) 2. Ignore body effect and channel length modulation 3. A transistor's intrinsic capacitance (cap) and gate cap are equal, i.e., Cint = Cg, γ = 1 4. The unit-sized transistor has Wunit = Lunit and intrinsic cap Cint = Cg = Cdb = Csb = 1.0fF. 5. For the unit sized inverter, β = (W/L)P / (W/L N = WP/WN = 2, WN = L = 250 nm 6. The unit sized transmission gate has a resistance Req,tr = 10kΩ and all caps of 1.0fF. a) (6 pts) How does the following circuit operate? In a few words/charts, describe what it does Sketch the waveforms of nodes X and Q given the inputs shown below. Initial state of signals X and Q are unknown (mark with xxx as needed) until the impact of the input signals propagate. X Q b) (4 pts) How would you size each transistor? Match the 2:1 inverter (including the clock). Draw the sizing next to the schematic. Calculate the switch model equivalent resistance(s) (note the equation given at the front of the exam for Req, switch model capacitance(s) (based on your sizing), and worst-case propagation delay through the circuit, max(tpLH,tpLH), where output is taken from Q and inputs are IN1 and IN2. c) (4 pts) Calculate the energy consumption from the VDD power supply of this circuit for the input pattern and time duration given in the timing diagram (previous page). Ignore the energy consumption related to driving IN1, IN2, and CLK. State any assumptions you need to make to determine a numerical value.

Assumptions for all problems (unless specified otherwise, give answers to 10% ): VDD(V) VT0( V) Body effect γ(V 0.5 ) VDSAT( V) k’ (A/V 2) λ(V -1 ) NMOS 2.0 0.4 0 0.5 500×10-6 0 PMOS -0.4 0 -0.5 -200×10-6 0 1. All transistors have the minimum length (Lunit = 250 nm) 2. Ignore body effect and channel length modulation 3. A transistor's intrinsic capacitance (cap) and gate cap are equal, i.e., Cint = Cg, γ = 1 4. The unit-sized transistor has Wunit = Lunit and intrinsic cap Cint = Cg = Cdb = Csb = 1.0fF. 5. For the unit sized inverter, β = (W/L)P / (W/L N = WP/WN = 2, WN = L = 250 nm 6. The unit sized transmission gate has a resistance Req,tr = 10kΩ and all caps of 1.0fF. a) (6 pts) How does the following circuit operate? In a few words/charts, describe what it does Sketch the waveforms of nodes X and Q given the inputs shown below. Initial state of signals X and Q are unknown (mark with xxx as needed) until the impact of the input signals propagate. X Q b) (4 pts) How would you size each transistor? Match the 2:1 inverter (including the clock). Draw the sizing next to the schematic. Calculate the switch model equivalent resistance(s) (note the equation given at the front of the exam for Req, switch model capacitance(s) (based on your sizing), and worst-case propagation delay through the circuit, max(tpLH,tpLH), where output is taken from Q and inputs are IN1 and IN2. c) (4 pts) Calculate the energy consumption from the VDD power supply of this circuit for the input pattern and time duration given in the timing diagram (previous page). Ignore the energy consumption related to driving IN1, IN2, and CLK. State any assumptions you need to make to determine a numerical value.
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The schematic of a inverter using a single MOSFET transistor is shown below: The threshold voltage of the transistor Q1 is |VT| = 1 V and channel length modulation can be neglected. (a) Identify a suitable model of the transistor for analysing the above circuit and describe the model mathematically, graphically or as an equivalent circuit. Sketch the voltage-voltage transfer characteristic, Vo - Vi, for the circuit, clearly identifying the state of the transistor based on the proposed model. (b) If the transistor is saturated where Vi < VA and not saturated where Vi > VA, derive an expression for Vo|Vi=VA in terms of the relevant circuit and transistor parameters. If kn = 100 μAV-2 and R = 100 kΩ, determine Vo|Vi=VA in terms of VDD. (c) Assuming no leakage current, calculate the VOH min of the inverter. If, instead, there is a leakage current with equivalent resistance of 3 MΩ when VGS < VT, determine the adjusted VOHmin. Calculate the power lost when Vi = VT/2 in these circumstances.
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