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Consider the circuit shown below. Suppose that all NMOS transistors are identical and all PMOS transistors are identical. Equivalent resistor for an NMOS transistor: RN = 8kohm Equivalent resistor for a PMOS transistor: RP = 24kohm Suppose that each circuit node (including outputs) has a capacitance value of 1pF. a) Derive a Boolean expression for the output F in terms of the inputs A and B. b) Calculate the worst-case and the best-case propagation delays, tPLH and tPHL values (total of 4 values).

Consider the circuit shown below. Suppose that all NMOS transistors are identical and all PMOS transistors are identical. Equivalent resistor for an NMOS transistor: RN = 8kohm Equivalent resistor for a PMOS transistor: RP = 24kohm Suppose that each circuit node (including outputs) has a capacitance value of 1pF. a) Derive a Boolean expression for the output F in terms of the inputs A and B. b) Calculate the worst-case and the best-case propagation delays, tPLH and tPHL values (total of 4 values).

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Consider the circuit shown below. Suppose that all NMOS transistors are identical and all PMOS transistors are identical. Equivalent resistor for an NMOS transistor: RN = 8kohm Equivalent resistor for a PMOS transistor: RP = 24kohm Suppose that each circuit node (including outputs) has a capacitance value of 1pF. a) Derive a Boolean expression for the output F in terms of the inputs A and B. b) Calculate the worst-case and the best-case propagation delays, tPLH and tPHL values (total of 4 values).

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Consider the circuit shown below, having an output F and inputs A and B. Suppose that all NMOS transistors are identical and all PMOS transistors are identical. Equivalent resistor for an NMOS transistor: RN = 8 kohm Equivalent resistor for a PMOS transistor: Rp = 24 kohm Suppose that each circuit node (Hint: output node and the node between transistors having A and B inputs) has an equivalent capacitance value of 1pF. Calculate the worst-case propagation delays, tPLH and tPHL (total of 2 values).
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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.
Solution
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In the dynamic logic circuit shown below, all the transistors have the minimum channel length, and their sizes (widths) are marked. The inverter at the output is a standard static CMOS inverter with a PMOS size of 2 and an NMOS size of 1 . For a unit-sized NMOS or PMOS transistor, the intrinsic capacitance at its drain or source terminal is CD, and the capacitance at its gate is CG. For unit-sized NMOS and PMOS transistors, their onresistances are RN and RP, respectively. CD = CG = 1 fF and RP = 2 RN = 2 kΩ. (a) Express y as a Boolean function of the inputs A, B, C and D in the evaluation phase (CLK = 1). (b) Find the capacitances at nodes y, a, b and c, respectively. (c) Let A = B = D = 1 and C = 0 and suppose nodes a, b and c are at 0 V in the pre-charge phase (CLK = 0). Estimate the time it takes for the voltage at y to decrease from VDD to VDD/2 in the evaluation phase. (d) Repeat (c) if nodes a, b and c are at VDD in the pre-charge phase. (e) If the inputs are C = 1 and A = B = D = 0 and suppose nodes a, b and c are at 0 V in the pre-charge phase. Considering the charge sharing effect, what is the voltage at node y in the evaluation phase? It is known VDD = 2.5 V, VTN = 0.5 V and the body effect of the transistors can be ignored.

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