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Problem 5. SRAM (22 pts) a. Considering the following 6T SRAM cell, please explain the sizing of N0, N1, and P1. What are the requirements on their relative strengths? (6 pts) b. For the 6T SRAM design, at what conditions, achieving the proper sizing will be difficult? (5 pts)

Problem 5. SRAM (22 pts) a. Considering the following 6T SRAM cell, please explain the sizing of N0, N1, and P1. What are the requirements on their relative strengths? (6 pts) b. For the 6T SRAM design, at what conditions, achieving the proper sizing will be difficult? (5 pts)

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Problem 5. SRAM (22pts) a. Considering the following 6T SRAM cell, please explain the sizing of N0, N1, and P1. What are the requirements on their relative strengths? (6pts) b. For the 6T SRAM design, at what conditions, achieving the proper sizing will be difficult? (5pts)

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For the amplifier below, following design information is provided: VDD = 3.3 V, R = 2.4 kΩ, ISS = 1.8 mA, k1 = k2 = 5 mA/V2, VTH,1 = VTH,2 = 0.5 V, λ = 0.1 V−1, γ = 0, ki′ = μ0Cox, ki = μ0 Cox(W L)i. Assume that both transistors are identical and in the saturation region. Finally, NMOS and PMOS bulk terminals are connected to the ground and VDD, respectively. a) What is the DC bias voltage for M1 and M2 given that the voltage drop across ISS is 0.4 V ? You can neglect the channel length modulation, here. Check that the transistors are in the correct operation-mode. b) The resistors will be realized using identical PMOS transistors M3 and M4. If the transistors to be used will have k3 = k4 = 1.5 mA/V2, what will be their overdrive voltages? Check that the transistors are in the correct operation-mode. c) What is the differential voltage gain AV,diff = Vout/Vid in dB ? d) ISS will be realized as a cascode current source. Assume that the voltage drop of 0.4 V is equally shared by the two transistors, M5 and M6 having k5′ = k6′ = 0.5 mA/V2 and VTH, 5 = VTH, 6 = 0.5 V. Assuming the gate voltages of both transistors are 1 V, find the W/L ratios of each device. Once again, you can neglect the channel length modulation here. e) Considering (d), how would the W/L ratios qualitatively change (increase/decrease/stays the same), if γ > 0 ? Explain your reasoning analytically, i. e. , using appropriate equations. f) Using the cascode current source, calculate the common-mode gain of the circuit AV, CM = Vout /Vin in dB, where Vin . s applied to the gates of both M1 and M2. Assume λ = 0.1 V−1 for M5 and M6. g) Calculate the CMRR of the circuit in dB.
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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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Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.

Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? 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Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle Learning and growing your brain through opportunities helps performance in school Believing your talents, abilities, and intelligence can be developed in different ways All of the above phrases describe the growth mindset Part B What is neuroplasticity? The ability to make new and stronger connections between the neurons in our brain as we learn The inability to change intelligence, which is fixed in the neurons in our brain from birth Having a fixed mindset in some ways, and a growth mindset in others Part C How do students with a growth mindset see their mistakes? As opportunities to learn and improve their brain As something that shouldn't happen in proper learning As reasons to give up and avoid further challenges Part D How can you use Mastering to develop a growth mindset and embrace your mistakes? Question what went wrong and use hints or provide problem feedback to develop a new strategy Repeat the question without changing your approach and input a different answer Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to stop trying when you fail because you are not smart enough and should choose a new subject to study. It encourages you to skip steps necessary to learn difficult concepts, and thus see results more quickly. Part F Which is NOT an element in developing expertise in a field? Giving up Asking for help Putting forth effort Trying new strategies Part G How do people with a growth mindset view and respond to challenges? They see challenges as signs their brains are getting weaker. They see challenges as a waste of effort and are embarrassed. They see challenges as opportunities to learn and push their abilities.
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