2. (25 points) Question 2: 25points One of your friends O. V. Ah makes a PCB with three inverters, but the traces between the power supply and the inverter were too

thin and long, resulting in the circuit shown in figure 2. Her board interfaces to a board made by T. Isha. Since it is too late to remake the board, O. V. Ah decides to figure out her worst case VOH and VOL among the three inverters and enforce this on T. Isha's circuit as the static discpline. What values would O. V. Ah calculate given the ON resistance of the N-MOSFET is Ron and the threshold voltage of the MOSFET is VTN? Vo DD I A₁0 ह Inverter 1 R₁ Page 2 of 16 FOY₁ R₁ A₂c R₁ F0Y/₂ R₁ A₂0- Inverter 2 Figure 2: A chain of inverters on a PCB R₁ foy, Y₂ Inverter 3/n 1. (25 points) Question 1: 25points Consider the logic inverter shown in Figure 1. If the ON resistance of the N-MOSFET is Ron and the threshold voltage of the MOSFET is VTN, accurately sketch the transfer characteristics of the inverter and clearly label the plot with VOн, VIH, VOL, and VIL in terms of the crcuit parameters, VDD, VTN, R₁, R2 and Ron. som DD R₁ H R₂ Ao- Figure 1: Logic Inverter contd.. Page 2 of 16 2. (25 points) One of your friends O. V. Ah makes a PCB with three inverters, but the traces between the power supply and the inverter were too thin and long, resulting in the circuit shown in figure 2. Her board interfaces to a board made by T. Isha. Since it is too late to remake the board, O. V. Ah decides to figure out her worst case VOH and VOL among the three inverters and enforce this on T. Isha's circuit as the static discpline. What values would O. V. Ah calculate given the ON resistance of the N-MOSFET is Ron and the threshold voltage of the MOSFET is VTN? R₁ www R₁ R₁ फुकुन Fo Y₁ FoY₂, A₂ A3 Inverter 1 Inverter 2 Figure 2: A chain of inverters on a PCB V DD I R₁ ww A₁0- Page 3 of 16 R₁ R₁ FoY₂ Y3 Inverter 3 Question 2: 25points. contd.. Page 4 of 16 Question 3: 25points 3. (25 points) One of your friends who loves the history of science D. Amin Poor, comes across the circuit implementation of the first neural network the Perceptron using the McCulloch & Pitts neuron shown in figure 3. He knows the circuit is a universal approximator but is confused about how to make the circuit implement an NAND gate. He comes to you for help since you are an expert in circuits. Can you choose the values of R₁, R2, R3, RB, VTN, and V₂ so that the circuit implements an NAND gate? If an exact value cannot be determined express it as a range. Assume the ON resistance of the N-MOSFET is Ron and the threshold voltage of the MOSFET is VTN. Assume the inputs swing from OV to VDD. VB is a bias voltage not an input. R₁ R₂ m R₂ A₁ A₂ 0- V. B R. B stá Page 5 of 16 V. DD R. L TOY A3 Figure 3: A circuit approximation of the McCulloch and Pitts Neuron