(x_(1))/(b)ar (x_(2))/(b)ar (x_(3))x_(4)x_(5)(+)/(b)ar (x_(1))x_(3)x_(4)(+)/(b)ar (x_(1))x_(2)(x_(3))/(b)ar (x_(4))x_(5)(+)/(b)ar (x_(2))/(b)ar (x_(3))x_(4)x_(5)

\

80fF

\ 2 Design\ Steps to be followed for design and characterization are described in the following list.\ Apply Shannon's decomposition to the function using

x_(1)

and

x_(2)

as control variables in any order.\ Draw the switch tree corresponding to the result and eliminate any possible redundancies. Perform necessary logic simplifications to the reduced functions in terms of

x_(3),x_(4)

and

x_(5)

.\ Draw the electrical schematic of the entire circuit excluding the staged buffer by replacing the switches with NMOS transistors and the inputs with complex gates. Do not forget to include the binary-high restoring feedback loop in your schematic.\ Now, you need to determine the channel dimensions of the devices to complete the electrical design. To this end, use minimum-size devices for the switches of the pass-gate.\ Design the complex gates to set

V_(TH)=(V_(DD))/(2)

for any one of their inputs or

{

(

:x_(5))

}, while also aiming for minimum footprint.\ The next step is to determine the channel dimensions of the devices in the binary-high restoring feedback loop. For that purpose, your goal is to calculate the sizes of the NMOS and PMOS devices of the feedback inverter for minimum footprint and

V_(TH)=425mV

in order to satisfy the condition (5.8) in your textbook. Moreover, size the PMOS feedback device MFB (refer to Fig. 5.4(a) of your textbook) for satisfying the condition (5.9) in your textbook with

V_(O)=350mV

(refer to

19.sp

in your textbook).\ The penultimate step is to design a staged buffer for optimal latency. In that respect, you may assume that it is acceptable for the output of the function to be inverted. Refering to Fig. 5.4(a) of your textbook, take

V_(INV)

as the output of the circuit instead of

V_(O)

.\ The last step of design is verification. However, you have to verify your intermediate designs in each step via simulations as well. Calculate the theoretical estimations and compare them with the results acquired from simulations whenever possible.\ Perform a final transient simulation by applying a pulse signal to one of

x_(3),x_(4)

or

x_(5)

that will cause a low-to-high and a high-to-low transition in succession, while keeping the other inputs constant. Define ad, as, pd and ps parameters of each transistor in this final input energy consumption (refer to Session 4) as a result of this simulation.\ Always choose appropriate values for pulse width and simulation time parameters that would allow the outputs to properly settle in your transient simulations. Choose a time step value that results in at least 1000 data points and set the rise/fall time parameters of the pulse sources equal to the time step of the simulation.

X1X2X3X4X5+X1X3X4+X1X2X3X4X5+X2X3X4X5 2 Design Steps to be followed for design and characterization are described in the following list. 1. Apply Shannon's decomposition to the function using X1 and X2 as control variables in any order. 2. Draw the switch tree corresponding to the result and eliminate any possible redundancies. Perform necessary logic simplifications to the reduced functions in terms of X3,X4 and X5. 3. Draw the electrical schematic of the entire circuit excluding the staged buffer by replacing the switches with NMOS transistors and the inputs with complex gates. Do not forget to include the binary-high restoring feedback loop in your schematic. 4. Now, you need to determine the channel dimensions of the devices to complete the electrical design. To this end, use minimum-size devices for the switches of the pass-gate. 5. Design the complex gates to set VTH=VDD/2 for any one of their inputs (X3,X4 or X5), while also aiming for minimum footprint. 6. The next step is to determine the channel dimensions of the devices in the binary-high restoring feedback loop. For that purpose, your goal is to calculate the sizes of the NMOS and PMOS devices of the feedback inverter for minimum footprint and VTH=425mV in order to satisfy the condition (5.8) in your textbook. Moreover, size the PMOS feedback device MFB (refer to Fig. 5.4(a) of your textbook) for satisfying the condition (5.9) in your textbook with VO=350mV (refer to 19.sp in your textbook). 7. The penultimate step is to design a staged buffer for optimal latency. In that respect, you may assume that it is acceptable for the output of the function to be inverted. Refering to Fig. 5.4(a) of your textbook, take VINV as the output of the circuit instead of VO. 8. The last step of design is verification. However, you have to verify your intermediate designs in each step via simulations as well. Calculate the theoretical estimations and compare them with the results acquired from simulations whenever possible. 9. Perform a final transient simulation by applying a pulse signal to one of X3,X4 or X5 that will cause a low-to-high and a high-to-low transition in succession, while keeping the other inputs constant. Define ad, as, pd and ps parameters of each transistor in this final input file with the junction lengths being equal to 5.5. Additionally, calculate the latency and energy consumption (refer to Session 4) as a result of this simulation. 10. Always choose appropriate values for pulse width and simulation time parameters that would allow the outputs to properly settle in your transient simulations. Choose a time step value that results in at least 1000 data points and set the rise/fall time parameters of the pulse sources equal to the time step of the simulation