ECE 410 Homework 6 Spring 2008 Problem 1 A NOR CMOS gate with the device/parasitic parameters below must drive (output to) the inputs of 3 NAND gates (one input on each gate) with the same MOSEFT gate dimensions as the NOR gate. VDD = 2.0V, Cox = 2fF/μm2, CDBp = 1fF, CDBn = 0. 5fF (W/L)p= 4/0.5, k’p =100μA/V2, |Vtp| = 0.5V, (W/L)n= 2/0.5, k’n =250μA/V2, Vtn = 0.6V, a) What is the total parasitic capacitance at the output of the NOR gate? b) What is the total load capacitance contributed by the 3 NAND gates? c) What is the total capacitance at the output of the NOR gate? d) What is the effective resistance between the output and VDD when the NOR gate pulls the output high? Use the “general” formula for channel resistance. e) Combining results from (c) and (d), what is the output RC time constant? Problem 2 Assume the following process parameters and constants: k’n = 100 μA/V2, k’p = 40μA/V2, Vtn=|Vtp|=0.5V, VSB = 0V and VDD = 2.5V. Ignore channel length modulation and other secondary effects. a) Use a computer (e.g., Excel, Matlab) to plot the I-V curve (ID vs. VD) for an nMOS transistor with W=1.5μm and L=0.6μm, VS = 0V at VG = 1V. Plot ID vs. VD from 0V to 2.5V with at least 10 steps. Be sure to properly account for transitions between the triode and saturation (active) regions. b) Repeat (a) at VG = 2V and VG = 2.5V. Include all three curves on the same plot. c) Repeat (a) and (b) for a pMOS device with W=3μm, L=0.6μm and VS = 2.5V and VG values of 2V, 1V, and 0V. Notice that to plot ID vs. VD, you will need to be careful how you represent the term VSD. Done correctly, your plot should be similar to the one shown in HW4 solutions. Problem 3 For a CMOS inverter with the following parameters: VDD = 3V, Vtn = 0.6V, Vtp = -0.82V, k’n = 100μA/V2, μn = 2.2μp: a) Determine the beta ratio, βn/βp, for a midpoint (switching threshold) of VM = 1.3V. b) Determine the relative device widths, Wp/Wn, for VM = 1.3V. Problem 4 A CMOS inverter with minimum sized transistors has βn =0.2mA/V2, βp = 0.1mA/V2 and Vtn=|Vtp|=0.6V.Assume VDD = 3.3V. a) What is the inverter gate switching threshold (midpoint) voltage VM? b) What is the resistance for each transistors using our general expression for MOSFET resistance in saturation? c) What are the rise and fall times of this circuit if the parasitic capacitance at the output is 9fF? d) If a load capacitance, CL = 25fF is added to the output, what are the new rise and fall times? e) What are the propagation delays for this circuit considering both parasitic and load capacitances? p. 1Problem 5 A CMOS inverter is designed with βp = 80µA/V2, βn =0.25mA/V2, Vtn=|Vtp|=0.5V and VDD = 2.5V. The total capacitance at the output is 50fF a) Using our general expression for MOSFET resistance in saturation, what is the resistance for each transistor? b) What is the rise time of this circuit? c) What is the fall time of this circuit? d) What is the high-to-low propagation delay for this inverter? e) What is the low-to-high propagation delay for this inverter? f) Do the relative results (rise vs. fall time, high-to-low vs. low-to-high propagation delay) make sense considering the relative pMOS and nMOS beta values? Briefly explain why or why not. Problem 6 A clever ECE410 student has noticed that the simulated worst-case rise time of a CMOS NAND gate is actually slower than the worst-case fall time, contrary to calculations based on the models give in class. The student proposes that a more accurate model of the NAND gate worst-case rise time should include an additional parameter. a) Specify the input transition sequence that would produce the worst-case rise time. Refer to your results from Lab 4 if necessary. Format your response like AB Æ CD, where the first number represents the input to the series transistor that is connected to the output. b) Sketch an RC model of the NAND gate during this transition including all parasitic capacitances and resistances for all transistors that are turned on. c) Derive an improved equation for the worst-case rise time based on your RC model. You should see that an additional term is necessary to more accurately model this transition. d) Based on this improved mode, will the worst-case rise time always be longer than the worst-case fall time? Briefly explain. p.
View Full Document
Unlocking...