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Considering the CMOS inverter shown in the figure below, (W/L)n = 1/4, (W/L)p = 1, and VDD = 3.3 V. Find (1) expression of Δt = t2−t1, using the integral method, (2) if C = 40 fF, the value of Δt = t2−t1, using the average current method, and (3) based on the result obtained in (2), determine the duration of T and the switching power dissipated in the inverter.

Considering the CMOS inverter shown in the figure below, (W/L)n = 1/4, (W/L)p = 1, and VDD = 3.3 V. Find (1) expression of Δt = t2−t1, using the integral method, (2) if C = 40 fF, the value of Δt = t2−t1, using the average current method, and (3) based on the result obtained in (2), determine the duration of T and the switching power dissipated in the inverter.

 

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Considering the CMOS inverter shown in the figure below, (W/L)n = 1/4, (W/L)p = 1, and VDD = 3.3 V. Find (1) expression of Δt = t2−t1, using the integral method, (2) if C = 40 fF, the value of Δt = t2−t1, using the average current method, and (3) based on the result obtained in (2), determine the duration of T and the switching power dissipated in the inverter.

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The technological parameters are μnCox = 4μpCox = 40 μA/V2, ∣γ∣ = 0.5 V1/2, 2ϕf = 0.5 V, λ = 0.02 V−1, Vtno = 0.6 V, and Vtpo = −0.8 V. Considering the CMOS inverter shown in the figure below, (W/L)n = 1/4, (W/L)p = 1, and VDD = 3.3 V. Find (1) expression of Δt = t2−t1, using the integral method, (2) if C = 40 fF, the value of Δt = t2−t1, using the average current method, and (3) based on the result obtained in (2), determine the duration of T and the switching power dissipated in the inverter.

The technological parameters are μnCox = 4μpCox = 40 μA/V2, ∣γ∣ = 0.5 V1/2, 2ϕf = 0.5 V, λ = 0.02 V−1, Vtno = 0.6 V, and Vtpo = −0.8 V. Considering the CMOS inverter shown in the figure below, (W/L)n = 1/4, (W/L)p = 1, and VDD = 3.3 V. Find (1) expression of Δt = t2−t1, using the integral method, (2) if C = 40 fF, the value of Δt = t2−t1, using the average current method, and (3) based on the result obtained in (2), determine the duration of T and the switching power dissipated in the inverter.
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Q1. Consider the CMOS inverter of which the transistors have the following parameters: μnCox = 4μpCox = 160 μA/V2, ∣γ| = 0.5 V1/2, 2Φf = 0.5 V, λ = 0.001 V−1, Vtno = 0.6 V, Vtpo = −0.8 V, (W/L)n = 1 and (W/L)p = 4. The supply voltage VDD = 3.3 V. The capacitive load at the output node is 20 pF. The input voltage Vin is expected to be a perfect periodic square wave with full swing (low level : 0 V, high level: VDD). (a) Calculate tl, the time required for the output voltage Vout to change from 0 V to the threshold voltage of the inverter, using the average-current method. (b) Write the expression of calculation of t2, the time required for the output voltage Vout to change from 2.9 V to the 0.4 V, using the analytical method (integral). Then calculate t2 using the average-current method. (c) Determine the maximum frequency of the periodic square wave input so that the output signal will have a full swing in each cycle. (d) Calculate the peak value of in, the NMOS transistor current, during the transition, and its average value over a clock cycle T. (The average value here is not the same as the average-current in the "average-current method" for delay estimation) (e) If the capacitive load is now changed to be 250 pF, what can be done to make tl and t2 unchanged?
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Problem 3: (Short Circuit Power Consumption) For the circuit in Figure 2, assume that the input Vin is a periodic square wave signal (called "clock") of frequency 200 MHz, and has a rising transition time (from 0−100% of VDD ) of 0.2 ns and a falling transition time (from 100−0% of VDD ) of 0.2 ns. For the inverter in the figure, find the short circuit power consumption. Use the procedural hints listed below. Procedural Hints:Calculate the short circuit duration, tsc. Short circuit currents occur when both nMOS and pMOS transistors are simultaneously ON. Use the rise/fall times given. Calculate the peak short circuit currents. For simplicity assume that Ipeak_sc_LH and Ipeak_sc_HL are equal, and calculate the latter only. To calculate Ipeak_sc_HL, , assume that the short circuit current for the H-to-L transition peaks when Vin = VDD/2 and Vout = 9 VDD /10 (this is an arbitrary choice assumed for this problem alone). Now calculate the pMOS transistor current - this will be Ipeak_sc_HL. . Question: Does the nMOS current equal the pMOS current? If not, how do you account for InMOS−IpMO ? Using your results from (1) and (2), calculate the short circuit power dissipation. Note: Assume that VDD = 1.0 Volts, (W/L)p = 3.5 /0.1, and (W/L)n = 2 /0.1. Transistor properties are given by the 90 nm model parameters handout posted on the class web-site. For the current calculation, use the transistor parameters (not the equivalent resistance parameters) and ignore channel length modulation. Assume that there is an 89 fF load on Out.

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