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Estimate the transient times of the CMOS inverter with the load capacitor, if a transistor (when it is conducting) can be approximated by a resistor of the value Req = 2 μiCox(W/L)i(|VGSi| − |Vti|) where subscript 'i' represents either 'n' or 'p' for an N- and P-MOSFET respectively and Cox = εox/tox⋅( Note: in Spice μi = UO[cm2 /(V⋅s)], and tox = TOX[m]). You can find the values of the transistor parameters in the 0.25 μm CMOS process Wp = 4 μmL = 0.25 μm Wn = 2 μm Figure 2: CMOS inverter

Estimate the transient times of the CMOS inverter with the load capacitor, if a transistor (when it is conducting) can be approximated by a resistor of the value Req = 2 μiCox(W/L)i(|VGSi| − |Vti|) where subscript 'i' represents either 'n' or 'p' for an N- and P-MOSFET respectively and Cox = εox/tox⋅( Note: in Spice μi = UO[cm2 /(V⋅s)], and tox = TOX[m]). You can find the values of the transistor parameters in the 0.25 μm CMOS process Wp = 4 μmL = 0.25 μm Wn = 2 μm Figure 2: CMOS inverter

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Estimate the transient times of the C M O S inverter with the load capacitor, if a transistor (when it is conducting) can be approximated by a resistor of the value
R e q = 2 μ i C o x ( W / L ) i ( | V G S | − | V t i | )
where subscript ' i ' represents either ' n ' or 'p' for an N - and P-MOSFET respectively and C o x = ε o x / t o x ⋅ ( Note: in Spice μ i = U O [ c m 2 / ( V ⋅ s ) ] , and t o x = T O X [ m ] ) . You can find the values of the transistor parameters in the 0.25 μ m CMOS process
W p = 4 μ m L = 0.25 μ m
W n = 2 μ m
Figure 2: CMOS inverter

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Consider a CMOS inverter with minimum gate lengths, Wn = 15, Wp = 35 , and equivalent capacitance at the output node of 80fF. Calculate tPLH and tpHL using the following methods. The numerical answers are shown. You need to show the equation, the equation with values substituted for the variables and the final value calculated. a) (5 pts) average current method (tPLH = 23.6 ps) b) (5 pts) velocity saturation approximation (tPLH = 47.3ps) Use the TSMC 0.18 um process parameters below. For any other parameters, use the transistor parameters in the tsmc018.mod.txt file.

Consider a CMOS inverter with minimum gate lengths, Wn = 15, Wp = 35 , and equivalent capacitance at the output node of 80fF. Calculate tPLH and tpHL using the following methods. The numerical answers are shown. You need to show the equation, the equation with values substituted for the variables and the final value calculated. a) (5 pts) average current method (tPLH = 23.6 ps) b) (5 pts) velocity saturation approximation (tPLH = 47.3ps) Use the TSMC 0.18 um process parameters below. For any other parameters, use the transistor parameters in the tsmc018.mod.txt file.
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Part 2: Analysis of a CMOS Inverter's Dynamic Behavior Objective: Perform hand calculations of switching delays through a CMOS inverter. Consider a CMOS inverter such as the one shown in Figure 2. The delay times, trise and tsunv , will be determined by the current-driving capacities of the PMOS and NMOS transistors, respectively, as well as the magnitude of the load capacitance CL. Figure 2. CMOS Inverter The rise time trice for a CMOS inverter can be calculated as: tnse = CLΔV IDAvg , where IDP wg is the average of the PMOS currents at the 10% point of the low-to-high transition (Vout = Vtow ) and at the 90% point (Voor = Vsow ). Likewise, the fall time tfall for a CMOS inverter can be calculated as: tsanl = CLΔV IDavg , where ID timg is the average of the NMOS currents at the 90% of the high-to-low transition (Vout = VSop ) and at the 10% point (Vous = V10%). ⇒ Calculate the expected rise and fall times, trise and tfall . Use LCM equations with a load capacitance value of 25 pF. Use VT0 = 0.4 V, kn′ = 432 μA/V2, |2ϕϝ| = 0.88 V, γ = 0.2 V1 /2, λ = 0 V−1, WN = 2 μm, and LN = 100 nm for the NMOS device. Use Vpv = −0.4 V, kp′ = 108 μA/V2, |2ϕF| = 0.88 V, γ = 0.2 V1 /2, λ = 0 V−1, Wp = 8 μm, and Lp = 100 nm for the PMOS device.

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Assume the following unless stated otherwise for a 0.25 μm CMOS process: VDD = 5 V, Lmin = 0.25 μm Vtn = 0.5 V or −1 V (choose accordingly), Vtp = −0.5 V μnCox = 265 μA/V2, μpCox = 90 μA/V2 Consider a resistively loaded inverter with a load of Ctot = 300 fF. a) Design the inverter (specify W, L values for the transistor, and RL) so that VOL = 0.025 V. b) Calculate all the other voltages of the voltage transfer characteristic. c) Find the noise margins and the area of the inverter.

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