7. Consider a CMOS inverter with the following parameters:nMOS: ๐ฝ๐ป๐ถ,๐ = ๐. ๐ ๐ฝ ๐๐๐ช๐๐ = ๐๐ ๐๐จโ๐ฝ2 (๐พโ๐ณ)๐ = ๐๐pMOS: ๐ฝ๐ป๐ถ,๐ = -๐. ๐ ๐ฝ ๐๐๐ช๐๐ = ๐๐ ๐๐จโ๐ฝ2 (๐พโ๐ณ)p = ๐๐The power supply voltage is 5 V, and the output load capacitance is 1.5 pF.(a) Calculate the rise time and the fall time of the output signal using(i) Exact method (differential equations)(ii) Average Current Method(b) Determine the maximum frequency of periodic square-wave input signal so that theoutput voltage can still exhibit a full logic swing from 0 V to 5 V in each cycle. [CO2-An](c) Calculate the dynamic power dissipation at this frequency.
Question
- Consider a CMOS inverter with the following parameters:nMOS: ๐ฝ๐ป๐ถ,๐ = ๐. ๐ ๐ฝ ๐๐๐ช๐๐ = ๐๐ ๐๐จโ๐ฝ2 (๐พโ๐ณ)๐ = ๐๐pMOS: ๐ฝ๐ป๐ถ,๐ = -๐. ๐ ๐ฝ ๐๐๐ช๐๐ = ๐๐ ๐๐จโ๐ฝ2 (๐พโ๐ณ)p = ๐๐The power supply voltage is 5 V, and the output load capacitance is 1.5 pF.(a) Calculate the rise time and the fall time of the output signal using(i) Exact method (differential equations)(ii) Average Current Method(b) Determine the maximum frequency of periodic square-wave input signal so that theoutput voltage can still exhibit a full logic swing from 0 V to 5 V in each cycle. CO2-An Calculate the dynamic power dissipation at this frequency.
Solution
This is a complex question that involves several steps. Here's how you can approach it:
(a) (i) Exact method (differential equations) The rise and fall times of the output signal can be calculated using the charging and discharging equations of a capacitor. The equations are as follows:
For charging (rise time): Vout(t) = VDD * (1 - exp(-t / (R * C))) For discharging (fall time): Vout(t) = VDD * exp(-t / (R * C))
Where: Vout(t) is the output voltage at time t, VDD is the power supply voltage, R is the resistance of the transistor, C is the output load capacitance.
(ii) Average Current Method The average current during charging and discharging can be calculated using the following equations:
For charging (rise time): Iavg = 1/2 * ฮผnCox * (W/L)n * (VDD - VTO,n)^2 For discharging (fall time): Iavg = 1/2 * ฮผpCox * (W/L)p * (VDD - |VTO,p|)^2
The rise and fall times can then be calculated using the equation: t = C * V / Iavg
(b) The maximum frequency of the input signal can be calculated using the rise and fall times. The period of the signal (T) is the sum of the rise and fall times. The frequency (f) is the reciprocal of the period.
(c) The dynamic power dissipation can be calculated using the equation: P = 1/2 * C * VDD^2 * f
Please note that you will need to substitute the given values into these equations to get the final answers.
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