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# Propagation delay time calculation for cmos inverter

### Propagation delay time calculation for CMOS inverter

Question: How you will calculate propagation delay time for CMOS inverter?

Solution: Propagation delay (tp) measures the speed of output reaction to input change. It is the sum of fall propagation delay and rises propagation delay.

t_p=\frac12(\;t_{pf}+t_{pr})....................(i)

Where

tpf =Fall propagation delay which is defined as the time for output to fall by 50% or reference to input change by 50%

If the input is step change then

t_{pf}=\ln\left(2\right)\;\tau_n.............(ii)

And

tpr = Rise time propagation delay which is defined as the time for output to rise by 50% or reference to input change by 50%.

If the input is step change (ideal case) then

t_{pr}=\ln\left(2\right)\;\tau_p.............(iii)

Substituting the equation (ii) and (iii) in equation (i) we get

\begin{array}{l}t_p=\frac12\{\ln\left(2\right)\;\tau_n+\ln\left(2\right)\;\tau_p\}\\\\\;\;\;=\frac12\;\ln\left(2\right)\;(\tau_n+\tau_p)\\\\\;\;t_p=0.35\;\;(\tau_n+\tau_p)\\\\\\\end{array}

Which is the total propagation delay of CMOS inverter.

Propagation delay time calculation for CMOS inverter

Read: Power consumption of a mos inverter

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