**Propagation delay time calculation for CMOS inverter**

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

**Solution:**

**Propagation delay (t _{p})** 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

t_{pf} =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

t_{pr} = 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**