# Transition time (rise time) and propagation delay

Recently in class I have encountered the following calculation of the propagation delay of the following digital circuit:

Could anyone please explain to me the addition of the rising time of X2 and C? I fail to understand why this addition is regarded as the "real" propagation delay.

• Did the question mention what family of devices are being used, CMOS, TTL, ECL, etc..? I am trying to make sense of where the divide by 2 comes from. – Entrepreneur Sep 9 '17 at 4:12
• I believe cmos... – Meir Franco Sep 9 '17 at 8:17
• I am surmising that by tr(C) they actually mean tr(Y0). The threshold voltage for CMOS logic levels is around 1/2 the supply voltage, so maybe they are emphasizing that the rise time of the input signal to reach the 0-->1 (0.5 supply voltage) threshold is non-zero and likewise with the output signal effect on the target destination. I am unsure. These delays are generally small compared to other delays. – Entrepreneur Sep 10 '17 at 23:41

I think it's because of the way propagation delay (say $t_{pLH}$) is defined. See the figure:
Now if you define real propagation delay ($t_{p,real}$) as the time duration between the point at which input started rising and the point at which the the output settles to final value, then one can write:
real propagation delay = time required for input to rise to 50% + propagation delay + time required for output to reach final value from 50% point. $$t_{p,real} = t_{pLH}+t_{in,0\to 50\%}+t_{out,50\to 100\%}$$