# Transfer function with separate time delays in each term

We've been given the problem below for our current assignment

As far as I can recall, I have never seen a transfer function with time units in the function itself, added onto each separate term. I have a good idea on how to handle the delay t_d=25ns, but I have no idea how to handle the delays on each term.

One idea I have had, is noticing the that the term t_d=25ns would imply that we need to find the response at t=25ns. As all other terms have delays in the range of microseconds to seconds, I thought that perhaps this would imply that these signals may not yet have "come into effect", leading to the only term being 100*10^3 s. But this seems like an improper transfer function, and Maple's DynamicSystems package won't accept it.

The title of the problem leads to me thinking that the terms and their delays will affect the phase of the transfer function - but the seconds are causing me so much confusion, that I don't know what to keep and what to leave out, when trying to figure out my response.

• They are lags, not delays; there is a difference. Of course time constants appear in transfer functions - they are constants and not independent variables. The classic first order lag TF is $\frac{\tau}{1+\tau s}$, which transforms to $e^{-t/\tau}$, where $\tau$ is the time constant. – Chu Apr 17 at 12:08
• Very interesting - our Prof has never mentioned this subject before! Do you have any resources where I could learn more? – user2687408 Apr 17 at 16:30