raja.cedt,
The system you show is analyzed in detail in the first few lectures at the link below. You get a delay differential equation whose solutions are (combinations of) exp(st) as usual. Explanation and analysis of this in time domain give a quick intuition to all results regarding negative feedback amplifiers and delay.
http://www.ee.iitm.ac.in/~nagendra/videolectures/doku.php?id=ee539_2011:startQuick summary of responses to a step:
* zero delay: exponential build up with a time constant 1/omega_u
* delay < 1/e/omega_u: Equivalently a two pole system(two real solutions for s); No overshoot---equivalent to overdamped two pole system
* delay = 1/e/omega_u: Two identical solutions for s; Fastest step response without overshoot---equivalent to critically damped two pole system
* 1/e/omega_u < delay < pi/2/omega_u: Infinitely many complex conjugate solutions for s, all in the left half plane; The lowest frequency solutions dominate---equivalent to underdamped two pole system
* pi/2/omega_u = delay: Infinitely many complex conjugate solutions for s, with at one pair on the imaginary axis; unstable
* pi/2/omega_u < delay: Infinitely many complex conjugate solutions for s, with at least one pole pair in the right half plane; unstable
* A "reasonable" amplifier without too much ringing while settling: delay < 0.5/omega_u
A real system with many parasitic poles behaves quite similarly to this. Graphs are shown in the videos at the link above.
Alexandar, linearizing exp(-s*tau) as 1/(1+s*tau) doesn't give the small signal response. The approximation is OK for very small delays, but gives incorrect results for critical damped case etc. and doesn't predict instability for any value of tau. linearizing it as (1-s*tau) does predict instability, but again at the wrong value of tau I believe.
Cheers
Nagendra
Nagendra