twisted pair differential signal common mode

Hi:

The design task is to design on-chip differential transmission line to
send signal. According to a lot of papers, edge coupled stripline is
used.

The cross-section is as below graph(might be lost). One key thing is
that there is no underneath common-mode return path.

________________________________________________
______ ______
dielectric |__+__| |__-___|
________________________________________________

Hi-Z substrate

________________________________________________

Then what is going to happen to common-mode signal? Common mode should
not be a propagating mode, however, its S21 parameter after several
reflections should be as below.

S21=A*Hx*T/(1-R2*R1*Hx*Hx)

R1 is source reflection coefficeint;

R2 is load reflection coefficeint;

Hx is propagation function, Exp(-gamma*L);

Common mode impedance will be quite high if there is no good return
path. Therefore, both source and load are not well terminated. Source
could be very like short, and load could be very like open.

Then R1=-1, R2=1; the S parameter could go infinity if Hx(w)=-1; It
could resonate;

It looks that twisted pair could survive this condition and goes well,
why? Also several IEEE papers also used above configuration on-chip and
goes fine, why?

You have told, "According to a lot of papers, edge coupled stripline is
used".

This implies that there will be ground beneath signal layer. Then how do you say, "One key thing is that there is no underneath common-mode return path. "

The ground below the signal is the return path for the signal.

The stripe-line I mentioned does not contain ground plane.