[SI-LIST] PCB Trace impedance algorithms

Dear si-list members,
   
  I am learning tool support for pcb designs. I have some questions regarding 
calculating impedance of a traces in PCB. I use allegro's built impedance 
calculator. I am also aware that there are various other calculator tools from 
UltraCAD, Polar Instruments etc. I am wondering how efficient and accurate 
these calculations are. I guess most of them use some kind of assumptions and 
have simplified closed form formulas to qucikly extimate the impedance. But can 
you people guide me as what is the exact technique or algorithm to calculate 
the impedance of a pcb trace say for a microstrip structure. Any papers or 
links to this study would be appreciated. In specific, since i am using allegro 
's calculator i would like to know how they calculate the impedance and what 
are the assumptions they take. I have seen most calculator allow single ended 
and differential trace calculations. Is it possible to extend these techniques 
to multiple traces. More importantly the accuracy of the
 formulas is of concern to me. When compared to full wave results these 
formulas from different tools give different result. So i am looking to learn 
what is the background behind these? Please advise me on this. Thanks in 
advance. Looking forward for your answers....
   
   
  Sam
                
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