# Re: differential impedance

Fred ([email protected])
Wed, 9 Apr 1997 14:58:48 +0800

Since nobody has really defined differential impedance, I'll try my luck.
First we are dealing with 2 and only 2 conductors. For purpose of this discussion the gnds or
planes are referred to as gnd and are not referred to as the conductors above. The structure
may have a gnd then or just be two conductors suspended in air where the gnd is far enough to
be ignored.

Case 1. Two conductors with a gnd. Cg1 is the self capacitance of conductor 1 to gnd. Cg2
is the self capacitance of conductor 2 to gnd. Cm is the mutual capacitance between the
two conductors. L1 is loop inductance of conductor 1. L2 is the loop inductance of
conductor 2. Lm is the mutual inductance between conductor 1 and conductor 2. If anyone
requires the definition of the loop inductance please let me know. In order to have
differential mode L1=L2 and Cg1=Cg2. That being the case we'll call (L1=L2) Lo and
(Cg1=Cg2) Co.
Z(diff) = 2*sqrt((Lo-Lm)/(Co+2Cm)) the term sqrt((Lo-Lm)/(Co+2Cm)) is called the
odd mode impedance. And.........just for reference the even mode impedance is
Z(even) = sqrt((Lo+Lm)/Co-2Cm)).

One can see the even mode impedance is NOT the same as differential impedance. If
the mutuals can be ignored then and only then 2*even=differential. In order to ignore
the mutuals they must be relatively small compared to the self C and L. In practical
terms this means the conductors must be seperated by a large distance so they do not
talk to each other. This essentially starts to defeat one of the purposes to have
differential impedance in the first place.

Case 2. Two conductors suspended in air. In order to have a definition one of the conductors
must act as the return. That being the case the differential is simply :
Z(diff) = 2*sqrt(L1/C1).

Hopes this helps you guys.

Best Regards,

Fred Balistreri
Applied Simulation Technology