[SI-LIST] Re: Multi-transmission line Zo

Jennifer,

Characteristic impedance of N-conductor line with a reference conductor is N
by N complex frequency-dependent matrix in general. A network that has
impedance matrix equal to the characteristic impedance matrix provides ideal
termination for the multi-conductor transmission line. For instance, a
2-conductor line with a reference conductor has 2x2 characteristic impedance
matrix. For loosely coupled lines the off-diagonal terms of the matrix are
small and the diagonal terms coincide with the characteristic impedance of
one-conductor line computed separately from the other signal conductor.
Though it is usually not the case. As an example, let's take 2-conductor
line with 7 mil strips separated by 10.5 mil on 4.5 mil substrate with
DK=4.2 and LT=0.02 defined at 1 GHz. Characteristic impedance of 7 mil strip
line is about 54.3 @ 1 GHz - this is ideal termination for the single-ended
strip (I neglect the imaginary part of the impedances for simplicity). The
differential impedance of this line is 102.42 Ohm @ 1 GHz. The single-ended
termination with 51.2 Ohm impedance will provide the minimal reflection for
the differential mode. 
Though, the total characteristic impedance of this two-conductor line is 
|54.25; 3.039|
|3.039; 54.25|
This is the ideal termination impedance matrix for this line for both
propagating modes (differential and common). See more on the theory of the
characteristic impedance in C. Paul, Decoupling the multi-conductor
transmission line equations, IEEE Trans. on MTT, v. 44, N8, 1996, p.
1429-1440.

Identification of the characteristic impedance directly from the
S-parameters of multi-conductor line can be done, but not easy task in
general. It is relatively straightforward if S-parameters are appropriately
de-embedded and may be simply not possible otherwise. Note, that precise
de-embedding of S-parameters is required for t-line parameters
identification on the base of both measurements and simulations with a
full-wave field solver.

Best regards,
Yuriy Shlepnev
www.simberian.com 

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Jennifer Maharani
Sent: Wednesday, January 28, 2009 5:24 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Multi-transmission line Zo

Hi all,

I have S-par of multi-line microstrip. How can I derive the single- 
ended characteristic impedance of each line?

Jenni


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