[SI-LIST] Re: mode conversion myth

Hi Eric,

You are correct. Here is a simple proof of no conversion from differential
to common mode in symmetrical multiports.
Let's take a 4-port structure with ports 1 and 2 on the left side (two ports
of a differential pair) and ports 3 and 4 on the right (another differential
pair). 
If multiport is reciprocal, the initial S-matrix descriptor can be written
as

|S11, S12, S13, S14|
|S12, S22, S23, S24|
|S13, S23, S33, S34|
|S14, S24, S34, S44|

Let's assume that the 4-port has mirror symmetry about the horizontal plane
- port 1 is symmetrical to port 2 and port 3 to port 4. The reflection
operator F can be written as 4 by 4 matrix as follows (see R.H. Dicke -
symmetry of waveguide junctions, in Montgomery, Dicke, Purcell Principles of
Microwave Circuits, 1964):

|0, 1, 0, 0|
|1, 0, 0, 0|
|0, 0, 0, 1|
|0, 0, 1, 0|

Matrices F and S must commute or F*S=S*F, that means:
S22=S11, S23=S14, S24=S13, S44=S33

Thus S-matrix of reciprocal multiport with the mirror symmetry (1 to 2 and 3
to 4) must look like that

|S11, S12, S13, S14|
|S12, S11, S14, S13|
|S13, S14, S33, S34|
|S14, S13, S34, S33|

From here it is obvious, that after the transformation into the mixed-mode
space we will always have common to differential and differential to common
blocks filled with zeroes. 
For instance:

S[D1,C1]=0.5*(S11-S21+S12-S22)=0.5*(S11-S12+S12-S11)=0
S[D1,C2]= 0.5*(S13-S23+S14-S24)=0.5*(S13-S14+S14-S13)=0
and so on...

It does not matter what is inside of the multiport as soon as the mirror
symmetry holds (may be also rotational). Unfortunately, this is almost
impossible on PCBs due to dielectric structure.

Happy New Year to Everyone!
Yuriy Shlepnev
www.simberian.com 


-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of eric bogatin
Sent: Tuesday, December 30, 2008 12:29 PM
To: si-list@xxxxxxxxxxxxx
Cc: eric@xxxxxxxxxxxxxxx
Subject: [SI-LIST] mode conversion myth

Hi folks-
 

I give a popular talk on separating myths from reality in signal integrity
(you can down load a copy here:
http://www.bethesignal.net/bogatin/index.php?cPath=29)

 

By popular demand, I am creating two spin off talks, one specifically on
myths about PDN design and one specifically on myths about differential
pairs. In prepping for these, I typically scan some of the questions and
comments from this list.

 

In the last few months, I've seen a number of comments people on this list
made about mode conversion in differential pairs. 

 

While it is possible to really screw up signal quality with a bunch of
differential impedance discontinuities, I have always been under the
impression that you will only get mode conversion- some of the differential
signal converting to common signal-  if there is an asymmetry between the
two lines that make up the differential pair, either in the signal or return
paths. This can be a length difference, a time delay difference, a line
width difference, a return path difference, etc.

 

You can have large line width changes, separation changes, even gaps in
return paths and see no mode conversion, if whatever you do to one line, you
do to the other line. Of course, when you go through a connector and the
return path has a discontinuity, it is sometimes difficult to make the
discontinuity symmetrical, but it is the symmetry of the discontinuity that
determines the amount of mode conversion, not the amount of discontinuity
that determines the mode conversion.

 

Does any one disagree with this comment?

 

In case you are curious, the other myths that I am covering in the diff pair
talk are:

 

-          the return current distribution in microstrip and stripline

-          when should the common signal be terminated

-          the use of differential mode and common mode vs differential
signals and common signals 

-          vias are bad and should be avoided

-          this one on mode conversion

 

Do you have your favorite myth you might want to share? If I use it, I will
try to give you credit.

 

comments are always welcome.

 

--eric

 

 

*******************************************************
Dr. Eric Bogatin, Signal Integrity Evangelist
Bogatin Enterprises
Setting the Standard for Signal Integrity Training
26235 W 110th Terr
Olathe, KS  66061
e:  <mailto:eric@xxxxxxxxxxxxxxxx> eric@xxxxxxxxxxxxxxx
v: 913-393-1305   cell: 913-424-4333   f: 913-393-0929
 <http://www.bethesignal.com/> www.BeTheSignal.com
Blog:  <http://www.bethesignal.com/blog> www.beTheSignal.com/blog
*********************************************** 

 

 



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