[SI-LIST] : Re: [old] Differential Reflection Question

Howard Johnson (howiej@sigcon.com)
Fri, 22 May 1998 16:20:34 -0700

Hi John, if you are still out there listening, the previous
response to your issue didn't seem to me to address your
question. It sounded to me like you were talking about
joining cables.

Here is (hopefully) a more direct response.

Assume I have a section of differential transmission line
with a differential impedance of Z0.

Assume I couple that into a load with differential impedance ZL
(doesn't matter whether ZL is a lumped-element load, or a
second section of differential transmission line with
characteristic impedance ZL).

The reflection that bounces off the joint will be of size:
Reflection_coefficient = (ZL - Z0)/(ZL + Z0)

Let's do an example using unshielded twisted-pair cabling (UTP).
Suppose I couple a section of category-5 100-ohm (nominal) UTP
cabling to a section of category-4 120-ohm (nominal) UTP
cabling (available only in France). The reflection off
the joint will be of (nominal) size:

Reflection_coefficient = (120 - 100)/(120 + 100) = 0.09

Now, what could go wrong with this simple example? If the
cable is inherently UN-balanced (i.e., more capacitance from
one side to ground than on the other), then you have a more
complicated situation. In general, there are four modes
of propagation (one differential mode and one common mode for
each of the two cables). The complete problem is described by
a 4x4 coupling matrix (whose entries vary with frequency).
Imperfections in the balance of the cable result in cross-coupling
between the differential modes and the common modes at the
joint, which is one of the things that creates EMI headaches.
Aside from that complication, differential transmission lines
behave pretty much like single-ended ones.

I hope this (belated) response have been helpful to you.

Best regards,
Dr. Howard Johnson

>
>
>
>On Wed, 1 Apr 1998, Lehew, John wrote:
>
>> In the High Speed Digital Design book and in a few other places it
>> states the percent reflection caused by a difference in impedance is:
>>
>> %Reflection=(Z1-Z2)/(Z1+Z2)
>>
>> This formula is typically used to calculate the reflection of a single
>> line referenced to a ground plane. Does this formula also apply to
>> differential/balanced lines where two lines carry one signal?
>>
>> Regards,
>>
>> John Lehew
>> Design Engineer
>> Compaq
>>
>>
>>
>>
>
>
>
_________________________________________________
Dr. Howard Johnson, Signal Consulting, Inc.
tel 425.556.0800 // fax 425.881.6149 // email howiej@sigcon.com

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