Differential Reflections

HIGH-SPEED DIGITAL DESIGN - online newsletter -
Vol. 2 Issue 21

*---------------------(QUESTION)---------------------*

DIFFERENTIAL REFLECTIONS

John Lehew writes:

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?

*--------------(REPLY FROM DR. JOHNSON)--------------*

Thanks for your interest in High-Speed Digital Design.

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 (it 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 the complication by unbalanced modes, differential transmission lines behave pretty much like single-ended ones.

Best regards,
Dr. Howard Johnson

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