My question is not directly related to your publications. In the past I have seen many discussions regarding the topic "differential impedance" (for example in the Silist reflector). All explanations I have found are related to PCBs (coupled Microstrip or Stripline geometry for a special differential impedance).
Now I have a flat cable. I think the differential impedance between two neighboring wires of this cable (S+ and S-) is the same as the single ended impedance between two neighboring wires of this cable (S and GND).
Is this correct? I have found a data sheet for a flat cable with information about single ended impedance for S G S G S G (for example 90 Ohm) and differential impedance for S+ S- S+ S- S+ S- (for example 135 Ohm). I don't understand these values. I think that in a flat cable, the balanced and the unbalanced transmission have the same behavior. What is your opinion?
Thanks for your interest in high-speed digital design.
The ribbon cable situation is fairly simple, so we can develop some good intuition about its impedance. I'll relate to you here some of the reasoning tricks I've been shown by others.
When I configure a cable in the G S G S G configuration (one ground per signal), the signal wires each exhibit a certain impedance from signal to ground. Call that impedance Z.
Let's now use this cable in a differential configuration, like this, G S+ G S- G. Here I have placed a ground between every conductor. This configuration exhibits a differential impedance of precisely 2*Z.
I hope that much is clear to you. The same principle is at work when I transmit a differential signal on two non-interacting pieces of 50-ohm coax. The total voltage between the two coaxial conductors is double the single-ended voltage, but the net current in each is the same, so the differential impedance between two coax cable used in a differential configuration would be 100 ohms. As long as the signal paths don't interact, the differential impedance is always precisely twice the single-ended impedance of either path.
Now let's consider a more common differential configuration like this: G S+ S- G (with one ground standing between each successive differential pair). The differential impedance of this structure is not 2*Z1. The existence of two antipodal (opposite) signals S+ and S- in close proximity creates a virtual ground at a point midway between the two signals. There might as well be a ground there, it wouldn't make any difference to the electromagnetic field patterns, because the voltage at that point is precisely zero anyway.
We could write this configuration as G S+ [virtual gnd] S- G, where the spacing on either side of the virtual ground is only half a space. This is the same thing as squashing the previous differential configuration G S+ G S- G to shrink the space on either side of the central ground conductor to half- size. In real life, if you were to squash the grounds closer to the signals like that, you would expect the differential impedance to drop, and it does. The differential impedance of the G S+ S- G configuration is always less than twice the single- ended impedance of the G S G S G configuration.
In practical cables with a single-ended impedance of 100 ohms the differential impedance in a G S+ S- G configuration usually works out to a value near 150 ohms (about 50arger). I am not at all surprised by your data.
About your specific question, if you use the configuration S+ S- S+ S- S+ S- without any grounds, you will get substantial amounts of crosstalk between the pairs (unless it's a twisted- pair ribbon cable, which you didn't mention). I don't recommend using that configuration for flat cables.
Dr. Howard Johnson