### Measuring differential pair loss requires both lines to calculate the attenuation.

Whether a high-speed serial link channel works is just as dependent on the losses in the channel as its differential impedance. It’s not enough to just meet an impedance spec and verify it using a test coupon. In many applications, it is also important to meet a loss spec and verify the attenuation of traces in a test coupon.

Measuring the signal-ended impedance of a trace in a test coupon is easy. All fab shops understand how to do this with a TDR. It is tempting to think that if you use the same line in a single-ended line or in a differential pair, a line is a line, and all you have to do is measure it once to know the differential impedance. After all, the other line in the pair isn’t even touching its partner.

Unfortunately, while the proximity of the other trace in a differential pair will not change its single-ended impedance, the proximity will strongly affect the differential impedance of the pair.

Just measuring the single-ended impedance of one line in a differential pair, either as an isolated line or when in the differential pair, is no indication of the differential impedance. The measurement can be off by as much as 10% for tightly coupled microstrip or stripline pairs. You have to go the extra step to measure the differential impedance using a dual TDR.

Likewise, you cannot accurately measure the loss in a differential pair by just measuring the loss of one of the lines, or of an isolated version of that line. The coupling between the lines will affect the measured attenuation.

Figure 1 is a comparison of the differential insertion loss of a differential stripline pair, and of just one of the lines as a single-ended line stripline.

We usually define the losses in a uniform transmission line as the attenuation, measured in dB. Since the loss, in dB, increases linearly with the length of the line, it is often more common to use the metric of the attenuation per length, measured in dB/inch. For example, Intel recommends differential pairs used in PCIe III interconnects have a loss less than 0.78 dB/inch at 4 GHz.

In addition to geometry features, raw material and processing conditions will affect loss in a differential pair, making it necessary to measure test coupons to verify the attenuation per length of differential pairs on the board.

Unfortunately, measuring the attenuation of a single line that may be isolated or part of a differential pair will provide a different attenuation than the actual differential impedance of the pair. The coupling between the lines will affect the differential attenuation. Here’s why:

Loss arises from conductor loss and dielectric loss. In stripline, attenuation from the dielectric loss is independent of coupling. If there were no conductor loss, measuring the attenuation of an isolated single-ended line or one line in a differential pair would give the same attenuation as the attenuation of the differential pair.
The attenuation from the conductor loss depends on the coupling in two ways. The attenuation is not due to just the series resistance alone, but the ratio of the series resistance to the differential impedance.

If the line width is kept fixed, and the two lines in a differential pair brought closer together, the differential impedance will decrease. Even if the series resistance were to remain constant, the attenuation would increase because the differential impedance decreased.

To complicate this further, the proximity of the two lines in the differential pair changes the current distribution in the conductors, changing the series resistance. Surprisingly, the series resistance goes down with tighter coupling as more of the return currents overlap and cancel. The current crowding in the signal traces does not start to increase the signal path series resistance until the spacing between the lines is much less than a line width.

The combination of these two effects means the attenuation will be higher in a differential pair than if measured as single-ended lines. This is all the more reason for all suppliers and users of high-speed differential channels to begin implementing a process to measure the attenuation of differential pairs for all high-performance boards.

Eric Bogatin, Ph.D., is a consultant and founder of Be The Signal (bethesignal.com); This email address is being protected from spambots. You need JavaScript enabled to view it.. His column runs periodically.