Frequent Obsession

by Dr. Howard Johnson. First printed in EDN magazine, October 12, 2006

I recently encountered yet another pc-board-trace specification written in the frequency domain. Why do people do that?

This particular specification calls for a worst-case trace loss of –3 dB at 11.2 GHz. The trace goes inside a piece of test equipment that works at 3.2 Gbps.

The specified frequency, 11.2 GHz, is much higher than the system data rate. You may infer from the specification that the system designer wants an extremely clean channel with rise and fall times far shorter than the data-bit interval.

Unfortunately, the specification may imply a clean channel, but it doesn't specify one. All it says is "worst-case trace loss of –3 dB at 11.2 GHz."

A number of systems that meet this overly stringent specification fail to deliver good performance at 3.2 Gbps.

For example, a 10th-order, Butterworth brick-wall lowpass filter with a –3-dB cutoff residing precisely at 11.2 GHz satisfies the specification to a tee, but its time-domain response rings prodigiously.

Similarly, a poorly terminated transmission line with hideous overshoot could still meet the letter of the specification, but probably not your idea of a "clean channel."

The ambiguity in this specification derives partly from its frequency-based orientation and partly from its lack of detail.

To address the lack of detail, you could add more frequency points to the specification; stipulate both magnitude and phase information; and call for a smooth, monotonic frequency response. These additions make a more impressive-sounding specification but fail to directly address your main concern: time-domain performance.

To control the time-domain shape of signals conveyed through any linear, time-invariant system, you should specify a time-domain test. My preferred arrangement is a step-response test. The test should call out four main points:

  1. The amplitude, rise time, and source impedance of the required step source.
  2. The method of connection to the system. Always provide test connectors for this purpose.
  3. The test load (50Ω, or 100Ω differential, in most cases).
  4. A template for the received step.

A good template specifies the required minimum and maximum rise time and may also require a monotonic step response or otherwise limit the size and number of ripples.

Make sure the template depicts the signal shape resulting from excitation with your practical test source, not just the raw "idealized" step response of the system given a perfect step input.

Frequency-domain instruments can play an important role in the measurement process but should not be the main focus of your specification.

For example, if you have a vector-network analyzer and you know how to use it, you can measure the S-parameter response of your system. Then use the FFT (Fast Fourier Transform) to compute the time-domain step response of your system. Measure that time-domain result against your template.

I like this hybrid approach because no time-domain instrument can surpass the accuracy, sensitivity, noise floor, and autocalibration routines inherent to a network analyzer. If you use a network analyzer, do it to gain these advantages, not because you have become, like too many engineers lately, simply obsessed with the frequency domain.

Time matters.