The actual rise time and frequency content of digital pulses may vary. The frequency spectrum of a PRBS digital data stream typically consists of bands centered around a fundamental and its odd harmonics. The fundamental frequency of the spectrum occurs at one half of the data rate. At 2.5Gb/s, this means that the fundamental frequency would occur around 1.25GHz with some contribution around the third (7.5 GHz) and fifth (12.5GHz) harmonics. The transmission vs. frequency response will be shown for various via geometries, together with eye patterns that incorporate the effects of the higher harmonics.

A PTH, or through via joining a surface pad or connector to an inner layer strip line trace, can behave as a parasitic element or transmission line discontinuity. It acts as a notch filter centered on a frequency primarily determined by the unused portion of the hole, sometimes referred to as a resonant stub. As a signal transitions into a plated through hole, some of the energy is reflected back to the source from the impedance discontinuity. The remaining energy proceeds through the via. The energy that is transitioning through the plated through hole uses the hole as a transmission line element whose parameters are defined by the physical dimensions of the structure (pad size, anti-pad size, etc.) It then reaches an impedance matched stripline layer. Some of the energy is transmitted into this layer and some continues to travel down the remaining via. Any portion of the plated through hole below the exiting stripline layer can be looked at as an open transmission element referred to as a stub.

The energy that passes the exiting stripline layer proceeds to the end of the stub and encounters an open circuit, and it is reflected back toward the source or converted to radiation.

At low frequencies a PTH element could simply be modeled as a lumped capacitor. At higher frequencies the round trip delay for this PTH element approaches the signal rise time and the simple capacitive approximation no longer holds. The length of the stub could be over 8mm in a backplane. As an example, in our 0.220" thick test board, the maximum stub was 5.0mm. The delay of pure FR-4 is approximately 7ps/mm or 175ps/inch. The calculated delay from the open end of the stub to the strip line layer is approximately 38ps. The calculated quarter wavelength frequency of this open stub element resembling an antenna is approximately 7 GHz. The actual observed frequency is always somewhat lower due to excess fringing capacitance and other effects from the details of the structure. For example, in the test board shown in Figure 2, the notch was measured at 4.5 GHz.

If the notch created by this resonance occurs at a frequency, which is close to the fundamental frequency, only a percentage of the transmitted signal would make it past the filter created by the stub (Figure 1).