## Mixing skin-effect and dielectric loss

Long, high-speed pc-board traces operate in a zone influenced by both skin-effect and dielectric losses. Both mechanisms attenuate the high-frequency portion of your signals but in slightly different ways. Figure 1 illustrates 36 mixtures of varying amounts of skin and dielectric effects, showing the step response in each case.

The top row of the chart, working from left to right, shows step-response
waveforms corresponding to successively increasing amounts of dielectric loss.
The dielectric loss in each case is rated in nepers of attenuation at some
arbitrary frequency, *ω*_{0}. (One neper equals 8.69 dB.)

The left side of the chart, working from top to bottom, shows step-response waveforms corresponding to successively increasing amounts of skin-effect loss. The middle area of the chart displays various combinations of both types of loss.

The horizontal axis for each waveform is calibrated in units of
2π/*ω*_{0} sec/division. For example, if the
skin-effect- and dielectric-loss specification frequency is set to 1 GHz
(*ω*_{0}=2π×10^{9} rad/sec), then the horizontal
axis reads at 1 nsec/division. If your loss calculations fall outside the range
of values in the chart, try recalculating your loss coefficients, assuming a
different value of *ω*_{0}. By scaling *ω*_{0},
you can always ensure that your total loss numbers land somewhere within the
values on the chart.

The vertical axis for each waveform is one unit (full-scale response) per division. Waveforms in successive columns are each offset horizontally by one unit of time, purely for convenience in reading the display. These waveforms were calculated using the technique of frequency-domain modeling.

Both the skin-effect and the dielectric-loss effect degrade digital signals
in the same fundamental way-by smearing the rising and falling edges-but some
differences exist. For the same degree of loss at *ω*_{0}, the
skin-effect step response displays a steeper initial rising edge, but a longer,
more lingering tail, than the dielectric-effect step response.

In the frequency domain, the differences in the slope of the initial rise imply that the dielectric effect induces a steeper, more severe roll-off at high frequencies than the skin effect. This scenario is consistent with the general principle that dielectric attenuation (in nepers or decibels) varies directly with frequency, and skin-effect attenuation varies only in proportion to the square root of frequency.