I just downloaded the Uncertainty Calculator and plotted Group Delay Accuracy for three different Sii. I wanted to see how mismatched terminations affect the accuracy of a group delay measurement: they seemed to make little to no difference.

The Uncertainty Calculator plots Accuracy (ns) versus Aperture (MHz) for Group Delay. Perhaps the vertical axis should've been labelled "Error" instead of "Accuracy." I was surprised that the error declines with increasing frequency aperture. Group delay is basically the derivative of phase with frequency. The derivative only becomes exact when delta frequency approaches zero. I understand that as delta frequency approaches zero, delta phase also becomes small and that it may no longer be large compared to the errors in the phase measurement, but the systemic phase error should fall out because the difference of adjacent phase measurements is being taken.

My intuition is apparently incorrect. My basic question is why does Group Delay Error decline with increasing frequency aperture? I'm looking for a brief, intuitive answer if one exists.

Please don't spend too much time on this.

Thanks, Jeff

The Uncertainty Calculator plots Accuracy (ns) versus Aperture (MHz) for Group Delay. Perhaps the vertical axis should've been labelled "Error" instead of "Accuracy." I was surprised that the error declines with increasing frequency aperture. Group delay is basically the derivative of phase with frequency. The derivative only becomes exact when delta frequency approaches zero. I understand that as delta frequency approaches zero, delta phase also becomes small and that it may no longer be large compared to the errors in the phase measurement, but the systemic phase error should fall out because the difference of adjacent phase measurements is being taken.

My intuition is apparently incorrect. My basic question is why does Group Delay Error decline with increasing frequency aperture? I'm looking for a brief, intuitive answer if one exists.

Please don't spend too much time on this.

Thanks, Jeff

> I just downloaded the Uncertainty Calculator and plotted Group Delay Accuracy for three different Sii. I wanted to see how mismatched terminations affect the accuracy of a group delay measurement: they seemed to make little to no difference.

>

> The Uncertainty Calculator plots Accuracy (ns) versus Aperture (MHz) for Group Delay. Perhaps the vertical axis should've been labelled "Error" instead of "Accuracy." I was surprised that the error declines with increasing frequency aperture. Group delay is basically the derivative of phase with frequency. The derivative only becomes exact when delta frequency approaches zero. I understand that as delta frequency approaches zero, delta phase also becomes small and that it may no longer be large compared to the errors in the phase measurement, but the systemic phase error should fall out because the difference of adjacent phase measurements is being taken.

>

This is covered in great detail on pages 292-295 of my book, but the essence is this:

In most instruments, the group delay is not computed by taking a derivative, but by taking a finite difference of delta-phase/delta-freq.

There is noise assoicated with the phase measurement, and the noise is nearly constant with frequency, so the noise contribution in the delta-phase is nearly constant and a major source of error. But as the denominator gets smaller, the noise divided by a smaller number grows makes the delay error grow. Thus the smaller the apeture the greater the error, due to noise.

On the other hand, the error due to source and load match essentially causes are ripple on the measurement, it is not random (like noise is) so as the apeture become small, the error at f1 and f2 (f2-f1 being the delta frequency) becomes almost identical, and disappears from the difference. As the apeture becomes large, the source and load match error increases. Because the effect of this erorr is ripple, and with longer cables the ripple becomes faster, the apeture at which the source and load match becomes uncorrleated is hard to determine, and so we do NOT specify group delay but give only an indication in the uncertainty analysis. I don't recall the exact detail but I think we presume that the source and load match are not correlated at apetures greater than 100 MHz, and are nearly correlated at apetures less than 10 MHz. Once the source and load match errors are fully uncorrelated, they become constant with delta frequency beyond than, so again larger delta means lower error.

> My intuition is apparently incorrect. My basic question is why does Group Delay Error decline with increasing frequency aperture? I'm looking for a brief, intuitive answer if one exists.

>

> Please don't spend too much time on this.

>

Just 3 pages is all.

> Thanks, Jeff