NanoVNA – interpolation – part 5

NanoVNA – interpolation – part 4 and prior articles discussed the possibility of significant error when calibration data is interpolated.

This article illustrates the effects with some very simple examples.

Test scenario

The test scenario is a NanoVNA-H4 with 5m length of RG58A/U to the reference plane. It has been OSL calibrated at the reference plane using a 1-101MHz 101 point sweep.

Result without interpolation of the calibration dataset

Above is a zoomed in view of 1-5MHz of a 1-101MHz 101 point sweep, there are measurements at every whole MHz value from 1 to 101. There are only 5 measurement points on this graph.

Of course the graph does include linear interpolation between each adjacent pair of measurement points. The question should be asked whether that is reasonable, and in this case it is as we are measuring the 50Ω load used for calibration and we would expect very low s11 (though less than perfect because the coax has been shuffled a little).

Result with interpolation of the calibration dataset

Above is a view of a 1-5MHz 101 point sweep using the same calibration dataset, there are measurements at every 40kHz from 1 to 5MHz. There are 101 measurement points on this graph, and the correction is based on just 5 points at 1, 2, 3, 4 & 5MHz.

Comparing the measurements with the previous case, the measurements reconcile at 1, 2, 3, 4 & 5MHz, but at other frequencies there is a departure that is periodic in nature. This is due to use of interpolation of the calibration dataset.

Another DUT case

Above is a view of a 1-5MHz 101 point sweep using the same calibration dataset, there are measurements at every 40kHz from 1 to 5MHz, but this time of the O calibration part, ie an OC termination. There are 101 measurement points on this graph, and the correction is based on just 5 points at 1, 2, 3, 4 & 5MHz.

The expected result is that s11 should be very close to 1+j0, but slightly lower due to the 0.08-0.17dB matched line loss in the 5m section of coax.

The measurements at 1, 2, 3, 4 & 5MHz are plausible. Note that for most of the plot, the magnitude of the real part of s11 is greater than one… that should not happen… it is the result of interpolation of the calibration dataset.

Should you simply artificially limit the values of s11 to fix your measurements? Sounds dodgy to me!

Conclusions

Be the devil's advocate of your own measurements, and investigate effects that are unexpected. Periodic variations that are synchronised to the calibration frequencies bear investigation.