NanoVNA – interpolation – part 2

NanoVNA – interpolation – part 1 introduced the principle on which VNA measurements are made and corrected based on a set of error terms derived from measurement of some known loads at the reference plane.

The technique of interpolation as a convenient means of increasing the utility and flexibility of a calibration data set was also introduced, and example raw (uncorrected) sweeps of an OC at the end of about 5m of RG58A/U were given to illustrate the challenge in interpolation with insufficient samples or control points.

A more common data flow is that shown above, where the correction terms are calculated for each of the frequencies in the calibration sweeps, and then those terms are interpolated to the frequencies actually used for a DUT measurement sweep.

One of those correction terms is Reflection Tracking shown above for the example case of an OC at the end of about 5m of RG58A/U. Not surprisingly, it has a similar oscillating characteristic to the s11 measurement of the line section with OC or SC termination, and the same challenge for interpolation exists.

To interpolate at some frequency with reasonable accuracy, there must be sufficient data points or control points in the neighborhood of that frequency.

A chart of s11 with OC or SC termination is easier to create and jaggyness is a sign that interpolation will lead to significant error.

There are a range of algorithms used for interpolation, The simplest is linear interpolation mentioned earlier. A more complicated approach is to spline interpolation where some function is fitted piecewise to the observations, the natural cubic spline is often a good technique for this type of data. (NanoVNA-App uses a Catmull Rom cubic spline.)

Whatever the method, insufficient control points results in poor accuracy, and whilst cubic splines give better accuracy with sufficient points (and usually fewer than a linear interpolation), with insufficient control points they go very wrong.

So, again, interpolation of the correction terms provides flexibility, but at a cost.

Some VNAs just don’t allow interpolation, those that do can usually be circumvented by measuring the DUT with the same sweep parameters (ie start, stop, step).