NanoVNA – interpolation – part 3

This article continues on from NanoVNA – interpolation – part 1 and NanoVNA – interpolation – part 2 which illustrated jagged scans at up to 900Mhz where the reference plane was displaced by 5m of RG58A/U.

A quite practical example where care must be taken is the following one at HF. Let's say you wanted to measure the feed point impedance of some HF antenna, and the online gurus explained that one way to do that was to calibrate the NanoVNA and normal antenna coax feedline as a fixture, setting the reference plane to the feed point end of the coax.

A Simsmith model for illustration

A Simsmith model was constructed of a 30m (~100′) length of RG213 with a short circuit termination, and the real and imaginary parts of s11 as would be seen by the NanoVNA were plotted.

Let's say you wanted to sweep from 1.5-33MHz (to include a little each side of the 160-10m bands… partly for reasons to be explained later.)

30m of RG213 @ 33MHz, step size 0.3MHz

Lets focus on the high frequency end where the jagged response is worse.

Again we see the periodic variation of s11 real and imaginary components as shown in the earlier articles. In the plot above, Simsmith as done a linear interpolation of the sweep points, and at 0.3MHz per step, the curves a jaggy. The actual minimum of the blue curve is at 33.88MHz, and the value is about 5% higher than the linear interpolation… which will introduce measurement noise to any VNA sweeps with such a configuration. Sweeps such as this are inputs to the calibration process.

30m of RG213 @ 33MHz, step size 0.1MHz

The plot above shows a smoother curve, probably smooth enough for good accuracy even with linear interpolation. Step size is 0.1MHz.

For a linear spaced sweep of 1.5-33MHz, we would want at least 315 scan points, so you might choose 401 on NanoVNAs that support that.

Notwithstanding that, some multiband antennas might have such sharp responses in the ham bands that more scan points are needed, or several scans of sub-ranges could also be used.

Again, inspect a raw (uncorrected) scan of the test fixture with OC or SC termination, if it is jagged, increase the steps for more accurate interpolations.

Cubic spline interpolations

Cubic spline interpolations use a set of three or more control points, and typically the end interval is not as accurate as the others, so it is wise to set the scan range for a little over scan to give better accuracy on the intervals of interest.

It also makes sense to overscan antenna sweeps for a bit more context.