Category: Measurement

Measured impedances looking into a uniform transmission line section with short circuit (SC) and open circuit (OC) terminations can provide the basis for calculation of characteristic impedance Zo.

We rely upon the following relationships:

\(Z_{sc}=Z_0 \tanh (\alpha + \jmath \beta )l\\\) and

\(Z_{oc}=Z_0 \coth (\alpha + \jmath \beta )l\\\)

Rearranging the formulas and multiplying, we can write:

\(Z_0^2=\frac{Z_{sc}}{\tanh (\alpha + \jmath \beta )l} \frac{Z_{oc}}{\coth (\alpha + \jmath \beta )l}\\\) \(Z_0^2=\frac{Z_{sc}}{\tanh (\alpha + \jmath \beta )l} Z_{oc}\tanh (\alpha + \jmath \beta )l\\\)

The tanh terms cancel out… provided the arguments are equal. Focus on length l, l for the short circuit measurement might not equal l for the open circuit measurement if the termination parts are not ideal (and they usually are not).

If the tanh terms cancel, we can simplify this to \(Z_0=\sqrt{Z_{sc}Z_{oc}}\). This is commonly parroted, apparently without understanding or considering the underlying assumption that l is equal for both measurements.

Another big assumption is that it is a uniform transmission line, ie that the propagation constant β is uniform along the line… including any adapters used to termination the line.

The third assumption is that the measured impedance values are without error.

Above is a plot of calculated Zo for a theoretical case of a line of ~10m length of Belden 8267 (RG213A/U) around the frequency of first resonances. This calculation essentially imitates perfect measurements of perfect DUTs. Continue reading Determination of transmission line characteristic impedance from impedance measurements

Most of the changes I have made to NanoVNA-App have been to align it with accepted standards and conventions.

This change is to the format of saved Touchstone, .s1p and .s2p, files.

Though the relevant specification is silent on the permitted decimal separator, the only one shown in examples is “.” so it is reasonable to interpret that the required separator is “.” which makes the file format locale independent (as were the first instruments using Touchstone format.

This release of NanoVNA-App writes “.” decimal separator, independent of locale.

The original reading code which was tolerant of either “.” and “,” is maintained, so it will continue to open files which might have been (incorrectly) saved using “,”.

NanoVNA-App-Setup-v1.1.209-OD15

Whilst following up another matter, I came across the following commit to Hugyen’s NanoVNA-H4 repository.

Remove R44 from NanoVNA-H4 Rev4.3, this resistor may damage U2 and the battery if the NanoVNA-H4 is not used for a long time and the battery is too low.

Above is an extract from the revised schematic committed, the change highlighted by the red arrow. R44 has been changed from 5.1kΩ to not populated. Continue reading NanoVNA-H4.3 R44 mod

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. Continue reading NanoVNA – interpolation – part 5

NanoVNA – interpolation – part 3 discussed selection of a sweep step size to provide sufficient data points for reasonably accurate interpolation.

When / where is interpolation used?

The VNA correction process uses measurements of some known conditions to create a calibration dataset, a table if you like of the sweep frequencies and calibration data. Commonly the calibration dataset is a table of the correction factors calculated from measurements of the knowns for each frequency of the calibration sweep. The correction factors are usually calculated for each frequency independently of adjacent frequencies.

When used to sweep a different range, interpolation can be used to interpolate those correction factors to the new measurement frequencies.

A 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. Continue reading NanoVNA – interpolation – part 4

NanoVNA – interpolation – part 3 discussed interpolation and introduced cubic spline interpolation.

NanoVNA-App v1.1.209-OD12 and prior used one of the special monotone types of cubic spline interpolation.

When used in VNA correction, the control points are often complex numbers with real and imaginary in broadly sinusoidal form and approximately 90° out of phase… so behavior on this scenario is important.

Above is a comparison of two types of interpolation on a pure sine wave. The green curve is the underlying sine curve, the orange dots are the samples or control points, the red curve is a linear interpolation, the blue dots are an example monotone cubic spline interpolation (monotone-cubic-spline.js). Continue reading NanoVNA-App v1.1.209-OD13 released