Category: NanoVNA

For a lossless line, the reactance looking into short section and open circuit terminated line sections is \(X_{sc}=Z_0 \tan \beta l\) and \(X_{oc}=Z_0 \frac1{\tan \beta l}\).

Noting that when \(\beta l= \frac{\pi}{4}, \tan \beta l=1\) so when the line section is π/4ᶜ or 45° or λ/8, then \(|X_{sc}|=|X_{oc}|=Z_0\).

We can use this property to estimate Z0 of an unknown practical low loss transmission line by finding the frequency where \(|X_{sc}|=|X_{oc}|\) and inferring that \(Z_0 \approx |X|\).

 

Above is a chart created using Simsmith’s transmission line modelling of the reactance looking into short section and open circuit terminated 10m sections of RF174. The blue and magenta lines intersect at X=51.16Ω whereas red R0=51.85Ω, about -1.3% error. The error depends on line loss, line length, frequency and the characteristics of the terminations. Continue reading Determination of transmission line characteristic impedance from impedance measurements – eighth wave method

Determination of transmission line characteristic impedance from impedance measurements discussed issues with the short circuit and open circuit terminations used with measurement of Zoc and Zsc for calculation of characteristic impedance of a line section.

Included was a model of the effect of small delay offset in one of the termination parts on an example scenario.

This article gives a Simsmith model that readers might find interesting to explore the effects of line length, offset, line characteristics, and frequency.

I have issues with Simsmith modelling of transmission lines, but nevertheless the model is informing.

The above example is 6m of RG58A/U with 5mm offset in the short circuit termination. Continue reading Determination of transmission line characteristic impedance from impedance measurements #2

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 Z0.

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 Z0 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