# nanoVNA – tuning stubs using TDR mode

From time to time I have discussions with correspondents who are having difficulties using an antenna analyser or a VNA to find / adjust tuned lengths of transmission lines. I will treat analyser as synonymous with VNA for this discussion.

The single most common factor in their cases is an attempt to use TDR mode of the VNA.

## Does it matter?

Well, hams do fuss over the accuracy of quarter wave sections used in matching systems when they are not all that critical… but if you are measuring the tuned line lengths that connect the stages of a repeater duplexer, the lengths are quite critical if you want to achieve the best notch depths.

That said, only the naive think that a nanoVNA is suited to the repeater duplexer application where you would typically want to measure notches well over 90dB.

## Is it really a TDR?

The VNA is not a ‘true’ TDR, but an FDR (Frequency Domain Reflectometer) where a range of frequencies are swept and an equivalent time domain response is constructed using an Inverse Fast Fourier Transform (IFFT).

In the case of a FDR, the maximum cable distance and the resolution are influenced by the frequency range swept and the number of points in the sweep.

$$d_{max}=\frac{c_0 vf (points-1)}{2(F_2-F_1)}\\resolution=\frac{c_0 vf}{2(F_2-F_1)}\\$$ where c0 is the speed of light, 299792458m/s.

Let’s consider the hand held nanoVNA which has its best performance below 300MHz and sweeps 101 points. If we sweep from 1 to 299MHz (to avoid the inherent glitch at 300MHz), we have a maximum distance of 33.2m and resolution of 0.332m.

Here is such a sweep of a cable of length around 1.2m.

The marker is close to the apparent peak of the response at about 11.8ns (1.17m), and each step of the marker is 1.3ns (0.129m).

If we sweep to 900MHz, we do get better resolution (albeit for shorter dmax).

The resolution is reduced to 0.435ns (0.043m)

If you want mm resolution for short line sections, you need a VNA that sweeps a much wider frequency range and / or much more sweep points.

Above, nanoVNA-saver results on the same DUT with smoothing of 100 sweeps produces a nice clean looking graph and a calculated distance to fault of 1.222m, mm resolution implied by the number format… but are you mislead?

## What can we do with the nanoVNA?

We can do a s11 sweep of a short circuit or open circuit line section (just as in the FDR / TDR case), but make the sweep quite narrow (ie high resolution) around a quarter wave or half wave resonance.

Above is a very narrow sweep with 1kHz resolution at 40MHz, ie 0.0025% resolution. From the interpolated resonance frequency of 40.4MHz and previously measured vf, we can calculate the physical length to be 1.224m… with resolution of 0.0000306m.

## Distance to fault

Many analysers and VNAs sport a Distance to Fault mode, and it is commonly a FDR implementation. These can be very effective productivity tools in identifying not just cable opens and shorts, but loose connectors, pinched cable etc.

The foregoing discussion shows that FDR / Distance to Fault may not be adequate for tuning of critical line sections, but it often has sufficient resolution for identifying the locality and severity of a fault.

Things have come a long way in the around 150 years since Oliver Heaviside successfully applied his mind to location of faults in submarine telegraph cables.

## Conclusions

Whilst the TDR mode of a VNA looks an appealing way to measure line length, with low end instruments like the nanoVNA it does not have adequate resolution for demanding applications.