Transmission lines – Page 6

nanoVNA – measuring cable velocity factor – demonstration – open wire line

The article nanoVNA – measuring cable velocity factor – demonstration demonstrated measurement of velocity factor of a section of coaxial transmission line. This article demonstrates the technique on a section of two wire copper line.

A significant difference in the two wire line is that we want the line to operate in balanced mode during the test, that there is insignificant common mode current. To that end, a balun will be used on the nanoVNA.

Above, the balun is a home made 1:4 balun that was at hand (the ratio is not too important as the fixture is calibrated at the balun secondary terminals). This balun is wound like a voltage balun, but the secondary is isolated from the input in that it does not have a ‘grounded’ centre tap. There is of course some distributed coupling, but the common mode impedance is very high at the frequencies being used for the test. Continue reading nanoVNA – measuring cable velocity factor – demonstration – open wire line

Last update: 28th October, 2020, 4:27 PM

nanoVNA – experts on improvised fixtures

A newbie wanting to measure a CB (27MHz) antenna with a UHF plug when his nanoVNA has an SMA connector sought advice of the collected experts on groups.io.

One expert advised that 100mm wire clip leads would work just fine. Another expert expanded on that with When lengths approach 1/20 of a wavelength in free space, you should consider and use more rigorous connections.

At Antenna analyser – what if the device under test does not have a coax plug on it? I discussed using clip leads and estimated for those shown that they behaved like a transmission line segment with Zo=200Ω and vf=0.8. Continue reading nanoVNA – experts on improvised fixtures

Last update: 9th October, 2020, 3:19 PM

Simsmith bimetal line type – revision #1

This article is a revision of an article Simsmith bimetal line type for Simsmith v17.2 and revisions to my own model for current distribution in a conductor.

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This article discusses various measurements and models of Wireman 551 windowed ladder line, including adapting Simsmith’s bimetal line type to bear on the problem.

Measurements

A starting point for characterising the matched line loss (MLL) of the very popular Wireman 551 (W551) windowed ladder line is the extrapolation of measurements by (Stewart 1999) to 1.8MHz. Since the measurements were made at and above 50MHz where the W551 has copper like performance, this is likely to underestimate actual MLL and such wide extrapolation introduces its own uncertainty. Nevertheless, the datapoint is MLL=0.00227dB/m.

This is a revision of an article written in Feb 2020, capturing revision of Simsmith to v17.2 and revision of my own current distribution model.

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Dan Maquire recently posted a chart summarising measurements of these lines.

For the purposes of this article, let’s tabulate the MLL at 1.8MHz in dB/m. Continue reading Simsmith bimetal line type – revision #1

Last update: 3rd October, 2020, 7:38 AM

A model of current distribution in copper clad steel conductors at RF – capturing conductor curvature

A model of current distribution in copper clad steel conductors at RF laid out a model for current distribution, though ignoring curvature of the conductor in calculating current density vs depth.

A model for current distribution in a conductor is that for a homogenous conducting half space with surface current parallel to the interface. Current density at depth d is given by the expression \(J_r=J_R\frac{J_0(kr)}{J_0(kR)}\) where δ is the skin depth \(δ=(ω \cdot µ \cdot σ)^{0.5}\) and \(k=\frac{1-\jmath}{\delta}\), σ is the conductivity). This takes into account curvature of the conductor surface, albeit with slower compute time.

Let’s compare the two algorithms on a test case at 1.8MHz being copper cladding of 67µm copper over a steel core for an overall diameter of 1.024mm (#18).

Above is a stacked image, the simpler algorithm is the feint plot.

There is a quite small difference in this case. When the expected loss of 400Ω line using the conductor is calculated, the result with the simpler algorithm is 1.3% less than the later one using the Bessel distribution.

Last update: 19th January, 2021, 10:41 AM

Distance to fault in submarine telegraph cables ca 1871 – the leap expanded

Distance to fault in submarine telegraph cables ca 1871 gave a mathematical explanation of the location of fault…

Now it is in terms of the three known values u,v,w and unknown x.
\(w(v-2x+u)=(v-2x+u)x+(v-x)(u-x)\\\)
\(x^2-2wx+vw+uw-uv=0\) from which you can find the roots.
\(x=w – \sqrt{(w-v)(w-u)}\\\)

I have been asked to expand the last ‘leap’.

So we have \(x^2-2wx+vw+uw-uv=0\) which is a quadratic, a polynomial of order 2.

The solution or roots of a quadratic \(ax^2+bx+c=0\) are given by \(x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\).

So, for our quadratic \(a=1, b=-2w,c=vw+uw-uv\), so \(x=\frac{2w \pm \sqrt{(2w)^2-4(vw+uw-uv)}}{2}\).

Dividing the top and bottom by 2 we get \(x=w \pm \sqrt{w^2-(vw+uw-uv)}\) which can be rewritten as \(x=w \pm \sqrt{(w-v)(w-u)}\).

We want the lesser square root \(x_-=w-\sqrt{(w-v)(w-u)}\) because x must be less than w, a constraint of the physical problem.

So when measurements gave \(v=1040 \Omega\) and \(w=970 \Omega\) we can calculate that the distance to fault is the lesser root, 210.3km from Newbiggen-by-the-sea. (The greater root would imply a -ve value for x or y which is not physically possible.)

Last update: 1st October, 2020, 6:47 PM

Distance to fault in submarine telegraph cables ca 1871

In the early days of submarine telegraph cables, the cable technology was a single core steel wire wrapped in gutta-percha worked against ground. Now the gutta-percha was not a uniform or durable insulation and leaks to ground (sea) were inevitable, and when the leakage became sufficient the cable could not longer be used and had to be repaired.

The earliest method of locating a cable fault was a binary chop… which would mean deploying a cable ship, grapnelling for the cable, hauling it to the surface with a special dividing cut and hold grapnel that severed the cable when tension was too great, buoying off one end and steaming back to the other to haul it on board, clean it up and test to the far cable station. New cable was spliced and the cable ship steamed back to find the buoy and pull that end on board, clean and test to the other end. This was done to localise the fault, and eventually replace a fault section of cable. During this longish period, the cable was out of service. Continue reading Distance to fault in submarine telegraph cables ca 1871

Last update: 30th September, 2020, 1:52 PM

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. Continue reading nanoVNA – tuning stubs using TDR mode

Last update: 23rd September, 2020, 2:17 PM

Finding the electrical length of the branches of an N type T – #4

Finding the electrical length of the branches of an N type T – #1 posed a problem, this article looks at one solution.

For convenience, here is the problem.

An interesting problem arises in some applications in trying to measure the electrical length of each branch of a N type T piece.

Let’s make some assumptions that the device is of quality, that the connection from each connector to the internal junction is a uniform almost lossless transmission line of Zo=50Ω. Don’t assume that the left and right branches above are of the same length (though they often are) and we should not assume that the nearest branch is of the same length as the others (and they are often not).

Before we start, we will calibrate the VNA entering the offsets appropriate to the OPEN and SHORT cal parts. In the case of my nanoVNA, measurement above 900MHz is very noisy, so the scan will be 100-890MHz (to avoid a glitch at 900MHz due to harmonic mode switching).

So, the problem is all the uncertain things that connect to the internal T junction. Lets connect a calibration quality 50Ω termination to the left hand port. We now know that the path from the male port to the remaining female port comprises lengths l2 and l1 of low loss 50Ω transmission line with a 50Ω resistor shunting at the junction of l1 and l2. Continue reading Finding the electrical length of the branches of an N type T – #4

Last update: 11th August, 2020, 12:51 PM

Finding the electrical length of the branches of an N type T – #3

Finding the electrical length of the branches of an N type T – #1 posed a problem, this article looks at one solution.

For convenience, here is the problem.

An interesting problem arises in some applications in trying to measure the electrical length of each branch of a N type T piece.

Before we start, we will calibrate the VNA entering the offsets appropriate to the OPEN and SHORT cal parts.

Last update: 11th August, 2020, 4:19 AM

Finding the electrical length of the branches of an N type T – #2

Finding the electrical length of the branches of an N type T – #1 posed a problem, this article looks at one simple solution.

For convenience, here is the problem.

An interesting problem arises in some applications in trying to measure the electrical length of each branch of a N type T piece.

Last update: 10th August, 2020, 2:52 PM