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.)

Review of MXITA SMA-8

The MXITA SMA-8 is a low cost torque wrench for 8mm, specifically for SMA connectors. It has an adjustable calibration, supplied at 1Nm but easily adjusted down to 0.6Nm to suit common brass SMA connectors, especially of doubtful quality.

I bought this after seeing several recommendations on a nanoVNA forum.

Above is the factory pic of the SMA-8. Continue reading Review of MXITA SMA-8

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

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

NEC sez…

I note the common introduction to online posts being NEC says, according to NEC, and the like.

Readers should take this to mean that the author denies their contribution in making assumptions and building the model, and the influence on the stated results.

It is basically a disclaimer that disowns their work. Continue reading NEC sez…

SDR# (v1.0.0.1732) – channel filter exploration

With plans to use an RTL-SDR dongle and SDR# (v1.0.0.1732) for an upcoming project, the Equivalent Noise Bandwidth (ENB) of several channel filter configurations were explored.

A first observation of listening to a SSB telephony signal is an excessive low frequency rumble from the speaker indicative of a baseband response to quite low frequencies, much lower than needed or desirable for SSB telephony.

500Hz CW filter

The most common application of such a filter is reception of A1 Morse code.

Above is a screenshot of the filter settings. Continue reading SDR# (v1.0.0.1732) – channel filter exploration

A Smith chart view of EFHW transformer compensation

I have written several articles on design of high ratio ferrite cored transformers for EFHW antennas.

Having selected a candidate core, the main questions need to be answered:

  • how many turns are sufficient for acceptable InsertionVSWR at low frequencies and core loss; and
  • what value of shunt capacitance best compensates the effect of leakage inductance at high frequencies?

Lets look at a simplified equivalent circuit of such a transformer, and all components are referred to the 50Ω input side of the transformer.

Above is a simplified model that will illustrate the issues. For simplicity, the model is somewhat idealised in that the components are lossless. Continue reading A Smith chart view of EFHW transformer compensation

Stacking of Yagis and antenna effective aperture

The matter of stacking Yagis for improved gain is it seems a bit of a black art (and it should not be).

A common piece of advice is to visualise the capture area of the individual Yagi, and to stack them so that their capture areas just touch… with the intimation that if they overlap, then significant gain is lost.

Above is a diagram from F4AZF illustrating the concept. Similar diagrams exist on plenty of web sites, so it may not be original to F4AZF. Continue reading Stacking of Yagis and antenna effective aperture

Desk review of the AAA-1C as an active dipole antenna

The AAA-1C is an amplifier for small receiving antennas by LZ1AQ. The amplifier is designed for use with one or two small loops or a short dipole (possibly comprising two small loops).

The datasheet contains some specifications that should allow calculation of S/N degradation (SND) in a given ambient noise context (such as ITU-R P.372). Of particular interest to me is the frequency range 2-30MHz, but mainly 2-15MHz.

The specifications would appear to be based on models of the active antenna in free space, or measurements of the device using a dummy antenna. So, the challenge is to derive some equivalent noise estimates that can be compared to P.372 ambient noise, and with adjustment for the likely effects of real ground.

Key specifications:

  • plot of measured output noise of the amplifier, and receiver noise in 1kHz ENB;
  • Antenna Factor (AF) from a simulation.

Above is the published noise measurements at the receiver input terminals. The graph was digitised and then a cubic spline interpolation used to populate a table. Continue reading Desk review of the AAA-1C as an active dipole antenna

Small untuned loop for receiving – a design walk through #4

Small untuned loop for receiving – a design walk through #1 arrived at a design concept comprising an untuned small loop loaded with a broadband amp with input Z being a constant resistive value and with frequency independent gain and noise figure.

In that instance, the design approach was to find a loop geometry that when combined with a practical amplifier of given (frequency independent) NoiseFigure (NF), would achieve a given worst case S/N degradation (SND). Whilst several options for amplifier Rin were considered in the simple analytical model, the NEC mode of the antenna in presence of real ground steered the design to Rin=100Ω.

A question that commonly arises is that of Rin, there being two predominant schools of thought:

  • Rin should be very low, of the order of 2Ω; and
  • Rin should be the ‘standard’ 50Ω.

Each is limiting… often the case of simplistic Rules of Thumb (RoT).

Let’s plot loop gain and antenna factor for two scenarios, Rin=2Ω and Rin=100Ω (as used in the final design) from the simple model of the loop used at Small untuned loop for receiving – a design walk through #2.

Above, loop gain is dominated by the impedance mismatch between the source with Zs=Rr+Xl and the load being Rin. We can see that the case of Rin=100Ω achieves higher gain at the higher frequencies by way of less mismatch loss than the Rin=2Ω case. Continue reading Small untuned loop for receiving – a design walk through #4