Measuring OC and SC transmission line sections

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed the potential for failure using this ‘no-brainer’ method of estimating differential mode characteristic impedance Zo, providing an NEC-4.2 model to demonstrate effects.

This article reports nanoVNA measurement of a two wire line where no common mode countermeasures were taken.

A little review of behavior of practical transmission lines

Above is a Smith chart of the complex reflection coefficient Γ (s11) looking into a length of nominally 142Ω transmission line of similar type to that in the reference article, the chart is normalised to Zref=142+j0Ω. Note the locus is a spiral, clockwise with increasing frequency, and centred on the chart prime centre Zref. More correctly it is centred on transmission line Zo, and the keen observer might note that the spirals are offset very slightly downwards, actual Zo is not exactly 142Ω, but 142-jXΩ where X is small and frequency dependent, a property of practical lines with loss. Continue reading Measuring OC and SC transmission line sections

Estimating transmission line Zo – λ/8 method – nanoVNA – success

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed the potential for failure using this ‘no-brainer’ method of estimating differential mode characteristic impedance Zo.

Well, as the article showed, it is not quite the no-brainer but with care, it can give good results. This article documents such a measurement of a 0.314mm cable.

The nanoVNA was carefully SOLT calibrated from 1 to 201MHz. Care includes that connectors are torqued to specification torque… no room here for hand tight, whether or not with some kind of handwheel adapter or surgical rubber tube etc.

Above is the Smith chart view over the frequency range from a little under λ/8 to a little over λ/8. It is as expected, a quite circular arc with no anomalies. Since the DUT is coax, and the connector is tightened to specification torque, we would expected nothing less. The situation may be different with two wire lines if great care is not taken to minimise common mode excitation. The sotware does not show Marker 2 properly, it should be between ‘c’ and ‘i’ of the word Capacitive. Continue reading Estimating transmission line Zo – λ/8 method – nanoVNA – success

A magnetics review of the VK3AMP Sontheimer directional coupler

This article documents a review of the magnetics of the ‘voltage’ transformer in the VK3AMP Sontheimer directional coupler. It is typically the most important component in determining InsertionVSWR and ReturnLoss at the lowest frequencies.

The transformer of interest is the one to the left, and if you follow the tracks, the multiturn winding is connected between ground and a track that routes across to the through line. The transformer primary appears in shunt with the through line. Continue reading A magnetics review of the VK3AMP Sontheimer directional coupler

Basic measurements of the VK3AMP Sontheimer directional coupler for a N2PK wattmeter

This article documents measurement and analysis of a VK3AMP Sontheimer directional coupler in an implementation of a 400W wattmeter design by N2PK (Kiciack nd).

I purchased one of the couplers for use with a DIY digital display, and although I have had it longer, it isn’t yet realised!

A common failing of almost all hammy Sammy designs is appalling InsertionVSWR at the lower end of the specified frequency range. This coupler is specified for 1.8-54MHz, and differently to most, has meaningful published characteristics.

In this implementation, 60mm lengths of solder soaked braid coax similar to Succoform 141 were used between the PCB and box N connectors. The expected matched line loss of both of these is about 0.01dB @ 50MHz.

The measurements here were made by VK4MQ using an Agilent E5061A ENA, data analysis by myself.

Above are the raw s parameter measurements plotted. It is a full 2 port measurement, and it can be observed that the device is not perfectly symmetric, quite adequate, and quite good compared to other ham designs that I have measured. Continue reading Basic measurements of the VK3AMP Sontheimer directional coupler for a N2PK wattmeter

Failure estimating transmission line Zo – λ/8 method – nanoVNA – Smith chart perspective

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed traps in using the λ/8 method to estimate Zo… it is not the no-brainer that is often suggested.

This article shows the use of the Smith chart to look for departures from pure transmission line behavior in that test, or any other that depends on measuring purely Zin of a length of line in purely differential mode with short circuit or open circuit termination.

Above is a Smith chart plot of what we should see looking into a line of similar characteristic swept from 1 to 20MHz. There is no magic there, this is basic transmission lines and Smith chart. Continue reading Failure estimating transmission line Zo – λ/8 method – nanoVNA – Smith chart perspective

Failure estimating transmission line Zo – λ/8 method – nanoVNA

Countless online discussions have online experts describing their various preferred methods for estimating the characteristic impedance of a transmission line… often without really testing whether their simple results are realistic, ie believable. Of course, being social media, it would be unsocial for another participant to question the results, so the unchallenged becomes part of ham lore.

Apparent gross failures are often wrongly attributed to factors like manufacturing tolerances, polluted line surface, other esoteric factors etc that might imply a knowledgeable author… but that is social media, an unreliable source of information.

Let’s explore an estimate using measurements with a nanoVNA using the popular eighth wavelength (λ/8) method.

λ/8 method

The λ/8 method relies upon the property of a lossless line terminated in an open circuit that differential impedance \(Z_d=\jmath X=- \jmath \left| Z_0 \right| cot \left(\pi/4\right)=- \jmath\left| Z_0 \right|\). So, if you measure the reactance looking into the λ/8 (\(\frac{\piᶜ}{4} \:or\: 45°\)), you can estimate Zo as equal to the magnitude of the reactance.

A similar expression can be written for the case of a short circuit termination and it leads to the same result that you can estimate Zo as equal to the magnitude of the reactance (an exercise for the reader).

The fact that the two cases lead to the same result can be used to verify that the line length is in fact λ/8 (they will not be equal if the length is a little different to λ/8)… though writeups rarely mention this, or perform the test.

So, the method depends critically on:

  • whether the line length is λ/8;
  • whether it is sufficiently low loss; and
  • whether the differential impedance measurement is valid.

Most online articles do not include details of the measurement setup, perhaps thinking that it not all that relevant. Of course, one of the greatest failings in experiments is to ignore some factor that is in fact relevant. Continue reading Failure estimating transmission line Zo – λ/8 method – nanoVNA

Surely there cannot be more forward power than the transmitter makes?

Let’s explore a simple numerical example of a practical line operating in Transverse Electro Magnetic (TEM) mode (the usual thing for practical coax lines at HF).

Let’s review the meaning of 50Ω line.

It means that the line geometry imposes a natural constraint on a wave travelling in the line that V/I=50… but remember that TEM waves are free to travel in (only) two directions. This natural ratio of V/I is called the characteristic impedance Zo. Continue reading Surely there cannot be more forward power than the transmitter makes?

Phase of s11 and Z

Antenna system resonance and the nanoVNA contained the following:

Relationship between angle of reflection coefficient and angle of impedance

It was stated above that the angle (or phase) of s11 or Γ is not the same as the angle (or phase) of Z.

Given Zo and Γ, we can find θ, the angle of Z.

\(
Z=Z_0\frac{1+\Gamma}{1-\Gamma}\)

Zo and Γ are complex values, so we will separate them into the modulus and angle.

\(
\left | Z \right | \angle \theta =\left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \\
\theta =arg \left ( \left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \right )\)

We can see that the θ, the angle of Z, is not simply equal to φ, the angle of Γ, but is a function of four variables: \(\left | Z_0 \right |, \psi , \left| \Gamma \right |, \& \: \phi\) .

It is true that if ψ=0 and φ=0 that θ=0, but that does not imply a wider simple equality. This particular combination is sometimes convenient, particularly when ψ=0 as if often the case with a VNA.

This article offers a simulation of a load similar to a 7MHz half wave dipole.

The load comprises L, L1, and C1 and the phase of s11 (or Γ) and phase of Z (seen at the source G) are plotted, along with VSWR. Continue reading Phase of s11 and Z