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

The quarter sized G5RV with hybrid feed

(Varney 1958) described his G5RV antenna in two forms, one with tuned feeders and the more popular form with hybrid feed consisting of a matching section of open wire line and then an arbitrary length of lower Zo coax or twin to the transmitter.

(Duffy 2005) showed that the hybrid feed is susceptible to high losses in the low Zo line as it is often longish, is relatively high loss line and operates with standing waves.

Lets look at measurement of a real antenna, broadly typical of the G5RV. The antenna measured is a G5RV rigged in Inverted V form, 11m height at the apex and around 8m at the ends. The feed line is 2mm diameter copper spaced 50mm with occasional plastic insulators.

To some extent, the measurements are dependent on the environment, and whilst there will be variation from one implementation to another, the measurements provide a basis for exposing the configuration challenge.

Screenshot - 01_05_16 , 19_33_56

Above is a plot of VSWR(50) essentially at the lower end of the matching section and low Zo line. The measurement is made looking into 0.5m of RG142 and a Guanella current balun that uses about 1m of 110Ω pair, it is essentially the load end VSWR of a hybrid feed were it used. Continue reading The quarter sized G5RV with hybrid feed

Antenna system resonance and the nanoVNA

With the popularity of the nanoVNA, the matter of optimisation of antenna systems comes up and the hoary chestnuts of ham radio are trotted out yet again.

Having skimmed a presentation published on the net, an interesting example is presented of an 80m half wave centre dipole with feed line and various plots from the nanoVNA used to illustrate the author’s take on things.

The author is obsessed with resonance and obsessed with phase, guiding the audience to phase as ‘the’ optimisation target. Phase of what you might ask… all the plots the author used to illustrate his point are phase of s11.

A model for discussion

I have constructed an NEC-4.2 model of a somewhat similar antenna to illustrate sound concepts. Since NEC-4.2 does not model lossy transmission lines (TL elements), we will import the feed point data into Simsmith to include transmission line loss in the model.

Above is the Simsmith model. Continue reading Antenna system resonance and the nanoVNA

Calculate Loss from s11 and s21 – convenient online calculator

I often need to calculate loss from marker values on a VNA screen, or extracted from a saved .s2p file.

Firstly, loss means PowerIn/PowerOut, and can be expressed in dB as 10log(PowerIn/PowerOut). For a passive network, loss is always greater than unity or +ve in dB.

\(loss=\frac{PowerIn}{PowerOut}\\\)

Some might also refer to this as Transmission Loss to avoid doubt, but it is the fundamental meaning of loss which might be further qualified.

So, lets find the two quantities in the right hand side using ‘powerwaves’ as used in S parameter measurement.

s11 and s21 are complex quantities, both relative to port 1 forward power, so we can use them to calculate relative PowerIn and relative PowerOut, and from that PowerIn/PowerOut.

PowerIn

PowerIn is port 1 forward power less the reflected power at port 1, \(PowerIn=P_{fwd} \cdot (1-|s11|^2)\).

PowerOut

PowerOut is port 2 forward power times less the reflected power at the load (which we take to be zero as under this test it is a good 50Ω termination), \(PowerOut=P_{fwd} \cdot |s21|^2 \).

Loss

So, we can calculate \(loss=\frac{PowerIn}{PowerOut}=\frac{\frac{PowerIn}{P_{fwd}}}{ \frac{PowerOut}{P_{fwd}}}=\frac{1-|s11|^2}{|s21|^2}\)

Noelec makes a small transformer, the Balun One Nine, pictured above and they offer a set of |s11| and |s12| curves in a back to back test. (Note: back to back tests are not a very reliable test.) Continue reading Calculate Loss from s11 and s21 – convenient online calculator

Measure transmission line Zo – nanoVNA – PVC speaker twin

There are many ways to get a good estimate of the characteristic impedance Zo of a transmission line.

One method is to measure the input impedances of a section of line with both a short circuit and open circuit termination. From Zsc and Zoc we can calculate the Zo, and the complex propagation constant \(\gamma=\alpha + \jmath \beta\).

Calculation of Zo is quite straightforward.

The solution for γ involves the log of a complex number \(r \angle \theta\) which is one of the many possible values \(ln(r) + j \left(\theta + 2 \pi k \right)\) for +ve integer k. Conveniently, the real part α is simply \(ln(r) \). The real part of γ is the attenuation in Np/m which can be scaled to dB/m, and the imaginary part is the phase velocity in c/m. The challenge is finding k.

Measurement with nanoVNA

So, let’s measure a sample of 14×0.14, 0.22mm^2, 0.5mm dia PVC insulated small speaker twin.

Above is the nanoVNA setup for measurement. Continue reading Measure transmission line Zo – nanoVNA – PVC speaker twin